Abstracts

Birgit Kaufmann

TBA

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.

Cristian Favio Coletti

On the elephant random walk

Eunghyun Lee

TBA

Herbert Spohn

Diffusion for tagged Toda quasiparticles

Karevski

TBA

Luigi Cantini

TBA

Malte Henkel

Schrodinger-invariance in the exactly solvable voter model

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.

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).

Rafael de Mattos Grisi

TBA

Rosemary Harris

TBA

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."

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.

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.

Tertuliano Franco

Finite reservoirs lead to Wentzell boundary conditions

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.