统计力学
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
We have performed Monte Carlo simulations for the investigation of dynamic phase transitions on a honeycomb lattice which has garnered a significant amount of interest from the viewpoint of tailoring the intrinsic magnetism in…
Disentangling irreversible and reversible forces from random fluctuations is a challenging problem in the analysis of stochastic trajectories measured from real-world dynamical systems. We present an approach to approximate the dynamics of…
We studied multiple quantum harmonic oscillators in the Tsallis statistics of entropic parameter $q$ in the cases that the distributions are power-like, separately applying the conventional expectation value, the unnormalized…
We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions. Our primary focus is on the different timescales involved in the evolution of the observables as they approach statistical…
It is commonly assumed that a large system, weakly coupled to a thermal environment through its boundaries, relaxes quasistatically towards the new equilibrium even when the temperature of the environment changes abruptly. Here we show how…
We study the effects of stochastic resetting on the Reallocating geometric Brownian motion (RGBM), an established model for resource redistribution relevant to systems such as population dynamics, evolutionary processes, economic activity,…
In two previous papers, the author raised the possibility of a special relativistic Liouville equation. The conclusion then was yes, such an equation is possible in 8N phase space if a Lorentz-invariant Universal (LiU) time can be defined…
We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations for characteristic scales identified through the spectral gap. This method retains both diffusion…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra,…
Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning a probability distribution of energy…
We consider the probability distributions of the subsystem (staggered) magnetization in ordered and disordered models of quantum magnets in D dimensions. We focus on Heisenberg antiferromagnets and long-range transverse-field Ising models…
The Hohenberg--Mermin--Wagner theorem states that there is no spontaneous breaking of continuous symmetries in spatial dimensions $d\leq2$ at finite temperature. At zero temperature, the classical/quantum mapping further implies the absence…
Biological and artificial systems encode information through several complex nonlinear operations, making their exact study a formidable challenge. These internal mechanisms often take place across multiple timescales and process external…
We discuss Hamiltonian Monte Carlo (HMC) and event-chain Monte Carlo (ECMC) for the one-dimensional chain of particles with harmonic interactions and benchmark them against local reversible Metropolis algorithms. While HMC achieves…
Understanding the dynamics of an epidemic spread is crucial for effective control measures. During the COVID-19 pandemic, quarantines were implemented to minimize infections while mitigating social and economic impacts, raising the question…
We analyze frustrated states of the one-dimensional dilute Ising chain with charged interacting impurities of two types with mapping of the system to some Markov chain. We perform classification and reveal two types of Markov chains:…
This study provides a comprehensive analysis of the ground state and thermodynamic properties of a spin-pseudospin chain representing a model of a one-dimensional dilute magnet with two types of nonmagnetic charged impurities. For this…