相关论文: On a Two-Temperature Problem for Wave Equation

We use the dynamical mean-field method to determine the origin of the large ratio of the zero temperature gap to the transition temperature observed in most charge density wave materials. The method is useful because it allows an exact…

We consider the motion of a particle under a continuum random environment whose distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we establish that the quenched density of the motion of the particle (after…

We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to…

Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schroedinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum…

This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the size of the graph and the edge weights are sampled from a…

Let $A$ be a finite set and $\phi:A^Z\to R$ be a locally constant potential. For each $\beta>0$ ("inverse temperature"), there is a unique Gibbs measure $\mu_{\beta\phi}$. We prove that, as $\beta\to+\infty$, the family…

It is shown that surface waves propagating against the external current, slowly varying in the horizontal direction in deep water, are governed by the equation which is tantamount to the Gross - Pitaevskii equation modelling the mean-field…

Taylor-Goldstein equation (TGE) governs the stability of a shear-flow of an inviscid fluid of variable density. It is investigated here from a rigorous geometrical point of view using a canonical class of its transformations. Rayleigh's…

We consider the one-dimensional stochastic heat equation driven by a multiplicative space-time white noise. We show that the spatial integral of the solution from $-R$ to $R$ converges in total variance distance to a standard normal…

The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…

The two gaps in a two-band clean s-wave superconductor are evaluated self-consistently within the quasiclassical Eilenberger weak-coupling formalism with two in-band and one inter-band pairing potentials. Superfluid density, free energy and…

In this paper, we elaborate the problem of energy-momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and M\"{o}ller to compute the…

In [Bailo, Carrillo, Hu. SIAM J. Appl. Math. 2023] the authors introduce a finite-volume method for aggregation-diffusion equations with non-linear mobility. In this paper we prove convergence of this method using an Aubin--Simons…

In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle…

In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which…

Turbulent relative dispersion is studied theoretically with a focus on the evolution of probability distribution of the relative separation of two passive particles. A finite separation speed and a finite correlation of relative velocity,…

We consider the random point processes on a measure space X defined by the Gibbs measures associated to a given sequence of N-particle Hamiltonians H^{(N)}. Inspired by the method of Messer-Spohn for proving concentration properties for the…

The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and…

A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body rotational kinetic energy. The prototype…

The truncated Korteweg-De Vries (TKdV) system, a shallow-water wave model with Hamiltonian structure that exhibits weakly turbulent dynamics, has been found to accurately predict the anomalous wave statistics observed in recent laboratory…