Talks

Having its origin in nuclear spectroscopy and statistics, Random Matrix Theory has pervaded nearly all fields of physics. The reason is that, starting with the seminal work of Bohigas, Giannoni and Schmidt, Random Matrix Theory has become synonymous with chaotic quantum systems which can be as diverse as atoms, nuclei, nucleons, black holes, and quantum computers, to name a few. Recently, a great deal of progress has been in chaotic many-body quantum systems, mainly through many studies of the Sachdev-Ye-Kitaev model. After an introduction to Random Matrix Theory, I will discuss manifestations of chaos in such systems including time scales and the effects of dissipation as well as connections with Jackiw-Teitelboim gravity.

Sum and order statistics of independent and weakly correlated random variables are asymptotically described by a handful of “universal” distributions, as established by the central limit theorem and its generalizations, and the Fisher-Tippett-Gnedenko theorem. On the other hand, while strongly correlated systems are abundant, only for a few exceptional cases can their sum or order statistics be determined analytically. In this talk I present a large class of systems with strong correlations for which the sum and complete order statistics can be solved exactly. I present a few examples that illustrate how this procedure works.

Detecting determinism and nonlinear properties from empirical time series is highly nontrivial. Traditionally, nonlinear time series analysis is based on an error-prone phase space reconstruction that is only applicable for stationary, largely noise-free data from a low-dimensional system and requires the nontrivial adjustment of various parameters. We present a data-driven index based on Fourier phases that detects determinism at a well-defined significance level, without using Fourier transform surrogate data. It extracts nonlinear features, is robust to noise, provides time-frequency resolution by a double running window approach, and potentially distinguishes regular and chaotic dynamics. We test this method on data derived from dynamical models as well as on real-world data, namely, intracranial recordings of an epileptic patient and a series of density related variations of sediments of a paleolake in Tlaxcala, Mexico.

In several biological systems, such as bacterial cytoplasm, cytoskeleton-motor complexes and epithelial sheets of cells, self-propulsion or activity is found to fluidize a glassy state that exhibits characteristic glassy features in the absence of activity. To develop a theoretical understanding of this non-equilibrium phenomenon, we have studied, using molecular dynamics and Brownian dynamics simulations, the effects of activity in several model glass-forming liquids. The activity in these systems is characterized by two parameters: the magnitude of the active force and its persistence time. If the persistence time is short, then the observed behavior is similar to that near the usual glass transition. For large but finite persistence times, the approach to dynamical arrest at low propulsion force goes through a phase characterized by intermittency. This intermittency is a consequence of long periods of jamming followed by bursts of plastic yielding. In the limit of infinite persistence time, the homogeneous liquid state obtained at large values of the active force exhibits several unusual properties: the average kinetic energy increases with increasing system size and a length scale extracted from spatial velocity correlations increases with system size without showing any sign of saturation. Similar correlations are also found for the self-propulsion forces, indicating a novel kind of self-organization. This active liquid evolves to a force-balanced jammed state when the self-propulsion force is decreased below a threshold value. The jamming proceeds via a three-stage relaxation process whose timescale grows with the magnitude of the active force and the system size.

In this talk, I aim to give a pedagogical overview of the rapidly developing field of 'stochastic resetting', relevant in many fields that typically involve a random search process. Stochastic resetting simply means interrupting the natural dynamics of a system at random times and resetting the system back to its initial condition. This resetting move breaks detailed balance and drives the system into a nonequilibrium stationary state. The approach to the stationary state is accompanied by an unusual ‘dynamical phase transition’. Moreover, the mean first-passage time to a fixed target becomes a minimum at an optimal value of the resetting rate. This makes the diffusive search process more efficient. Recent experiments in optical traps have verified some of the theoretical predictions, but also have raised new interesting questions. Going beyond the classical regime, there have been recent developments in quantum resetting also. I hope to explain why stochastic resetting has emerged in recent years as an exciting field of research in nonequilibrium statistical physics.

We investigate classic diffusion with the added feature that a diffusing particle is reset to its starting point each time the particle reaches a specified threshold. In an infinite domain, this process is non stationary and its probability distribution exhibits rich features. In a finite domain,we define a nontrivial optimization in which a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset point, which corresponds to maximal performance. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost.

We study the decay rate that characterizes the late-time exponential decay of the first-passage probability density of a diffusing particle in a one-dimensional confining potential, starting from the origin to a position located at a fixed position on the positive side. For general confining potential, we show that the decay rate (a measure of the barrier crossing rate) has three distinct behaviors as a function of the target location, depending on the tail of the confining potential on the negative size. In particular, for potentials that increase asymptotically linearly on the negative side, we show that a novel freezing transition occurs at a critical value of the target location the decay rate increases monotonically as the distance to the location decreases till a critical value below which it freezes to constant. Our results are established using a general mapping to a quantum problem and by exact solution in three representative cases supported by numerical simulations. We show that the freezing transition occurs when the gap between the ground state (bound) and the continuum of scattering states vanishes in the associated quantum problem. We find that such a freezing transition is also present in the case of a run-and-tumble particle in a confining potential that grows linearly on both sides.

Transition paths are rare stochastic events occurring when a system, thanks to the effect of fluctuations, crosses successfully from one stable state to another by surmounting an energy barrier. Even though they are of great significance in many mesoscale processes ranging from biomolecular folding to colloidal transport, their direct determination is often challenging due to their short duration as compared to other relevant time-scales of the system. In this talk, I will present experimental results on the transition paths dynamics of colloidal beads embedded in distinct fluids such as glycerol/water mixtures, polymer and micellar solutions, hopping over energy barriers separating two optical potential wells. We find a significant reduction in the mean transition path times of the particle in the polymer and micellar solutions, both exhibiting viscoelasticity, as compared to those measured under similar energy landscapes in viscous glycerol/water mixtures with the same zero-shear viscosity. Our experimental results are in quantitative agreement with a model based on the generalized Langevin equation and demonstrate that such a decrease in a viscoelastic fluid can be described in terms of an effective viscosity probed by the bead during the barrier-crossing process, which quantitatively coincides with that measured by linear microrheology at a frequency determined by the inverse of the mean transition path time. Moreover, by measuring the mean velocity profiles of the bead along transition paths, we confirm that this quantity establishes a fundamental relationship between mean transition path times and equilibrium rates in thermally activated processes of small-scaled systems in contact with both Markovian and non-Markovian baths.

Scaling, that is, the reduction in the number of variables in a problem due to a symmetry under change of scale, is an unexpectedly widespread phenomenon. Aggregation, on the other hand, is a process which appears in a large number of apparently unrelated physical systems. In this talk, I aim to present the way in which scaling can be used to simplify the understanding of such processes in their various guises, whether they are studied via rate equations, described as stochastic processes, whether they involve two-body reactions or more complex schemes, and so on. I aim mainly to give a set of examples showing what can be done with simple means.

In a kinetic exchange model of opinion formation, popularly known as the BChS model, an order disorder transition can be induced when the fraction of negative interaction between the agents exceeds a certain value. In this case, the negative interaction plays the role of noise. In the discrete version, when the opinion can take values -1, 0 and 1, the dynamical rules used in the model allow no transition between the two extreme states. However, increasing the magnitude of the interaction strength, it is possible to have extreme switches of opinion values. We consider such stronger interaction that occurs with a probability and acts as a second source of noise. We present here how this noise enhances the disorder using several different approaches and topologies.

Using the Galam model of opinion dynamics I show that polarization is the natural byproduct of open and informal discussions among agents in a given society. However, the phenomenon of polarization is found to be multifaceted with one sided, segregated, fluid and rigid polarizations. In the case of a homogeneous social community with only floaters (rational agents), repeated discussions among small groups of agents lead gradually toward unanimity along one side with one sided polarization. However, tie breaking prejudice may select the initial minority side to win over. In addition, polarization can appear as the juxtaposition of non-mixing social groups sharing different prejudices about the issue at stake. It is a segregated polarization. But including a small proportion of contrarian agents among the floaters turns the polarization fluid with agents keeping shifting sides yet preserving a collective split between two opposite groups. In contrast, the presence of few stubborn agents drive the community toward a rigid polarization with frozen individual opinions distributed in two opposite groups. In turn, rigid polarization triggers the eventual emergence of hate between the two opposed blocks.

S. Galam, Unanimity, Coexistence, and Rigidity: Three Sides of Polarization, Entropy 25(4), 622 (2023)

Multilayer networks are widespread in natural and manmade systems. Key properties of these networks are their spectral and eigenfunction characteristics, as they determine the critical properties of many dynamics occurring on top of them. In this paper, we numerically demonstrate that the normalized localization length β of the eigenfunctions of multilayer random networks follows a simple scaling law given by β = x*/(1 + x*), with x*= γ( beff ^ 2 / L) ^ δ,  γ, δ ∼ 1 and beff being the effective bandwidth of the adjacency matrix of the network, whose size is L. The reported scaling law for β might help to better understand criticality in multilayer networks as well as used as to predict the eigenfunction localization properties of them.

Friendship networks have been widely studied, However, little is known about enemy networks, if they exist. I will present a dynamical model that simulates the creation of links of friends and also enemies, in order to compare with experimental results taken in schools in Mexico and Hungary. The agreement between the experimental data and the theoretical results is very good and allows us to verify the hypotheses of the model on social behavior.

Diffusion is a fundamental process that governs various physical, chemical, and biological phenomena. When particles move in restricted spaces, their behavior can deviate significantly from our intuitive expectations. In this lecture, we explore the history, most important results, new results, and insights into diffusion under confinement. We will focus on the application of the projection method to narrow channels and tubes where the coordinate frame is placed at the axis curve of the tube or channel, using the Frenet-Serret moving frame as the coordinate system to study the diffusion of bounded Brownian point-like particles. This covariant description for the diffusion equation maps the shape of a general channel in two dimensions or a tube in three dimensions to a straight tube or channel seen in a non-Cartesian space. In other words, this description mimics traveling within a moving frame that travels through the midline, which allows us to constantly keep the perspective of being confined by a straight channel or tube. Significant contributions of this method include the possibility of extending the study of geometrical confinement to variable cross-section as well as the possibility of considering more general parametric curves to describe the channel or tube axis. Finally, we will talk about the Fick-Jacobs- Zwanzig equations when Brownian particles are under stochastic resetting.

Thermodynamics and statistical mechanics, its quantum counterpart, are traditionally described with statistical ensembles in quantum or classical mechanics. Canonical typicality[1] has related thermodynamics for a system to ensembles of global energy eigenstates of system and its environment analyzing their cardinality. Extending the concept of relational time [2-4] to complex relational time, we show that the canonical density for a system emerges from a maximally entangled global state of system and environment through relational complex time evolution between system and environment without the need to maximize the entropy or to count states [5].

[1] S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, Canonical typicality, Phys. Rev. LeT. 96, 050403 (2006).

[2] D. N. Page and W. K. WooTers, Evolution without evolution: Dynamics described by stationary observables, Phys. Rev. D 27, 2886 (1983).

[3] A. R. H. Smith and M. Ahmadi, Quantizing time: Interacting clocks and systems, Quantum 3, 160 (2019).

[4] S. Gemsheim and J. M. Rost: Emergence of time from quan- tum interaction with the environment, Phys. Rev. LeT. 131, 140202, (2023).

[5] S. Gemsheim and J. M. Rost: Statistical mechanics from relational complex time with a pure state, arXiv:2405.06401, accepted for publication in PRD (2024).

Quantum chaos can be diagnosed through the analysis of level statistics using the spectral form factor. This is the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole), when the system is chaotic. We discuss how this structure can be detected through the dynamics of two physical quantities accessible to experimental many-body quantum systems — the survival probability and the spin autocorrelation function — and how this manifestation of many-body quantum chaos implies relaxation times that grow exponentially with system size. However, quantities that exhibit the correlation hole are non-self-averaging. This means that the correlation hole is only visible after large averages over initial states or disorder realizations are performed, which is computationally and experimentally costly. We explain how self-averaging can be ensured by opening the system to an environment.

Lindblad master equations have been very successful in describing relevant phenomena of open quantum systems. For central systems composed of weakly coupled parties, the usual phenomenological approach introduces dissipation neglecting the internal interaction. This is no longer valid in the strong coupling regime, where a careful derivation of the so-called dressed state master equation reveals the presence of combined decay mechanisms. In this talk, we discuss some features of strongly coupled hybrid systems, and the exact solvability of certain dressed-state master equations without any source of driving. In particular, it will be argued that some of these equations present a simpler solution in the strong coupling regime compared to the phenomenological case.

Authors: Tilen Čadež (IBS, Daejon), Dillip Kumar Nandy (IBS, Daejeon), Dario Rosa (ICTP, Sao Paulo), Alexei Andreanov (IBS, Daejeon), and Barbara Dietz (IBS, Daejeon)

Interest in the Rosenzweig-Porter model, a parameter-dependent random- matrix model which interpolates between Poisson and Wigner-Dyson (WD) statistics describing the fluctuation properties of the eigenstates of typical quantum systems with regular and chaotic classical dynamics, respectively, has come up again in recent years in the field of many-body quantum chaos. The reason is that it exhibits parameter ranges in which the eigenvectors are Anderson-localized, non-ergodic (fractal) and ergodic extended, respectively. The central question is how these phases and their transitions can be distinguished through properties of the eigenvalues and eigenvectors. We propose characteristics of the short- and long-range spectral correlations as measures to explore the transition from Poisson to WD statistics. Furthermore, we performed in-depth studies of the properties of the eigenvectors and find that the ergodic and Anderson transitions take place at the same parameter values and the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

Nonlinear evolution is not a usual phenomenon in quantum physics. It is possible to define a time-evolution for an ensemble of equally prepared systems in a somewhat unusual way: take N systems, apply an entangling unitary transformation, measure all but one of the systems and, depending on the measurement results, keep or throw away the remaining system. This procedure applied to the whole ensemble results in a new ensemble, the state of which being a nonlinear transformation of the initial quantum state. Entanglement distillation protocols  are a prime example of this procedure. Iterating the above type of protocols can lead to nontrivial time-evolution, which can become chaotic [1]. We discuss various properties of the emerging dynamics for one- and two-qubit systems. For increasingly noisy initial states, a sudden change in the character of the evolution occurs, similar to a phase transition [2,3]. In the case of qubit pairs, asymptotic entanglement can depend sensitively on the initial state [4]. We report on the realization of a couple of steps for two of the protocols in optical experiments [5,6]. Furthermore, we discuss possible applications, e.g. benchmarking quantum computers [7].

[1] T Kiss, I Jex, G Alber, S Vymětal, Physical Review A 74 (4), 040301 (2006); A Gilyén, T Kiss, I Jex, Scientific Reports 6 (1), 20076 (2016).

[2] M Malachov, I Jex, O Kálmán, T Kiss, Chaos: An Interdisciplinary Journal of Nonlinear Science 29 (3) (2019).

[3] A Portik, O Kálmán, I Jex, T Kiss, Physics Letters A 431, 127999 (2022).

[4] T Kiss, S Vymětal, LD Tóth, A Gábris, I Jex, G Alber, Physical Review Letters 107 (10), 100501 (2011).

[5] G Zhu, O Kálmán, K Wang, L Xiao, D Qu, X Zhan, Z Bian, T Kiss, P Xue, Physical Review A 100 (5), 052307 (2019).

[6] D Qu, O Kálmán, G Zhu, L Xiao, K Wang, T Kiss, P Xue, New Journal of Physics 23 (8), 083008 (2021).

[7] A Cornelissen, J Bausch, A Gilyén, arXiv:2104.10698 (2021; A Ortega, O Kálmán, T Kiss, Physica Scripta 98 (2), 024006 (2023).

More than 500 years back Leonardo da Vinci reported in his Notebook an experiment showing that the tensile strengths of nominally identical specimens of iron wire decrease with increasing length of the wires: Fracture strength tend to vanish in the macroscopic limit – the reason for nonexistence of very tall trees, very big animals, etc. This is the earliest and precise evidence of Extreme Statistics in the nature (in the breaking properties of solids). Since then, following Alan Griffith’s (1921) nucleation theory of brittle fracture, Fredric Thomas Pierce (2026) and Henry Ellis Daniels’s (1945) statistical model and theory of Fiber-Bundle strengths, Ray-Chakrabari-Duxbury-Leath-Benguigui-Pradhan-Hansen’s (1985-2010) developments on statistical fracture analysis in disordered solids & Fiber-Bundle-Models, and the latest observations on the socio-statistical inequality measures (Gini & Kolkata) of damage or avalanche statistics by Biswas-Chakrabarti (2021-) led to some major understanding about the fracture dynamics in disordered solids. This enlightening story, which is still missing in our Condensed Matter Physics textbooks, will be very briefly discussed.

Selected References:

A. A. Griffith, Phenomena of Rupture and flow in solids, Philosophical Transactions of the Royal Society London, A 221 163 (1921)

F. T. Pierce, Tensile Tests for Cotton Yarns, Part V: The Weakest Link, Journal of Textile Institute, 17, T355 -T368 (1926)

H. E. Daniels, The Statistical theory of the strength of the bundles of threads, Proceedings of the Royal Society London A, 183, 404 (1945)

P. Ray & B. K. Chakrabarti, A microscopic approach to statistical fracture analysis of disordered brittle solids, Solid State Communication 53, 477 (1985)

P. M. Duxbury, P. D. Beale & P. L. Leath, Size effects of electrical breakdown in quenched random media, Physical Review Letters 57, 1052 (1986)

P. C. Hemmer & A. Hansen, The Distribution of Simultaneous Fiber Failures in Fiber Bundles, ASME Journal of Applied Mechanics, 59, 909 (1992)

S. Zapperi, P. Ray, H. E. Stanley & A. Vespignani, First-Order Transition in the Breakdown of Disordered Media, Physical Review Letters, 78, 1408 (1997)

B. K. Chakrabarti and L. G. Benguigui, Statistical Physics of Fracture & Breakdown in Disordered Systems, Oxford Univ. Press, Oxford (1997)

S.Pradhan & B. K. Chakrabarti, Precursors of catastrophic in the Bak-Tang-Wiesenfeld, Manna and random fiber bundle models of failure, Physical Review E, 65, 016113 (2001)

S. Pradhan, A. Hansen & B. K. Chakrabarti, Failure Processes in Elastic Fiber Bundles, Review of Modern Physics, 82, 499 (2010)

S. Biswas & B. K. Chakrabarti, Social inequality analysis of fiber bundle model Statistics and prediction of materials failure, Physical Review E, 104, 044308 (2021)

Diksha, S. Kundu, B. K. Chakrabarti & S. Biswas, Inequality of avalanche Sizes in models of fracture, Physical Review E 108, 014103 (2023)

Diksha, G. Eswar & S. Biswas, Prediction of depinning transitions in interface models using Gini & Kolkata indices, Physical Review E 109, 044113 (2024)

I will discuss recent results on market microstructure in the Glosten-Milgrom and the Kyle models, based on stochastic thermodynamics. These results provide insights on the market impact phenomenology and on the value of information, as measured by the expected profit that can be extracted from trading using side information.

We present a statistical analysis of the individual income data provided by the Mexican National Institute of Statistics and Geography, or by its official name “Instituto Nacional de Estadística y Geografía” (INEGI, https://www.inegi.org.mx/). The data analyzed was obtained through a survey of the Mexican population and was conducted approximately every 4 years to cover the time period from 1984 to 2018. The number of records in each one of these surveys is variable. On the other hand, low and middle income individuals predominate in the samples. What is interesting is that with this restriction of the data we are still able to see the combination of the two distributions that successfully fit individual income empirical data: the gamma and power law distributions. For the power-law statistical fit, we determine the cutoff parameter that minimizes the Anderson-Darling statistic and from this point we determine the best power-law exponent. This methodology was presented by us in (1). We analyze the evolution over time of the power law exponent for the period in which the data were analyzed together with other results related to the cutoff parameter and the Gini index of the income distribution studied.

(1) On fitting the Pareto-Levy distribution to stock market index data: selecting a suitable cut off value. H.F. Coronel-Brizio, A.R. Hernández-Montoya. Physica A 354 437-449 (2005). Doi:10.1016/j.physa.2005.03.001

Artificial Intelligence refers to a field of research in computer science that explores methods and software enabling machines to perceive their environment and utilize learning to maximize goal achievement. In the last decade, Machine Learning, a subset of AI focused on developing and studying statistical algorithms that can learn and generalize from data to perform tasks without explicit instructions, has emerged as an exciting and dynamic area of modern research and application. It plays a central role in tackling complex problems and complements traditional statistical methods in addressing data-intensive challenges. This talk will primarily focus on time series feature-based analysis, which involves developing representations of time series measurements in terms of characteristics and patterns in the data, known as features. Capturing the dynamic properties of time series in appropriate features can enable efficient use of ML methods and enhance understanding of the underlying phenomena. Specifically, we will describe an approach for building a feature-based representation of time series of financial returns from the S&P500 index. This approach utilizes a small, informative subset of features to capture dataset properties, including basic pairwise interactions between the multivariate time series. We will then discuss the findings in the context of the system.