统计力学
We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED) algorithm for computing mid-spectrum eigenvalues and eigenvectors (shortly, eigenpairs) of quantum many-body…
Coherence resonance (CR) characterizes noise-induced regularity in excitable systems, yet its evaluation in quiescent biological media is often obscured by flattened energy landscapes and complex nonlinear dynamics. In this study, we…
Wilson loops provide the central gauge-invariant probe of confinement in lattice gauge theory. This survey reviews the statistical-mechanical formulation of lattice gauge ensembles, the strong-coupling and duality mechanisms behind area…
A polar tracer immersed in an active bath is known to be propelled forward and therefore activated. Here we report that the induced dynamics of an inertial tracer can be much richer than expected. We investigate a heavy polar tracer…
Random walks in random environments (RWRE) model transport in quenched disorder, incorporating spatial heterogeneity, trapping, random drift, and random geometry. This paper summarizes discrete and continuous time formulations, identifies…
Lorentz lattice gases (LLGs) are discrete-time transport models in which a point particle moves ballistically between lattice sites and is scattered by randomly placed, quenched local scatterers such as ``rotators'' or ``mirrors.'' Despite…
Magnetic particles underpin a broad range of technologies, from water purification and mineral processing to bioseparations and targeted drug delivery. The dynamics of magnetic particles in high-gradient magnetic fields-encompassing both…
We applied the Tsallis statistics with the conventional expectation value to a system of free particles, adopting the equilibrium temperature which is often called the physical temperature. The entropic parameter $q$ in the Tsallis…
Economic inequality emerges from the interplay between regional growth-rate differences and the interaction network that couples regions. We propose a minimal income-dynamics model, where heterogeneity is governed by growth-rate…
Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally…
The freely jointed chain is often applied to model the thermodynamics of single polymer chains, but the traditional formulation of the model lacks internal energy changes due to bond stretching. For this reason, the extensible freely…
A glass is conventionally obtained by cooling a bulk supercooled liquid through its glass transition temperature. The discovery of ultrastable glasses prepared using physical vapor deposition, together with the recent multiplication of…
We show that the thermodynamics of $N$ identical fermions maps onto that of distinguishable particles governed by a collective statistical potential -- the microscopic origin of degeneracy pressure. Known to be purely repulsive for ${N=2}$,…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
Non-integer dimensionality is central to fractal and complex systems, yet it is rarely represented as an explicit lattice on which classical statistical-mechanical models can be directly simulated. Here we introduce random-h fractional…
We investigate the $N$-queens problem as a lattice gas -- a model in which $N$ queens are placed on an $N \times N$ chessboard with pairwise repulsive interactions along shared rows, columns, and diagonals -- from the perspective of…
Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here,…
When coupling thermal baths at different temperatures, negative differential thermal conductivity is typically attributed to nonlinear interactions in the connecting medium. In this work, we demonstrate that such an effect can arise purely…
We present a symmetry-based formulation of nonlinear fluctuating hydrodynamics (NFH) for one-dimensional many-particle systems with generic homogeneous nearest-neighbor interactions. We derive the hydrodynamic equations solely from symmetry…
Predicting how systems respond to external perturbations far from equilibrium remains a fundamental challenge across physics, chemistry, and biology. We present a unified response framework for stochastic Markov dynamics that integrates…