Talks

Abstract: I will discuss a kind of thermalisation, and emergent hydrodynamics, in left-right nonreciprocal Heisenberg chains. This work is done with Nisarg Bhatt and Subroto Mukerjee.

Abstract: On a mesoscale, suspensions of locally heated colloidal particles can to some extent be described like ordinary isothermal systems with effective parameters that can be predicted for sufficiently symmetric setups. This still holds, to a lesser degree, for asymmetrically heated ("Janus”) particles that turn into active, self-propelling microswimmers, due to unbalanced thermal gradients. I will discuss informative signatures of the local nonequilibrium, accessible to mesoscale observers. Some increasingly coarse-grained paradigmatic situations that we have recently considered comprise active Brownian heat engines, polarization-density patterns emerging in activity gradients, ensuing active ratcheting, and time-reversal symmetry breaking fluctuations in non-reciprocal field theories.

Abstract: The surprising collective phenomena that emerge when particles can move autonomously have inspired many physicists to join the field of active matter. In sharp contrast to the delta-correlated thermal motion of (dead) particles in equilibrium, the autonomous motion of active particles is correlated over finite time scales. Recently, the emergence of complex chaotic flows that phenomenologically resemble turbulence and appear in a range of biological and physical active matter systems has attracted much interest. In this talk, I will show that even the simplest model of active particles -- self-propelled point particles -- can feature mesoscale flows with streams and vortices, i.e. a form of 'active turbulence'. Emergence of these collective flows is surprising as there are strictly no spatial correlations in the forces particles use to self-propel. I will furthermore show that another simple model where self-propulsion forces are spatially correlated displays similar chaotic flows, suggesting the possibility of a universality class distinct from the current classification scheme by Alert et al. 2022.

Abstract: Active Brownian particles have an active component in their dynamics, besides spontaneous thermal fluctuations. For self-propelled synthetic particles, the activity is generated by phoretic motions in response to inhomogeneity fields created by the particle itself. The resultant active dynamics have persistence in motion up to a characteristic timescale, the persistent time (\tau_R). Although activity is often synonymously defined by the self-propulsion speed, a more reliable measure of activity requires comparing it with the Brownian diffusivity, i.e., by using Péclet number. The self-propelled particles undergo exotic dynamical variations when they interact with a confinement, such as, a harmonic potential, possessing an intrinsic timescale, e.g., relaxation time (\tau_k). This poses an important question; how do their activity gets affected by the confinement? 

    In this talk, I will discuss our recent studies on the dynamics of active Brownian particles confined to a harmonic potential. This has been experimentally achieved by a combination of self-thermophoresis, and self-diffusiophoresis of Janus colloids in an optical trap, besides performing Brownian dynamics simulations and analytical calculations to complement our understanding. We observe an intriguing dynamical transition, governed by an interplay between \tau_R and \tau_k. As \tau_R becomes longer than \tau_k, an activity dominated motion progressively transforms into activity suppressed dynamics even at a higher Péclet number. 

Abstract: Quantum spin Hall edge channels are protected against backscattering under time-reversal symmetry. However, all observations of the quantum spin Hall effect have shown that reproducible fluctuations

shape the quantization plateau when the chemical potential is tuned through the bulk gap. Here, we investigate these conductance fluctuations in high-mobility micron-sized HgTe quantum wells. By performing temperature and gate-dependent measurements, we conclude that "charge puddles" (in the narrow-gap material) interacting with the edge channels via a Kondo-type interaction results in fluctuations in the quantum spin Hall conductance. 

Abstract: We report computational evidence of a new type of disordered phase in crystals resulting from entropy driven self-assembly of hard convex polyhedra. The disorder was reflected in the orientations of the anisotropic particles and not in the positions of the centers of geometry. Despite the lack of order, particle orientations were not random and exhibited strong correlations. The correlations were manifested in terms of discrete rotational motions in a fixed number of absolute orientations, while maintaining equal populations and specific measure of pairwise angular differences among the discrete values. This gave rise to a discretely mobile phase in the low density solid and a quenched disordered state at high pressure. This finding can be interpreted as the simplest example of correlated disorder in crystalline materials.

Abstract: Isotropic and continuous localised perturbations created by an external point source cause a spherically symmetric shock wave with the energy of the system increasing as power law in time. The analytical solution of the Euler equation providing the time development of the shock wave, is a classic problem in gas dynamics. In this study, we demonstrate the independence of the exponents of various non-dimensionalized thermodynamic quantities from the driving parameter. We further demonstrate that the Euler equation does not agree with the molecular dynamics results in terms of power law exponents for any driving parameter, based on our extensive event-driven molecular dynamic simulations of hard sphere gas. We state that this mismatch resulted from ignorance of the contribution of heat conduction and viscosity terms, and that the gap can be fixed by taking into account the Navier-Stokes equation. The findings of the molecular dynamic simulation and our direct numerical solution of the Navier-Stokes equation are consistent, demonstrating the significance of viscosity and heat conduction in shock problems. 

Abstract:  Generalized Langevin equations present a popular way of describing tracers in complex environments. In this talk I discuss, starting from a quadratic model of a colloid in a viscoelastic bath, how the usual form of Langevin equation is not always correct. In fact, the correct form has an additional term that can be dropped for the equilibrium scenario, but not when out of equilibrium. The effect of the extra term can be best understood if we look at the condioned expectations of tracer observables, like a mean conditional displacement. I will also show some numerical results for the non-linear couplings, where our predictions from the linear model hold.

Abstract: Noises are ubiquitous in all natural, real-life systems. Surprisingly, in some cases we show that noises can do something far more drastic than simply generating fluctuations: these can make even the systems unstable, creating an entirely new state, a  prospect not expected in equilibrium systems. We establish this result theoretically by using a minimal, two-variable, noisy continuum model with a non-zero noise cross correlation, where one of the variables is autonomous being independent of the other, whereas the second one depends explicitly on the former. Introducing cross-correlations of the two noises in the two dynamical equations, we show that depending upon the details of the nonlinear coupling between the dynamical fields, such cross correlations can induce instabilities in the models that are otherwise stable in the absence of any cross-correlations. We argue that this is reminiscent of the roughening transition found in the Kardar-Parisi-Zhang equation in dimensions greater than two. Phenomenological implications of our results will be discussed.

[Reference: S. Mukherjee, Phys. Rev. E 108, 024219 (2023)]

Abstract: Machine learning algorithms are routinely used to answer fundamental problems in molecular biology. I will talk about one example of using Bayesian mixture modeling to identify diverse regulatory mechanisms hidden in high-dimensional categorical data.  Although the problem may seem specific to Biology, the method can be generalised to other kinds of data and therefore can be applied to problems in other domains as well.

Abstract: Recent HiC experiments have revealed that eukaryotic chromosomes fold into hierarchical structures with sizes ranging from hundreds of megabase pairs of chromosome territories to a few kilobase pair loops. Multiple pieces of evidence suggest that the spatial organization of the chromosomes and the function of a cell are related. Several studies have shown that the Mb-sized hierarchical units called "topologically associating domain" (TAD) are functional units of chromosomes. We developed a computational framework to link the structural modifications of chromatin to gene regulation. This framework generates an ensemble of 3D conformations of a given genomic locus using a polymer model where the HiC contact map is an input. We further correlate such chromatin conformations to the transcription level of the encoded genes by considering the markov chain. In particular, we have demonstrated that the deletion of CTCF binding domain between two consecutive TADs leads to a significant change in the gene expression level of the encoded genes, namely sox9 and kcnj2, responsible for limb development. Such a change in transcription level is quantitatively consistent with experiments. Further insight from the polymer-based 3D conformation reveals that the higher transcription level of the kcnj2 gene after TAD border deletion is caused by the specific enhancers in the sox9 TAD. Together, these analyses advance our understanding of the relationship between the spatial architecture of the chromosome and function of the cell and can give new directions into therapeutic studies. 

Abstract: The effects of various active processes on the glassy dynamics of collective cellular motions are fundamental for many biological processes. Most of our understanding in this direction comes from either experiments or simulations of various confluent models. However, the biological significance of the problem demands a broad theoretical framework for deeper insights. Here, we extend one of the most popular theories of equilibrium glasses, the random first-order transition (RFOT) theory, for confluent systems with self-propulsion. The theoretical predictions show excellent agreements with existing and new simulation data. One crucial result of this work is the modification of self-propulsion due to confluency. Our results show that the qualitatively distinctive trends of the two types of self-propulsion survive even in the confluent systems. The extended RFOT theory gives a negative Kauzmann temperature for the readily found sub-Arrhenius regime, implying that, strictly speaking, the RFOT theory is not applicable there. However, the theory predicts a super-Arrhenius behavior in a different parameter space. Our simulations show that this prediction is valid in general for confluent systems. These results provide an intriguing test ground for various theories of glasses. 

Abstract: I will start with a brief introduction to non-abelian anyons  and explain how Majorana modes and their generalisations - parafermion modes- can be engineered at the edges of integer and fractional quantum Hall systems  respectively. Then I will discuss some of the signatures of these modes  involving the Josephson effect and also our recent work on how edge  reconstruction, which is ubiquitous in the quantum Hall systems, can affect the observation of these modes. 

Abstract:  We consider a Klein-Gordon chain that is periodically driven at one end and has dissipation at one or both boundaries. We discuss the steady state properties of this system for the cases where thermal noise is either absent or  is present.  It is shown that, in the absence of noise, the system has multiple attractors with finite basins of attraction, while in the presence of noise  this  leads to nonunique steady states.

Abstract: In this presentation, we provide a theoretical framework to analyze discrete time-crystalline (DTC) phases in the dissipative dipolar systems subjected to a two-pulse excitation scheme. As a particular realization, we choose a quantum many-body system that exhibits prethermalization due to the presence of the quasi-conserved quantities. The analysis uses a fluctuation-regulated quantum master equation which captures the dissipative effects of the drive and dipolar coupling on the dynamics regularized by the thermal fluctuations. We find that the effects of such dissipation lend stability to the dynamics and are directly responsible for the robustness. Specifically, we find that longer fluctuation correlation time enhances the stability of DTC. We also obtain the lifetime of such a robust period doubling response, a salient feature of the DTC phase, by varying several system parameters. Our results are in good agreement with the recent experimental findings in dipolar systems using Nuclear Magnetic Resonance (NMR) spectroscopy.

Abstract: We find that, in the presence of weak incoherent effects from surrounding environments, the zero temperature conductance of nearest neighbour tight-binding chains exhibits a counter-intuitive power-law growth with system length at band edges, indicating superballistic scaling. This fascinating environment assisted superballistic scaling of conductance occurs over a finite but extended regime of system lengths. This scaling regime can be systematically expanded by decreasing the coupling to the surrounding environments. There is no corresponding analog of this behavior for isolated systems. This superballistic scaling stems from an intricate interplay of incoherent effects from surrounding environments and exceptional points of the system's transfer matrix that occur at every band edge. 

Abstract: Liquid crystalline topological defects have found renewed interests in active nematic systems, which describe living cell populations with orientational order [1], but these developments were mostly on 2D systems. Here I present two of our recent work inspecting 3D effects of topological defect lines. In the first part, we characterize 3D dynamics of topological defect lines in molecular liquid crystal, through comparison with their 2D counterpart [2]. In the second part, we study the role of topological defects in growing colonies of bacteria, showing that 3D effect may result even in a qualitative change in the way defects influence on cells [3].

[1] A. Doostmohammadi and B. Ladoux, Trends Cell Biol. 32, 140 (2022).

[2] Y. Zushi and K. A. Takeuchi, Proc. Natl. Acad. Sci. USA 119, e2207349119 (2022).

[3] T. Shimaya and K. A. Takeuchi, PNAS Nexus 1, pgac269 (2022).

Abstract: An oscillator driven by a periodic Zeitgeber gets entrained with a phase difference (the phase of entrainment) that depends on the underlying free-running period of the oscillator. Intriguingly, this physical phenomenon is thought to give rise to variations in “body time” of individual humans – the phase of entrainment between the body’s master circadian clock and the external rhythms of day and night. Small differences in the endogenous circadian clock periods give rise to a 12-hour range of “times” across individuals or even tissues within an individual. An exciting open challenge in the field of chronobiology and chrono-medicine is to accurately measure body or tissue time, to then allow for personalized, circadian-time based development of therapeutics. 

Here I will talk about our lab’s recent efforts in establishing the fundamental limits of decoding time from gene expression measurements. Given the well-established idea of super-Poissonian noise in single-cell gene expression, the lowest resolution at which cellular time can be accurately decoded is currently unknown. To address this, I will first discuss the experimental approaches we have developed to simultaneously measure RNA levels of multiple genes in mouse embryonic fibroblasts, at single cell and single molecule resolution. To analyze such datasets we have developed algorithms based on stochastic processes, to first learn the patterns of noisy gene expression and then infer single cell time of test samples. Using these approaches, I will quantitatively demonstrate that decoding time from single cells is not possible. Remarkably however, averaging over as low as 20-30 cells allows for time-inference with as low as 1-hour error with only 3 genes, thereby providing a conceptual framework for spatially resolved circadian-time inference. Finally, I will use Kuramoto oscillator theory to discuss the implications of our results in understanding inter-cellular coupling of peripheral body tissues, contrasting them to earlier studies on neurons in the brain.

Abstract: MicroRNAs (miRNAs) are small noncoding RNAs that regulate gene expression post-transcriptionally in eukaryotes by binding with target mRNAs and preventing translation. miRNA mediated feedback motifs are ubiquitous in various genetic networks that control cellular decision making. A key question is how such a feedback mechanism may affect gene expression noise. To answer this, we have developed a mathematical model to study the effects of a miRNA-dependent negative-feedback loop on mean expression and noise in target mRNAs. Combining analytics and simulations, we show the existence of an expression threshold demarcating repressed and expressed regimes in agreement with earlier studies. The steady-state mRNA distributions are bimodal near the threshold, where copy numbers of mRNAs and miRNAs exhibit enhanced anticorrelated fluctuations. Moreover, variation of negative-feedback strength shifts the threshold locations and modulates the noise profiles. Notably, the miRNA-mRNA binding affinity and feedback strength collectively shape the bimodality. We also compare our model with a direct auto-repression motif, where a gene produces its own repressor. Auto-repression fails to produce bimodal mRNA distributions as found in miRNA based indirect repression, suggesting the crucial role of miRNAs in creating phenotypic diversity. Together, we demonstrate how miRNA-dependent negative feedback modifies the expression threshold and leads to a broader parameter regime of bimodality compared to the no-feedback case. 

Abstract: Understanding the fundamental principles governing bacterial motility and navigation is crucial for gaining insights into various critical phenomena, including the transmission of infectious diseases and the development of biofilms. A significant challenge for swimming bacteria is to efficiently and purposefully navigate through intricate habitats, such as the complex and structured environment of soil. 

During this presentation, I shall discuss the intricate relationship between the microscale navigation of bacteria and their larger-scale movement in diverse and heterogeneous environments. We involve a combination of experimental analysis using the soil bacterium Pseudomonas putida and active particle modeling. Specifically, we examine the motility patterns of these bacteria in agar, emphasizing the remarkable characteristics of their movement in disordered environments. 

Unlike E. coli, our investigation uncovers the transient subdiffusion of bacteria in agar, a result of intermittent trapping. This discovery highlights a dynamic hop-and-trap mechanism with trap times that follow a power-law distribution. In this talk, I will focus on elucidating the implications of these findings and their potential impact on our understanding of bacterial behavior in complex environments.

Abstract: To study fluctuations in the weakly asymmetric simple exclusion process at large space scale $x\varepsilon^{-1}$, large time scale $t \varepsilon^{-\chi}$ and weak hopping bias $b \varepsilon^{\kappa}$ in the limit $\varepsilon \to 0$ we develop a mesoscale mode coupling theory (MMCT) that allows for probing the crossover at $\kappa=1/2$ and $\chi=2$ from Kardar-Parisi-Zhang (KPZ) to Edwards-Wilkinson (EW) universality. The dynamical structure function is shown to satisfy an integral equation that is independent of  the microscopic model parameters and has a solution that yields a scale-invariant function with the KPZ dynamical exponent $z=3/2$ at scale $\chi=3/2+\kappa$ for $0\leq\kappa<1/2$ and for $\chi=2$ the exact Gaussian EW solution with $z=2$ for $\kappa>1/2$. At the crossover point it is a function of both scaling variables which converges at macroscopic scale to the conventional mode coupling approximation of KPZ universality for $\kappa<1/2$. This fluctuation pattern confirms long-standing conjectures for $\kappa \leq 1/2$ and is in agreement with mathematically rigorous results for $\kappa>1/2$ despite the numerous uncontrolled approximations on which mode coupling theory is based.

Abstract: In this talk, we shall discuss how memory affects the behaviours of random walks. A model of random walks with memory will be introduced and its asymptotic properties will be investigated. (Based on a joint work with Krishanu Maulik and Tamojit Sadhukhan). 

Abstract: Apart from its intrinsic interest, the classic combinatorial problem of maximum matchings (aka maximally packed dimer covers) of a  graph is also a key ingredient in theories of vacancy-induced local moment formation in frustrated magnets as well as constructions of topologically protected zero modes of a class of disordered Hamiltonians. Here, we study the random geometry of regions of a diluted lattice that carry the monomers of any maximally-packed dimer cover, and identify some interesting percolation phenomena associated with these monomer-carrying regions. 

Abstract: In this talk, we are going to discuss two aspects of strong Hilbert space fragmentation. The first is its prethermal realization in a driven interacting fermion chain. The second is its role in a non-Hermitian interacting Hatano-Nelson model; here its presence is a key element in ensuring the reality of the eigenspectrum of the model in the limit of strong interaction. 

Abstract: The dynamics of non-Hermitian quantum systems have taken on an increasing relevance in light of quantum devices which are not perfectly isolated from their environment. The interest in them also stems from their fundamental differences from their Hermitian counterparts, particularly with regard to their spectral and eigenvector correlations. We discuss such correlations across a localisation transition in non-Hermitian quantum systems. As a concrete setting, we consider non-Hermitian power-law banded random matrices which have emerged as a promising platform for studying localisation in disordered, non-Hermitian systems. We show that eigenvector correlations show marked differences between the delocalised and localised phases. In the delocalised phase, the eigenvectors are strongly correlated as evinced by divergent correlations in the limit of vanishingly small complex eigenvalue spacings. On the contrary, in the localised phase, the correlations are independent of the eigenvalue spacings. We explain our results in the delocalised phase by appealing to the Ginibre random matrix ensemble. On the other hand, in the localised phase, an analytical treatment sheds light on the suppressed correlations, relative to the delocalised phase. 

Abstract: It is well established that the melting of two-dimensional (2D) crystals occurs through the unbinding of topological defects, first the unbinding of dislocation pairs and later dissociation into disclinations. However, when the constituent particles are aspherical in shape, topological defects due to their orientational property also appear in the system. Therefore, such orientational defects are expected to also play a role in the melting of 2D liquid crystalline (LC) systems. Here, we report the results of molecular dynamics simulations of a 2D LC system consisting of soft ellipses. The Gay-Berne (GB) potential governs the interaction between the constituent ellipses. We focused our study on the systems’ high-density states as the orientational property remains relevant only up to liquid crystalline nematic phases. We observed an interplay of positional and orientational defects during the melting of the 2D solid phase. We constructed a phase diagram for the dense GB system in the (ρ,T) plane. As an extension of this study, we also looked at the influence of an underlying substrate in the phase behavior of the 2D LC system. We have found substrate-induced freezing, melting, and structural depinning transitions occurring in the system as a function of the substrate periodicity parameter.

Abstract:Soft-matter, such as polymers, membranes, liquid-crystals provide the basic building blocks for biological systems, for example, a cell. Association of proteins to biological membranes is well known. An ensemble of rod like  proteins attached to a membrane can deform it locally and thereby change  the shape of a closed membrane vesicle. The rods themselves often create  interesting patterns on membranes and this can be understood using physics  of nematic liquid crystals. In this context I will discuss the case of  spontaneous formation of membrane tubes from vesicles.

Abstract: Epithelial cell monolayers expand on substrates by forming finger-like protrusions in the collective boundary which are created by leader cells. Information transmission and communication between individual entities in the cohesive collective lead to long-range order, vortical structures, and disorder-ordered phase transitions. We ask the following questions: does a leader cell continue to be the leader during the migration? How do stochastic changes in densities influence leader cell emergence during collective migrations? We investigated leader formation using MDCK cells which were initially patterned in circular shapes on glass substrates. Experiments show that cells in leader phase (n=35) have higher radial velocities, increased areas during migration, and ballistically propel (MSD = 2.2) outwards. 66% of the leader cells transitioned into a surfer phase (MSD = 1.9) which moved azimuthally at the interface. Interestingly, 34% of the leader cells divided into daughter cells after 90 minutes and a similar fraction transitioned back from the surfer to leader cells during migration. In contrast, cells in the interior initially showed super diffusive behaviors (MSD = 1.6) that change to diffusive (MSD = 1.06), and sub diffusive (MSD = 0.93) over the 15 hour of migrations. We used a particle-based model to simulate the dynamics of the ensemble during collective migrations that are governed by orientational Vicsek and inter-cellular interactions between neighboring particles. The model also includes bending, curvature-based motility, acto-myosin contractile cable forces, density dependent noise, and proliferations. We show that border forces are essential in leader cell formation and the overall areal expansions of epithelial monolayers on substrates. We also demonstrate that regions of increased cell density occur behind the leader cell edge that agree with experimental results. These results demonstrate the relationships between transitions from leader cells to surfers in collective dynamics that suggest a dominant role for acto-myosin contractility during collective epithelial behaviors. 

Abstract:Eukaryotic cells encapsulate DNA molecules within a protein-membrane scaffold called the nuclear envelope, in part to protect the genome from mechanical stresses caused by internal and external forces as a consequence of cell migration, cell division or tissue compression. While it is known that an improperly assembled nuclear envelope is associated with DNA damage, cancer and laminopathies it remains unclear how the nuclear envelope organises DNA to provide mechanical resistance in the first place. Here, we show how protein components of the nuclear envelope organise DNA to increase the mechanical stability of DNA molecules to withstand forces that would otherwise damage double-stranded DNA. We use a bottom-up reconstitution approach coupled with optical tweezer experiments, theoretical physics and cell biology to investigate how the chromatin cross-bridging factor BAF the inner nuclear membrane protein LEM2 and DNA self-organize. Our data point to a mechanism where BAF-LEM2 organize DNA into regular loops and further jointly compact into large fluid-like dna-protein co-condesates . As a result, DNA is mechanically protected in several ways: Firstly, DNA respond to increasing external forces with increased compaction forces, suggesting that the protein-bound DNA molecule is mechanically stabilized. Secondly , forces with the potential to damage DNA percolate through the co- condensate, reducing the mechanical stress on individual DNA strands. Our study quantitatively describes a conserved and previously unknown molecular mechanism by which cells use the nuclear envelope as a self-assembling buffer against spontaneously occurring mechanical stress to protect DNA from damage, suggesting a first preventive mechanism that adds to the cell's ability to repair DNA damage or responsively change chromatin properties. 

Abstract: The Notch pathway, an example of juxtacrine signaling, is an evolutionary conserved cell-cell communication mechanism. It governs emergent spatiotemporal patterning in tissues during development, wound healing and tumorigenesis. Communication occurs when Notch receptors of one cell bind to either of its ligands, Delta/Jagged of neighboring cell. In general, Delta-mediated signaling drives neighboring cells to have an opposite fate (lateral inhibition) whereas Jagged-mediated signaling drives cells to maintain similar fates (lateral induction). Here, by deriving and solving a reduced set of 12 coupled ordinary differential equations for Notch-Delta-Jagged system on a hexagonal grid of cells, we determine the allowed states across different parameter sets. We also show that Jagged (at low dose) acts synergistically with Delta to enable more robust pattern formation, despite its lateral induction property; this effect is due to competition with Delta over binding with Notch, as experimentally observed in the case of chick inner ear development. Finally, we show that how Jagged can help to expand the bistable (both Uniform and Hexagon phases are stable) region, where a local perturbation can spread over time in an ordered manner to create a biologically relevant, defect-free lateral inhibition pattern. 

Abstract: By using infinite density matrix renormalization group (iDMRG) algorithm based on the formalism of matrix product states and matrix product operator, we study two cases: [1] the ground state of the quantum one-dimensional Hubbard model, and [2] the magnetization of the classical two-dimensional Ising model. Our results are consistent with the analytical solutions of the Hubbard model and the Ising model. We emphasize that the same method of iDMRG is used to solve the quantum case and the classical case.

[1] Ground-state properties of the one-dimensional Hubbard model with pairing

potential, Myung-Hoon Chung, Edmond Orignac, Didier Poilblanc, Sylvain Capponi, Physica B 604 (2021) 412665

[2] Infnite density matrix renormalization group method for solving the Ising model, Myung‑Hoon Chung, J. Korean Phys. Soc. 82 (2023) 776

Abstract: We studied 10 different systems of coupled Logistic Maps with linear or nonlinear coupling and delay ranging from 0 to 4. They fall in two distinct universality classes depending on the coarse grained long range order observed at a transition. We also propose a quantifier for zigzag and checkerboard patterns and find a critical behavior over a range of parameters. 

Abstract: Nucleation is often observed in nature and the presence of impurities in every real and experimental system is unavoidable. Impurities play a major role in the nucleation process. It could speed-up or slow-down the nucleation rate depending on the nature of the interactions. We have studied the behaviour of the droplet free energy and nucleation rate in two dimensional Ising lattice-gas with varying interaction strength in the presence of randomly positioned static/dynamic impurities. For the static case, the barrier height decreases with increasing impurity density enhancing the nucleation rate when impurities interact neutrally with both solute and solvent. The rates obtained using the simulation (forward flux sampling method) fit a Becker-Doring expression for different impurity densities [1]. In the case of dynamic impurities, at low temperatures we observe preferential occupancy of the impurities at the boundary positions of the nucleus enhancing the nucleation rate by lowering of the effective interfacial free energy. Further, we simulate the system for different interaction coupling strengths of the impurity with solute (J+) and solvent (J-) particles. Depending on the positional occupancy of the impurities, we find three regions in the parameter space. These are, regions where impurities prefer to inhabit the solute phase, the solvent phase, and the boundaries. We also observe a saturation in barrier height with decreasing symmetric interaction strengths (J+=J-=j) for dynamic impurities which corresponds to the phase where impurities are completely excluded from the nucleus. References 1. D. Mandal and D. Quigley, Soft Matter 17, 8642–8650 (2021).  

Abstract: We present a universal theory of strange metal behavior in a model of a Fermi surface coupled a two-dimensional quantum-critical scalar field with a spatially random Yukawa coupling. With the assumption of self-averaging randomness, similar to that in the Sachdev-Ye-Kitaev model, numerous observed properties of a strange metal are obtained, including the linear-in-temperature resistivity. We also describe the breakdown of self-averaging at the lowest temperatures: this emergent low temperature regime also has a resistivity which is nearly linear-in-temperature, and extends into a quantum-critical phase away from the quantum-critical point, as observed in several cuprates.

Abstract: I will show how the analysis of electron waiting times and the correlation between them help in understanding topological Andreev bound states in an Andreev interferometer where a superconducting loop with a controllable phase difference is connected to a quantum spin Hall edge. The edge state helicity enables the transfer of electrons and holes into separate leads controlled by the phase difference of the loop. In this setup, Majorana bound states occurs at $\phi=\pi$ and electron waiting times are sensitive to it. The two different waiting times show opposite behaviors when we consider the correlation between them. Some of the cross-distributions also show unique features indicating the appearance of Majorana bound states.

Abstract: Thermalization of a small quantum system strongly coupled to macroscopic surroundings corresponds to convergence of the state of the small system to the marginal of the global Gibbs state with time. Two different theories can be formulated regarding how such convergence might happen. The first is the open system approach, where the surroundings is taken as a thermal bath. The second is based on eigenstate thermalization hypothesis (ETH), where the whole system and surroundings is taken as one macroscopic isolated system. We show that a simple model often used to describe double quantum dots gives a perfect setting where both approaches can be investigated numerically on equal footing. This allows a fair comparison between them, elucidating their fundamental differences. We clearly demonstrate that these two approaches describe physics at widely different time and length scales 

Abstract: We analyze the anisotropic Dicke model in the presence of a periodic drive and under a quasiperiodic drive. The study of drive-induced phenomena in this experimentally accessible model is important since although it is simpler than full-fledged many-body quantum systems, it is still rich enough to exhibit many interesting features. We show that under a quasiperiodic Fibonacci (Thue-Morse) drive, the system features a prethermal plateau that increases as an exponential (stretched exponential) with the driving frequency before heating to an infinite-temperature state. In contrast, when the model is periodically driven, the dynamics reaches a plateau that is not followed by heating. In either case, the plateau value depends on the energy of the initial state and on the parameters of the undriven Hamiltonian. Surprisingly, this value does not always approach the infinite-temperature state monotonically as the frequency of the periodic drive decreases. We also show how the drive modifies the quantum critical point and discuss open questions associated with the analysis of level statistics at intermediate frequencies. 

Abstract: The realization of microscopic heat engines has gained a surge of research interest in statistical physics, soft matter, and biological physics. A typical microscopic heat engine employs a colloidal particle trapped in a confining potential, which is modulated in time to mimic the cycle operations. Here, we use a lanthanide-doped upconverting particle (UCP) suspended in a passive aqueous bath, which is highly absorptive at 975 nm and converts near infra red (NIR) photons to visible, as the working substance of the engine. When a single UCP is optically trapped with a 975 nm laser, it behaves like an active particle by executing motion subjected to an asymmetric temperature profile along the direction of propagation of the laser. The strong absorption of 975 nm light by the particle introduces a temperature gradient and results in significant thermophoretic diffusion along the temperature gradient. However, the activity of the particle vanishes when the trapping wavelength is switched to 1064 nm. We carefully regulate the wavelength-dependent activity of the particle to engineer all four cycles of a Stirling engine by using a combination of 1064 nm and 975 nm wavelengths. Since the motion of the particle is stochastic, the work done on the particle due to the stiffness modulation per cycle is random. We provide statistical estimation for this work averaged over five cycles which can be extended towards several cycles to make a Stirling engine. Our experiment proposes a robust set-up to systematically harness temperature which is a crucial factor behind building microscopic engines. 

Abstract: Dynamical phase transitions are singular changes in the distribution of dynamical observables and reflect as a non-analyticity in their large deviation functions. I shall present a class of stochastic processes where the distribution of time-integrated (empirical) observables is singular and it relates to phase transitions of dynamical trajectories. These illustrative simple examples include Brownian motion on a sticky surface or in the presence of an absorbing wall where we consider a set of empirical observables like the local time, average velocity, and area. I shall show how to obtain the large deviation function of these observables using a backward Fokker-Planck approach, in which singularities emerge from a competition between survival and diffusion. I shall also discuss an equivalent scenario of these dynamical phase transitions in terms of tilted operators, which is analogous to the familiar mechanism of phase transitions in terms of the degeneracy of the transfer matrix in the Ising model. We show that at the singular point, effective dynamics undergo an abrupt transition. Extending on the tilted operator approach, we show that similar phase transitions may generically arise in non-ergodic Markov chains. This scenario is robust and generalizable for non-Markov processes and for many-body systems, which can even lead to a sequence of such dynamical transitions. 

Abstract: Using a recently introduced model of pulsating active matter we investigate its rare dynamics at high density conditions with respect to an order parameter in its size distribution. We find that for small systems these result in emergent cycling and arrested dynamical phases which may dynamically co-exist, via intermittent plastic yielding, as a function of box geometry. We ascribe these transitions to boundary effects imposed by the box geometry that result in dynamic slow down in its average steady state, and which remarkably `templates' the nature of the dynamical transition. We explain these results from the perspective of a master curve between the order parameter and average repulsion which hold for different box geometries, number of particles and densities. 

Abstract: We investigate the dynamics of tracer particles in the random average process (RAP), a single-file system in one dimension. In addition to the position, every particle possesses an internal spin variable $\sigma (t)$ that can alternate between two values, $\pm 1$, at a constant rate $\gamma$. Physically, the value of $\sigma (t)$ dictates the direction of motion of the corresponding particle and for finite $\gamma$, every particle performs a non-Markovian active dynamics. Herein, we study the effect of this non-Markovianity in the fluctuations and correlations of the positions of tracer particles. We analytically show that the variance of the position of a tagged particle grows sub-diffusively as $\sim \zeta_{\text{q}} \sqrt{t}$ at large times for the quenched uniform initial condition. While this sub-diffusive growth is identical to that of the Markovian/non-persistent RAP, the coefficient $\zeta_{\text{q}} $ is rather different and bears the signature of the persistent motion of active particles through higher point correlations (unlike in the Markovian case). Similarly, for the annealed (steady state) initial condition, we find that the variance scales as $\sim \zeta_{\text{a}} \sqrt{t}$ at large times with coefficient $\zeta_{\text{a}} $ once again different from the non-persistent case. Although $\zeta_{\text{q}}$ and $\zeta_{\text{a}} $ both individually depart from their Markov counterparts, their ratio $\zeta_{\text{a}} / \zeta_{\text{q}}$ is still equal to $\sqrt{2}$, a condition observed for other diffusive single-file systems. This condition turns out to be true even in the strongly active regimes as corroborated by extensive simulations and calculations. Finally, we study the correlation between the positions of two tagged particles in both quenched uniform and annealed initial conditions. We verify all our analytic results by extensive numerical simulations.

Abstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First, we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  We will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index and find optimal annealing schedules for optimization.  Second, we will reveal a new implicit bias of stochastic gradient descent (SGD) that forces highly overparameterized neural networks to converge to very simple networks with many fewer effective degrees of freedom than their parameter count.  Intriguingly, this implicit bias arises through position dependent diffusion terms in accurate Langevin dynamics models of SGD; the position dependent diffusion tensor vanishes on simple networks, leading to SGD dynamics freezing on simple saddle points in the training error landscape. 

Abstract: Perceptual decision-making frequently requires making rapid, reliable choices upon encountering noisy sensory inputs. To better define the statistical processes underlying perceptual decision-making, we characterize the choices of participants visualizing a system of nonequilibrium stationary physical dynamics and compare such choices to the performance of an optimal agent computing Wald’s sequential probability ratio test (SPRT). Participants viewed movies of a drifted Brownian particle and had to judge the motion as leftward or rightward. Overall, the results uncovered fundamental performance limits consistent with recently established thermodynamic tradeoffs involving speed, accuracy, and dissipation. Specifically, decision times are sensitive to entropy production rates. To achieve a given level of accuracy, participants require more time than that predicted by the SPRT, indicating suboptimal integration of available information. Given such suboptimality, we develop an alternative account based on evidence integration with a memory time constant. Setting the time constant proportionate to the deviation from equilibrium in the stimuli significantly improves trial-by-trial predictions of decision metrics with respect to SPRT. This study shows that perceptual psychophysics using stimuli rooted in nonequilibrium physical processes provides a robust platform for understanding how the brain decides on stochastic information. 

Abstract: The collective motion of social agents that arises from their interactions has been the subject of intense scientific research. Understanding the collective dynamics of human crowds is critical for improving pedestrian traffic flow, ensuring crowd safety, effective urban planning, and preventing crowd disasters. In particular, the analysis of real-life mass events, such as religious gatherings, music concerts, sporting matches, and transportation hubs, has been essential for modeling crowd behavior with the goal of preventing life-threatening situations such as crushes, stampedes, and trampling. Analyzing crowd dynamics and pattern formation in human data is a crucial first step towards a successful human-crowd modeling.

To understand the crowd behavior one has to rely on experimental data using real human beings. Pedestrian traffic flow has been studied empirically in a wide variety of situations, using both experimental methods and motion tracking of real crowds. When two streams of pedestrians cross at an angle, striped patterns spontaneously emerge as a result of local pedestrian interactions. Several urban situations produce crossing flows, such as streams of pedestrians crossing at a sidewalk intersection, or subway commuters passing each other when entering and exiting a public transport, such as a metro car. It is very common to notice that pedestrians in a crosswalk often form multiple lanes of traffic. Such spontaneous pattern formation is an example of self-organized collective behavior, a topic of intense interdisciplinary interest.

In this presentation, I wish to talk about numerical strategies that were developed to study the geometric properties of striped patterns, which arise as a consequence of two crossing flows. In [1], we presented two novel computational methods for analyzing striped patterns in pedestrian data: (i) an edge-cutting algorithm, which detects the dynamic formation of stripes and allows us to measure local properties of individual stripes; and (ii) a pattern-matching technique, based on the Gabor function, which allows us to estimate global properties of the striped pattern at a time. We found an invariant property: stripes in the two groups are parallel and perpendicular to the bisector at all crossing angles. I shall also present our ongoing research, where we are working on another elegant approach to detect the stripes using matrices constructed out of the crossing information of two agents from opposite groups.

Reference:

[1] P. Mullick, S. Fontaine, C. Appert-Rolland, A.-H. Olivier, W. Warren and J. Pettré. Analysis of emergent patterns in crossing flows of pedestrians reveals an invariant of 'stripe' formation in human data. PLoS Computational Biology 18 (6), e1010210 (2022).

Abstract: The Mpemba effect is a counter-intuitive relaxation phenomenon where a hotter system relaxes to equilibrium faster than a cooler system, when both systems are quenched to the same low temperature. The effect was first shown for freezing of water. However,  the effect is more general and can be studied in the context of relaxation dynamics of even systems far from equilibrium, an example being driven granular systems. In this talk, I will describe the Mpemba effect in trapped colloidal particles. Additionally, I will discuss the difficulties in defining the Mpemba effect and outline possible mechanisms behind it. 

Abstract: Measuring entropy production of a system directly from the experimental data is highly desirable since it gives a quantifiable measure of the time-irreversibility for non-equilibrium systems and can be used as a cost function to optimize the performance of the system. Although numerous methods are available to infer the entropy production of stationary systems, there are only a limited number of methods that have been proposed for time-dependent systems and, to the best of our knowledge, none of these methods have been applied to experimental systems. Herein, we develop a general non-invasive methodology to infer a lower bound on the mean total entropy production for arbitrary time-dependent continuous-state Markov systems in terms of the moments of the underlying state variables. The method gives surprisingly accurate estimates for the entropy production, both for theoretical toy models and for experimental bit erasure, even with a very limited amount of experimental data. 

Abstract: We investigate steady-state current fluctuations in two models of run-and-tumble particles (RTPs) on a ring of $L$ sites, for {\it arbitrary} tumbling rate $\gamma=\tau_p^{-1}$ and density $\rho$; model I consists of standard hardcore RTPs, while model II is an analytically tractable variant of model I, called long-ranged lattice gas (LLG). We show that, in the limit of $L$ large, the fluctuation of cumulative current $Q_i(T,L)$ across $i$th bond in a time interval $T \gg 1/D$ grows first {\it subdiffusively} and then {\it diffusively} (linearly) with $T$, where $D$ is the bulk diffusion coefficient. Remarkably, regardless of the model details, the scaled bond-current fluctuations $D \langle Q_i^2(T,L) \rangle/2 \chi L \equiv {\cal W}(y)$ as a function of scaled variable $y=DT/L^2$ collapse onto a {\it universal} scaling curve ${\cal W}(y)$, where $\chi(\rho,\gamma)$ is the collective particle {\it mobility}. In the limit of small density and tumbling rate $\rho, \gamma \rightarrow 0$ with $\psi=\rho/\gamma$ fixed, there exists a scaling law: The scaled mobility $\gamma^{a} \chi(\rho, \gamma)/\chi^{(0)} \equiv {\cal H} (\psi)$ as a function of $\psi$ collapse onto a scaling curve ${\cal H}(\psi)$, where $a=1$ and $2$ in models I and II, respectively, and $\chi^{(0)}$ is the mobility in the limiting case of symmetric simple exclusion process (SSEP). For model II (LLG), we calculate exactly, within a truncation scheme, both the scaling functions, ${\cal W}(y)$ and ${\cal H}(\psi)$. We also calculate spatial correlation functions for the current, and compare our theory with simulation results of model I; for both models, the correlation functions decay exponentially, with correlation length $\xi \sim \tau_p^{1/2}$ diverging with persistence time $\tau_p \gg 1$. Overall our theory is in excellent agreement with simulations and complements the findings of Ref. {\it arXiv:2209.11995}. 

Abstract: Measurements of any property of a microscopic system are bound to show significant deviations from the average, due to thermal fluctuations. For time-integrated currents such as heat, work, or entropy production in a steady state, it is in fact known that there will be long stretches of fluctuations both above as well as below the average, occurring equally likely at large times. In this talk, we will demonstrate that for any finite-time measurement in a nonequilibrium steady state—rather counter intuitively—fluctuations below the average are more probable. This discrepancy is found to be higher when the system is further away from equilibrium. For overdamped diffusive processes, there is even an optimal time when time-integrated current fluctuations mostly lie below the average. We will demonstrate that these effects are consistent with a nonmonotonic skewness of current fluctuations and provide evidence that they are easily observable in experiments. We also discuss their extensions to discrete space Markov jump processes and implications to biological and synthetic microscopic engines.  

Abstract: We study the spectral properties of a multiparametric system having particle-hole symmetry in random matrix setting. We observe a crossover from Poisson to Wigner-Dyson like behavior in average local ratio of spacing within a spectrum of single matrix as a function of effective single parameter referred to as complexity parameter. The average local ratio of spacing varies logarithmically in complexity parameter across the transition. This behavior is universal for different ensembles subjected to same matrix constraint like particle-hole symmetry. The universality of this dependence is further established by studying interpolating ensemble connecting systems with particle-hole symmetry to that with chiral symmetry. For each interpolating ensemble the behavior remains logarithmic in complexity parameter. We verify this universality of spectral fluctuation in case of a 2D Su-Schrieffer-Heeger (SSH) like model along with the logarithmic dependence on complexity parameter for ratio of spacing during transition from integrable to non-integrable limit. 

Abstract: TBA

Abstract: The effects of random field ( in full circular symmetry) on the critical behaviours of anisotropic XY ferromagnet in three dimensions are studied systematically by using Monte Carlo Simulation. The critical temperature Tc below which ferromagnetic phase appears , has been found to decrease in presence of random field.The compensating field (the prescribed amount of field which retains the critical temperature Tc for isotropic XY ferromagnet) has been studied as a function of the strength of anisotropy. The compensating field was found to depend linearly on the strength of anisotropy.

Abstract: We consider a "true" discretization of the Vicsek model (TDVM) on an off-lattice two-dimensional geometry to probe the transition of collective motion as the system switches its symmetry from discrete to continuous. The TDVM consists of particles able to move in the plane in a discrete set of q equidistant angular directions, as in the active clock model (ACM), where the dynamical rules of particle alignment and movement are inspired by the prototypical Vicsek model (VM). The influence of system parameters (i.e. noise level, average system density, system size) on the flocking dynamics is investigated and the system is observed to exhibit six different self-organized patterns (gas, cluster, macrophase, microphase, cross-sea, and liquid) as a function of q. Furthermore, the relation between the number fluctuations, the nature of the coexistence phase, the pinned property of the orientation vector, and the nature of ordering has been investigated. Our findings contribute to the understanding of important qualitative differences in the phase separation of collective dynamics.

Abstract: Shape asymmetry is the most abundant in nature and attracted great interest in recent research. The phenomenon is widely recognised: a free ellipsoidal Brownian particle displays anisotropic diffusion during short time intervals, which subsequently transitions to an isotropic diffusion pattern over longer time scales. We have further expanded this concept to incorporate active ellipsoidal particles characterized by an initial self-propelled velocity. We derived the analytical expressions and simulation results of the persistence probability of an active anisotropic particle without any external potential and with an external harmonic potential. This work provides analytical and simulation results of diffusion coefficients of an active ellipsoidal particle. In comparison to a passive particle, we demonstrate that the long-term diffusion coefficient of an active particle is influenced by both the magnitude of the propulsion velocity and the rotational diffusion coefficient. We have also studied the approximations of different results for diffusion coefficients in t≪D_\theta^{-1} time-scale. Further we have studied the persistence probability p(t) of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability of a stochastic variable that has not changed its sign in a given fixed time interval. We have investigated two cases: (1) diffusion of a free active particle and (2) that of a harmonically trapped particle. 

Abstract: Spatiotemporal pattern formation plays a key role in various biological phenomena including Epithelial Mesenchymal Transition (during cellular differentiation and cancer initiation). Though the reaction-diffusion systems enabling pattern formation have been studied phenomenologically, the bio-mechanical underpinnings of these processes has not been modeled in detail. Here, we present the emergence of multistable spatiotemporal patterns due to transcriptional/cooperative gene regulation, host-circuit interaction, and protein dimerization. We investigate the patterns formed due to the coupling of inherent multistable behavior of transcriptional toggle switches (bistability), toggle triads (tristability), coupled with their molecular diffusion, with varying diffusion coefficients, across a two-dimensional tissue. In another setup of diffusible cellular environment, we investigate emergent spatiotemporal bistability by a motif with non-cooperative positive feedback, that imposes a metabolic burden on its host. Spatiotemporal diffusion coupled with competitive protein dimerization and autoregulatory feedback induces higher order spatiotemporal multistabilty — quadra-, hexa-, and septastabilty. These analyses offers valuable insights into -the design principles of synthetic bio-circuits, and suggest mechanistic underpinnings of biological pattern formation. 

Abstract: TBA