Related papers: Spectral gap for stochastic energy exchange model …

We prove a spectral gap inequality for the stochastic exchange model studied by Gaspard and Gilbert and by Grigo, Khanin and Sz\'asz in connection with understanding heat conduction in a deterministic billiards model. The bound on the…

A fundamental problem of non-equilibrium statistical mechanics is the derivation of macroscopic transport equations in the hydrodynamic limit. The rigorous study of such limits requires detailed information about rates of convergence to…

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary…

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N-by-N box, with boundary conditions which are ``plus'' except for small regions at the corners which are either free or ``minus.'' The…

We study an ideal-gas-like model where the particles exchange energy stochastically, through energy conserving scattering processes, which take place if and only if at least one of the two particles has energy below a certain energy…

We present a simple strategy to derive universal bounds on the spectral gap of reversible stochastic exchange models on arbitrary graphs. The Kipnis-Marchioro-Presutti (KMP) model, the harmonic process (HP), and the immediate exchange model…

We give a lower bound on the spectral gap for a class of binary collision processes. In 2008, Caputo showed that, for a class of binary collision processes given by simple averages on the complete graph, the analysis of the spectral gap of…

Passive states are special configurations of a quantum system which exhibit no energy decrement at the end of an arbitrary cyclic driving of the model Hamiltonian. When applied to an increasing number of copies of the initial density…

We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on…

It is an well established fact that statistical properties of energy level spectra are the most efficient tool to characterize nonintegrable quantum systems. The study of statistical properties and spectral fluctuation in the interacting…

We propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with Markov processes on graphs. We argue that the spectral statistics of such an ensemble (after ensemble averaging) depends…

This paper studies a billiards-like microscopic heat conduction model, which describes the dynamics of gas molecules in a long tube with thermalized boundary. We numerically investigate the law of energy exchange between adjacent cells. A…

We present a method for bounding, and in some cases computing, the spectral gap for systems of many particles evolving under the influence of a random collision mechanism. In particular, the method yields the exact spectral gap in a model…

For more than 50 years, an elegant energy gap (EG) law developed by Englman and Jortner [Mol. Phys. {\bf 18}, 145 (1970)] has served as a key theory to understand and model nearly exponential dependence of nonradiative transition rates on…

Stochastic oscillations in individual cells are usually characterized by a non-monotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach of stochastic oscillations in a minimal hybrid…

A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full description of the low-energy spectra based…

We study the stationary dynamics of energy exchange in an ensemble of phase oscillators, coupled through a mean-field mechanical interaction and added with friction and an external periodic excitation. The degree of entrainment between…

We consider a class of stochastic reaction-diffusion equations also having a stochastic perturbation on the boundary and we show that when the diffusion rate is much larger than the rate of reaction, it is possible to replace the SPDE by a…

It has been unknown in kinetic theory whether the linearized Boltzmann or Landau equation with soft potentials admits a spectral gap in the spatially inhomogeneous setting. Most of existing works indicate a negative answer because the…

This paper consider the mesoscopic limit of a stochastic energy exchange model that is numerically derived from deterministic dynamics. The law of large numbers and the central limit theorems are proved. We show that the limit of the…