Abstracts

Marton Balazs

Second class particles just walk sometimes

I will review some old and not so old results about second class particles going crazy and performing simple random walk sometimes. This is really out of their usual character which is typically self-interacting hence far more complicated than a simple random walk.

Joint work with Gyorgy Farkas, Peter Kovacs, Attila Rakos; Lewis Duffy, Dimitri Pantelli. But the main motivation of course comes from Gunter and his coauthors' work.

Thierry Bodineau

Some results from the macroscopic fluctuation theory

We consider diffusive microscopic dynamics driven out of equilibrium by external reservoirs. In a steady state for a small forcing regime, we will explain how the large deviation functional of the density can be computed perturbatively by using the macroscopic fluctuation theory. This applies to general domains in any dimension and to diffusive dynamics with general transport coefficients. We will also show that a macroscopic description predicts a universal behavior of the large deviations of the current for systems in contact with 2 types of reservoirs. Using the example of the SSEP, we will explain that such a macroscopic description may no longer be valid for reservoirs with weak contacts.

Luigi Cantini

An integrable approach to macroscopic fluctuation theory for the multispecies SSEP

We study the macroscopic fluctuation theory (MFT) of a multispecies generalization of the symmetric simple exclusion process on the infinite line. We show that the corresponding MFT saddle-point equations define an integrable system, of Landau--Lifshitz type, which can be solved exactly via a Lax pair and the inverse scattering method. This yields the cumulant generating function of the multispecies current and the optimal density profiles conditioned on a prescribed current fluctuation. We find that the generating function depends on the boundary data through a single scalar variable, extending a known single-species result to the multispecies setting.

Sakuntala Chatterjee

A novel mechanism of ordering in a coupled driven system: vacancy induced phase separation

We study a coupled driven system where two different species of particles, along with some vacancies or holes, move on a landscape whose shape fluctuates with time. The movement of the particles is guided by the local slope of the landscape, and the shape is also affected by the presence of different particle species. The nature of this coupling plays a crucial role in the formation of long range order in the system. When a particle species pushes the landscape in the same (opposite) direction of its own motion, it it called an aligned (a reverse) bias.

Aligned bias promotes ordering while reverse bias destroys it. In the absence of vacancies, the system reduces to the previously studied LH model for which different kinds of ordered and disordered phases were observed upon tuning the coupling between the particle and landscape dynamics. These phases could be explained as a competition or cooperation between aligned bias and reverse bias coming from different particle species. This interplay is expected to remain unaffected even when vacancies are present since vacancies do not impart any kind of bias on the landscape. However, we find that the presence of vacancies effectively weakens the reverse bias and this significantly changes the outcome of the competition between the two bias types. 

As a result, novel ordered phases emerge which were not seen before. We analytically calculate the new phase boundaries within the mean field approximation. We show that even when the aligned bias is weaker than the reverse bias, it is possible to find long ranged order in the system. We discover two new phases where the particle species showing weaker aligned bias phase separate and the other species with stronger reverse bias stays mixed with the vacancies. We call these phases finite current with partial phase separation (FPPS) and vacancy induced phase separation (VIPS). The landscape beneath the phase separated species takes the shape of a macroscopic hill in FPPS phase. However, in the VIPS phase it has the shape similar to a plateau whose height scales as square root of the system size. We explain the formation of these phases using flux balance condition in steady state."

Cristian Coletti

Two repelling random walks on ℤ

Fernando P. A. Prado, Cristian F. Coletti, Rafael A. Rosales

We consider two interacting random walks on ℤ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter β≥0. When β=0 both processes are independent symmetric random walks on ℤ, and hence recurrent. We show that both random walks are further recurrent if β∈(0,1]. We also show that these processes are transient and diverge in opposite directions if β>2. The case β∈(1,2] remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.

Chiara Franceschini
Degree-preserving conservative processes and a unified approach for their hydrodynamics

In this talk I will consider a broad class of interacting systems characterized by a single conservation law and satisfying the "degree-preserving property", namely, the Markov generator of the processes preserves the degree of polynomials of the state variables up to two. This property, together with a few general assumptions, makes it possible to study many different models within the same framework. In particular, it allows us to rigorously derive their hydrodynamic behavior without having to analyze each model separately.

Joint work with: Patrícia Gonçalves, Kohei Hayashi, Makiko Sasada.

Tertuliano Franco

Heat Equation with Wentzel boundary conditions as a limit of random particle systems

In this talk we consider two interacting particle systems in the finite box with N sites, namely, independent random walks and symmetric exclusion processes. Both systems are in contact with a finite reservoir, where the exit rate is proportional to the inverse of $N^\theta$, where is $\theta$ nonnegative. We prove the hydrodynamic limit for these models, which are given by the heat equation with Wentzell boundary conditions at the boundary at the critical parameter , and exhibit a dynamic phase transition. Moreover, the Wentzell boundary condition is non-linear in the exclusion setting at the critical parameter $\theta=1$. Joint work with Patrícia Gonçalves and Matheus Franco

Stefan Grosskinsky

Large-scale dynamics in aggregation models with product kernels

We study mean-field limits of interacting particle systems with interaction kernels of product form. One example is the inclusion process with a bilinear kernel, where the partition of total mass evolves according to the well-studied Poisson-Dirichlet diffusion in the scaling limit. This complete result relies on self-duality properties of the model, which are not present for the exchange-driven growth model with a non-linear product kernel originally introduced in [PRE 68, 031104 (2003)]. Depending on the non-linearity, the model may exhibit (instantaneous) gelation and we can derive only partial results for the scaling limit.

This is joint work with Paul Chleboun, Simon Gabriel and Angeliki Koutsimpela.

Rosemary Harris

TBA

Malte Henkel

Schrodinger-invariance in the exactly solvable voter model

Exact single-time and two-time correlations and the two-time response function are found for the order-parameter in the voter model with nearest-neighbour interactions. Their explicit dynamical scaling functions are shown to be continuous functions of the space dimension $d>0$. Their form reproduces the predictions of non-equilibrium representations of the Schr\"odinger algebra for models with dynamical exponent ${z}=2$ and with the dominant noise-source coming from the heat bath.

Hence the ageing in the voter model is a paradigm for relaxations in non-equilibrium critical dynamics, without detailed balance, and with the upper critical dimension $d^*=2$.

Dragi Karevski

1d-quantum gases under inhomogeneous gain and loss processes with dephasing

We present a Wigner function-based approach for the particle density evolution in fermionic (or bosonic) open quantum many-body systems, including the effects of dephasing. The main focus is put on chains of noninteracting particles coupled to Lindblad baths. The dissipative processes, described by linear and quadratic jump operators, are modulated by inhomogeneous couplings. Following a semiclassical approach, we find the differential equation governing the Wigner function evolution, which can be solved in closed form. We also present extensions to few-body losses that naturally arise during cold atoms experiments. 

Birgit Kaufmann

Analysis of multi-species asymmetric diffusion models

Starting from the results of a joint article with G. Schutz, we investigate scaling properties of multi-species asymmetric diffusion models. We use the methods of topological data analysis (TDA) which is possible to the formulation of the diffusion models as generalized growth models, leading to a multidimensional point clouds. It turns out that the universal scaling exponents of the asymmetric and symmetric diffusion models can be reproduced by TDA.

Eunghyun Lee
Integrable multispecies long-range swap model

We introduce new integrable long-range swap models for multispecies interacting particle systems on the one-dimensional lattice. Each particle waits an independent exponential time of rate and, upon activation, searches to the right for the nearest weaker particle. When such a particle is found, the two particles exchange positions, producing a long-range swap. The resulting dynamics define a class of non-local interacting particle systems that generalize classical exclusion-type processes. A distinguishing feature of the model is how a particle treats sites occupied by particles of the same species during its search for a weaker particle. This leads to two distinct dynamics, referred to as the pushing and blocking versions. Although these models exhibit different microscopic behaviors, both are shown to be integrable through a unified algebraic framework. Furthermore, this construction yields a continuous family of integrable long-range swap models obtained by interpolating between the pushing and blocking dynamics. We also discuss extensions in which the interpolation parameters depend on the particle species, and present explicit formulas for the transition probabilities of finite -particle systems.

Philipp Maass

Weak pinning and long-range anticorrelated motion of phase boundaries in driven diffusive systems

We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current fluctuations and a weak pinning at long times [1]. The weak pinning manifests itself in a saturated width of the domain wall position fluctuations that increases sublinearly with the system size. As a function of time t and system size L, the width w(t,L) follows a scaling behavior w(t,L) = L^(3/4) f(t/L^(9/4)), where the scaling function f(u) is constant for u<<1 and for u>>1 scales as f(u)~u^(1/3). An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture these scaling features.

[1] S. Schweers, D. F. Locher, G. M. Schütz, P. Maass, Phys. Rev. Lett. 132, 167101 (2024).

David Mukamel

Transport and condensation of driven tracers in narrow channel

Transport of a driven tracer in a narrow channel of bath particles is discussed. In particular, the effect of particle overtaking on the transport properties of the channel is considered within a 1d model of driven tracer in a quiescent medium. The model is shown to exhibit a phase transition at a finite transition rate. The transition separates a phase in which the stationary bath density profile , as seen from the tracer’s frame, is extended, to a phase with a localized bath density profile. While the tracer’s velocity vanishes in the extended phase,  in the thermodynamic limit, it remains finite in the localized phase. This is in contrast with the well-known equilibrium case of a non-driven tracer, for which the profile is localized whenever overtaking takes place. The phase diagram of the model, as well as the tracer velocity and the bath density profile in both phases, are studied, demonstrating their distinct features.

In the case of more than one tracer, the bath particle’s density profile is shown to induce an effective strong attraction between the driven tracers leading to their condensation.

Serguei Popov

Semi-infinite particle systems with exclusion interaction

We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. We review some recent results we have in collaboration with Mikhail Menshikov and Andrew Wade; these are mainly about the behaviour of the leftmost particle (namely, its transience/recurrence properties), and the rate of escape to infinity (in the transient case). Also we study this process in a random environment, i.e., when these parameters are chosen at random with some common distribution for all the particles, independently; then, we obtain results about the stable cloud decomposition of the system.

Vladislav Popkov

Golden Mean universality revisited

We find that Golden Ratio dynamical exponent is not just an exotic prediction of Mode-Coupling Theory requiring fine tuning of all system parameters. Instead,  the Golden Mean universality appears as a robust feature of a wide class of Markov processes as a consequence of a global symmetry.

Ellen Saada

hydrodynamic limit of the directed exclusion process

In a joint work with Assaf Shapira and Federico Sau, we derive the Euler (hyperbolic) hydrodynamic limit  for the directed exclusion process (DEP), a  one-dimensional conservative interacting particle system  that preserves particle–hole symmetry while breaking  left–right symmetry.  The proof  relies on an explicit multi-process coupling which guarantees a strong form of attractiveness  and macroscopic stability for the particle system.

Herbert Spohn

 Diffusion of a tagged Toda fluid quasiparticle

The Toda chain is an integrable classical many-body system.  Its conservation laws are determined through the eigenvalues of a Lax matrix, while the positions of quasiparticles are linked to time-dependent eigenvectors.  In thermal equilibrium  the Lax matrix  is random and thus eigenvectors are well localized. This allows one to  follow numerically the random  motion of a single quasiparticle, which is predicted to be diffusive with a coefficient computed  from TBA. Such simulations serve as a novel stringent test of generalized  hydrodynamics. This is joint work with A. Brollo, A. Dhar, A. Kundu, I. Mukherjee, S. Subhash. siparticles

Ali Zahra

Long-range correlations in a locally constrained exclusion process

We introduce a novel exclusion process with a simple local kinetic constraint that leads to a nonequilibrium steady state with a remarkable transition between a homogeneous phase with short-range correlations and a clustered phase with long-range correlations and spontaneous breaking of translation invariance. The metastable dynamics of particle clusters lead to a coarsening cascade and glassy dynamics, as well as an intriguing faster-is-slower effect, where an increasing asymmetry in the flow direction leads to a decrease of the stationary current.
Work in collaboration with Stephan Grosskinsky and Gunter Schutz. ArXiv:2503.12632