MrEmir Sezik

Non-Equilibrium Universality Classes

Phase transitions have been the focal point of statistical physics for the past 50 years. Concepts such as universality classes and scaling relations have been shown to be powerful tools in understanding and classifying a variety of systems that have no apparent microscopic connection. In the 1970s, Halperin and Hohenberg proposed the definitive catalogue for dynamical systems relaxing to a thermal steady state. Their classification provides an extensive and universal catalog for understanding equilibrium dynamical systems exhibiting scaling phenomena. In my research, I try to extend this catalogue to non-equilibrium systems and identify the types of interaction that induce a genuine non-equilibrium universality classes. Surprisingly, we find that the classification is surprisingly robust to violations of detailed balance. For example, for non-reciprocal systems with run-and-chase type dynamics, the transition into an oscillatory state falls under the Model A transition. True non-equilibrium universality classes are reserved for flocking or spin systems with vision-cone interactions, where the dynamics become much more complicated. 

Collective Excitations and Non-equilibrium Steady States

Landau-Ginzburg paradigm suggests that identifying the relevant symmetries and the order parameter of the system is sufficient enough to describe the phases of a system. However, it has been evident that this paradigm is hard to implement in active matter systems where there are many relevant non-linear terms that affect the dynamics of a system. Previous studies in the literature suggest that for active matter systems a better connection with the microscopic dynamics and macroscopic description is needed to understand the phases of these systems. Characterising the macroscopic correlations is particularly hard as they are, most of the time, off-lattice. For these systems, the collective excitations are not fourier waves but something else entirely. Having analytical control over their collective excitations would allow us to characterise the macroscopic behaviour of the systems without resorting to a Landau-Ginzburg top-down approach. As a first step, using Doi-Peliti field theory, we propose a prescription to calculate non-equilibrium steady states of active matter systems. The usage of Doi-Peliti field theory allows for a controlled approximation and systematises the perturbative expansion. 

Fluctuating Interactions

Fluctuating pairwise interactions are understood to drive fluid-like states in dense biological systems. These states find a broad range of functionalities, such as directing growth during morphogenesis and forming aggregates with heightened mechanical response. However, a tractable model capturing the role of microscopic fluctuating interactions in these structural transitions is crucially lacking. Motivated by the success of p-spin models in the theory of structural glass transitions, offering an analytically tractable setting to study dynamical arrest, metastability, and the Gardner transition in thermal systems, we study a p-spin model with fluctuating pairwise couplings as a schematic model for interaction-mediated fluidisation. We find that while stronger fluctuations suppress the glass transition, more persistent fluctuations have the opposite effect, illustrating how microscopic fluctuations control the glass transition.

Conditional Statistics in Active Matter

Active matter systems typically consist of endowing a Brownian particle with an additional, typically persistent, degree of freedom that undergoes a stochastic evolution and is coupled uni-directionally to the position. Such a coupling drives the system out of equilibrium and generally produce non-Gaussian statistics, rendering the analysis of the particle's motion, through the calculation of visit probabilities, survival probabilities, first-passage properties and extreme statistics non-trivial. The visit probability, quantifying whether a particle has reached a given point for the first time by a specified time, provides access to various extreme value statistics and serves as a fundamental tool for characterising these stochastic models. However, previous studies have largely neglected how the visit probability depends on the internal degree of freedom driving the active particle. Keeping track of the internal degree of freedom allows for a more comprehensive understanding of their statistics. We calculate such statistics in one-dimension for a Run-and-Tumble particle using Doi-Peliti field theory and extract the total volume covered. Furthermore, we also show that conditional splitting probabilities, quantifying the likelihood of exiting an interval for the first time via either boundary in a given internal state, combined with Bayes' theorem can be used to partially infer the assumedly hidden state of an active particle from detecting the particle exiting at either interval boundary. We demonstrate the viability of this boundary-based inference scheme for different classes of processes and argue for its broad applicability across fields concerned with the control of driven stochastic processes.