相关论文: Characteristics of Equilibrated Nonlinear Oscillat…

We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with…

A numerical framework is proposed and analyzed for computing the ground state of Bose--Einstein condensates. A gradient flow approach is developed, incorporating both a Lagrange multiplier to enforce the $L^2$ conservation and a free energy…

We establish a new non-equilibrium scaling regime in the short time evolution of one-dimensional interacting open quantum systems subject to a generic heating mechanism. This dynamical regime is characterized by uncompensated phonon…

We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…

We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process. We apply our method to…

We investigate the spectral and dynamical properties of the fractional nonlinear Schr\"odinger (fNLS) equation with harmonic confinement. In this setting, the classical Laplacian is replaced by its fractional power…

We consider an open one dimensional lattice gas on sites $i=1,...,N$, with particles jumping independently with rate 1 to neighboring interior empty sites, the {\it simple symmetric exclusion process}. The particle fluxes at the left and…

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…

For a class of translation-invariant free-fermion systems (including those with uniform nearest neighbor hopping) on a $d$-dimensional $L \times \cdots \times L$ hypercubic lattice, we prove that, starting from an arbitrary pure initial…

We measure spectra, spatial correlation functions and probability density functions (PDFs) for waves amplitudes for generalized one-dimensional nonlinear Schrodinger (NLS) equation of focusing type with saturated nonlinearity. All…

Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved…

Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the…

Systems whose potential energies consists of pieces that scale as r^-2 together with pieces that scale as r^2, show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude for ever. Despite this pulsation these…

In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, $\ddot{x}+\alpha x\dot{x}+\beta x^3+\gamma…

The thermal response of nonequilibrium systems requires the knowledge of concepts that go beyond entropy production. This is showed for systems obeying overdamped Langevin dynamics, either in steady states or going through a relaxation…

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of non-interacting oscillators. We follow a non-perturbative approach, proposed earlier by us for the free Brownian particle. The…

Discrete nonlinear Schr\"oginger equation (DNLS) of the form, $i \frac{dC_n} {dt}$ = $C_{n+1}$ + $C_{n-1}$ - $ \chi_n [|C_{n+1}|^2 + |C_{n-1}|^2 - 2 |C_n|^2] C_n$ is used to study the formation of stationary localized states in one…

We propose the method of statistical description of broad class of dynamic systems (DS) whose equations of motion are determined by two state depending functions: 1) "energy" - the quantity which conserves in time and 2) "entropy" - the…

We consider multiscale Hamiltonian systems in which harmonic oscillators with several high frequencies are coupled to a slow system. It is shown that the oscillatory energy is nearly preserved over long times eps^{-N} for arbitrary N>1,…

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schr\"odinger equation as a representative model. We formulate a thermodynamic description of the…