Statistical Mechanics
We show that in classical spin systems the precise nature of the late-time hydrodynamic tails of the autocorrelation functions of a generic observable is determined by (i) the dynamical critical exponent and (ii) the equilibrium…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
The numerical integration of stochastic growth equations on non-Euclidean networks presents unique challenges due to the nonlinearities that occur in many relevant models and of the structural constraints of the networks. In this work, we…
Molecular motors are in charge of almost every process in the life cycle of cells, such as protein synthesis, DNA replication, and cell locomotion, hence being of crucial importance for understanding the cellular dynamics. However, given…
We study integrability breaking and transport in a discrete space-time lattice with a local integrability breaking perturbation. We find a singular distribution of the Lyapunov spectrum where the majority of Lyapunov exponents vanish in the…
We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion statistics in which particles tend to coalesce more than ordinary bosons. We derive the microscopic occupation multiplicities of 1-body quantum…
We revisit a two-temperature Nos\'e-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs…
We investigate the response of a system of hard spheres to two classes of perturbations over a range of densities spanning the fluid, crystalline, and glassy regimes within a molecular dynamics framework. Firstly, we consider the relaxation…
We consider the boundary driven Quantum Symmetric Simple Inclusion Process (QSSIP) which describes a one-dimensional system of bosonic particles with stochastic nearest-neighbor hopping, modeled as a Brownian motion, with gain/loss…
Building upon the knowledge of the distribution of the first positive position reached by a random walker starting from the origin, one can derive new results on the statistics of the gap between the largest and second-largest positions of…
In this work, we investigate the effects of chirality, accounting for translational diffusion, on active Brownian particles in two and three dimensions. Despite the inherent complexity in solving the Fokker-Planck equation, we demonstrate a…
In this work, we propose two models of coupled harmonic oscillators under Brownian motion to computationally study the applications of fluctuation theorems. This paper also illustrates how to analytically calculate free energy differences…
In this study, we reveal nontrivial quantum physics in an infinite-temperature system. By performing an unbiased quantum Monte Carlo simulation, we study a hybrid model composed of hard-core bosons, whose hopping amplitude is mediated by…
The thermodynamics of mesoscopic systems driven by time-varying temperatures is crucial for understanding biological systems, designing nanoscale engines, and performing micro-particle cooling. In this work, we analyze an underdamped…
Quantum mechanics broadly classifies the particles into two categories: $(1)$ fermions and $(2)$ bosons. Fermions are half-integer spin particles, obeying Pauli's exclusion principle and Fermi-Dirac statistics. Whereas bosons are integer…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
The study of the response of magnetic nanoparticles (MNP) assemblies to an external alternating magnetic field is of great interest for applications such as hyperthermia. The key quantity here is the complex susceptibility and its behavior…
The mathematical definitions of distinct concepts that are needed in building an ergodicity detection algorithm are introduced in a framework. This algorithmic framework is expressed in a discrete setting in an accessible manner for broader…
Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion…
Collective longitudinal and transverse propagating modes in molten Carbon at $T=5500$~K and pressure range $10$-$40$ GPa are reported from {\it ab initio} based as well as machine learned molecular dynamics. A striking exotic feature in…