相关论文: Semiclassical and relaxation limits of bipolar qua…

In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…

This article concerns the long-time dynamics of quantum particles in the semi-classical regime. First, we show that for the nonlinear Hartree equation with short-range interaction potential, small-data solutions obey dispersion bounds and…

We propose a generalization of quantum mechanical equations in the hydrodynamic form by introducing, into the Lagrangian density, terms taking into account the diffusion velocity at zero and finite temperatures and the diffusion pressure…

Semidiscretization in time is studied for a class of quasi-linear evolution equations in a framework due to Kato, which applies to symmetric first-order hyperbolic systems and to a variety of fluid and wave equations. In the regime where…

A novel formulation of second-order relativistic viscous fluid dynamics based on the effective Boltzmann equation for quasi-particles with medium-dependent masses is briefly reviewed.~The evolution equations for the shear and bulk…

We discuss the problem of N anyons in harmonic well, and derive the semi-classical spectrum as an exactly solvable limit of the many-anyon Hamiltonian. The relevance of our result to the solution of the anyon-gas model is discussed.

The large-time asymptotics of the density matrix solving a drift-diffusion-Poisson model for the spin-polarized electron transport in semiconductors is proved. The equations are analyzed in a bounded domain with initial and Dirichlet…

In this paper a new semi-implicit relaxation scheme for the simulation of multi-scale hyperbolic conservation laws based on a Jin-Xin relaxation approach is presented. It is based on the splitting of the flux function into two or more…

In this paper, we study the Cauchy problem of a time-dependent drift-diffusion-Poisson system for semiconductors. Existence and uniqueness of global weak solutions are proven for the system with a higher-order nonlinear…

We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin $S$, which in the case of $S=1/2$ interpolates between the Lipkin-Meshkov-Glick and the Ising model. For…

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine…

It is well-known that due to the lack of a technique to obtain the a-priori $L^{\infty}$ estimate of the artificial viscosity solutions of the Cauchy problem for the one-dimensional Euler-Poisson (or hydrodynamic) model for semiconductors,…

This article analyzes the formulation of space-time continuous hyperbolic hydrodynamic models for systems of interacting particles moving on a lattice, by connecting their local stochastic lattice dynamics to the formulation of an…

We consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve…

The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial…

A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…

We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the…

A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a…

We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution is proposed, for…