Statistical Mechanics
We quantify nonlinear interactions between coupled complex processes, when the system is subject to noise and not all its components are measurable. Our method is applicable even when the system cannot be continuously monitored over time,…
We study the fate of a forager who searches for food performing a random walk on lattices. The forager consumes the available food on the site it visits and leaves it depleted but can survive up to $S$ steps without food. We introduce the…
Hair cells actively drive oscillations of their mechanosensitive organelles--the hair bundles that enable hearing and balance sensing in vertebrates. Why and how some hair cells expend energy by sustaining this oscillatory motion in order…
Scale invariance is a hallmark of criticality in complex dynamical systems. While random external inputs or tunable stochastic interactions are typically required to produce critical behavior, it remains unclear whether scale-invariant…
Correlated classical and quantum many-particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging…
The effective conductivity of the infinite checkerboard (chessboard) and analogous higher-dimensional checkered structures, are considered. An algebraic expression is derived by accounting for the symmetries of the structures.
We explore the capability of a Large Language Model (LLM) to perform specific computations in mathematical physics: the task is to compute the coordinate Bethe Ansatz solution of selected integrable spin chain models. We select three…
We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
In the first part of these short lecture notes, we will present an introduction on (auto-)correlation functions and linear-response functions in the language of a physicist. In particular, the fluctuation-dissipation theorem in classical…
Recent experiments have revealed heterogeneous dissipation in optically trapped systems, often anticorrelated with local positional fluctuations, exposing a structural gap in the scalar stochastic thermodynamic description. While the…
We introduce a universal criterion for criticality in mean-field rotor Hamiltonians based on the geometric structure of the constant-energy shell. Rather than characterizing the onset of a phase transition through the conventional…
Point-cloud persistent homology (PH) -- computing alpha or Rips complexes on spin-position point clouds -- has been widely applied to detect phase transitions in classical spin models since Donato et al. (2016), with subsequent studies…
We investigate the behavior of the length of the longest weakly increasing subsequences (weak LIS) of $n$-step random walks with nonzero integer increments $k = \pm 1, \pm 2, \dots$ given by a zero-mean, symmetric heavy tailed mass…
We identify a new class of non-Hermitian causal processes that produce statistically significant temporal correlations invisible to conventional spectral methods. Using a generative model with a strictly causal memory kernel, we demonstrate…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
Multifractal Detrended Fluctuation Analysis (MFDFA) has emerged as a standard tool for characterizing scale invariance in complex systems, yet its application to discrete spin models is frequently marred by reports of ``spurious…
In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its…
For diffusion process involving the force $F(x)$ and the diffusion coefficient $D(x)$, the continuity equation $\partial_t P_t(x)=- \partial_xJ_t(x)$ gives the dynamics of the probability $P_t( x)$ in terms of the current $J_t(…
We measured the energy efficiency of information erasure using silicon DRAM cells capable of counting charges on capacitors at the single-electron level. Our measurements revealed that the efficiency decreased as the erasure error…