Statistical Mechanics
Whether in search of better trade opportunities or escaping wars, humans have always been on the move. For almost a century, mathematical models of human mobility have been instrumental in the quantification of commuting patterns and…
In this note we announce some results extending our recent work with A. Toufik on the free-fermion point q=i of the Haldane-Shastry chain to the case with an even number N of sites. The resulting long-range version of the Heisenberg XX…
Dynamical quantum phase transitions are non-analyticities in a dynamical free energy (or return rate) which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analyticity in two and three…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…
Active matter and driven systems exhibit statistical fluctuations in density and particle positions, providing an indirect indicator of dissipation across multiple length and time scales. Here, we quantitatively relate these measurable…
Biological sensors rely on the temporal dynamics of ligand concentration for signaling. The sensory performance is bounded by the distinguishability between the sensory state transition dynamics under different environmental protocols. This…
Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to…
We study the full distribution $P(E)$ of the ground-state energy of a single quantum particle in a potential $V(\boldsymbol{x}) = V_0(\boldsymbol{x}) + \sqrt{\epsilon} \, v_1(\boldsymbol{x})$, where $V_0(\boldsymbol{x})$ is a deterministic…
Thermal pure state algorithms, which employ pure quantum states representing thermal equilibrium states instead of statistical ensembles, are useful both for numerical simulations and for theoretical analysis of thermal states. However,…
The inverse problem of statistical mechanics is an unsolved, century-old challenge to learn classical pair potentials directly from experimental scattering data. This problem was extensively investigated in the 20th century but was…
An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its…
We present an experimental and numerical study of a piezoelectric energy harvester driven by broadband vibrations. This device can extract power from random fluctuations and can be described by a stochastic model, based on an underdamped…
A lot has been said about the vibrational density of states (DoS) in liquids. A more recent discussion introduces contradictions with earlier results, and here I briefly review several pieces of evidence from modeling, experiments and…
We consider the fractional Langevin equation far from equilibrium (FLEFE) to describe stochastic dynamics which do not obey the fluctuation-dissipation theorem, unlike the conventional fractional Langevin equation (FLE). The solution of…
Spatiotemporal patterns, which are of interest in statistical physics and nonlinear dynamics, form on the tape-peeling trace. Recently, we have proposed a mathematical model to describe these pattern formation in the tape-peeling trace. In…
In this thesis we study in detail the self-intersection properties of Random Walks. Although notoriously hard to tackle, these properties are crucially related to the excluded-volume effect and other central features of real polymers. Our…
Boids, developed by Craig W. Reynolds in 1986, is one of the earliest emergent models where the global pattern emerges from the interaction between many individuals within the local scale. In the original model, Boids follow three rules:…
Non-Maxwellian distributions are commonly observed across a wide range of systems and scales. While direct observations provide the strongest evidence for these distributions, they also manifest indirectly through their influence on…
The focus of our study in this paper is on the active dynamics and a fractional generalized Langevin equation with a memory kernel K(t). The Fokker-Planck equation is obtained by deriving it from a second-order differential equation. The…
Using a path integral approach, we derive and study the hydrodynamic equations and large deviation functions for three active lattice gases. After a review of the path integral for master equations, we first look at a one dimensional model…