相关论文: The Derivation of the Boltzmann Equation from Quan…
The rigorous derivation of the Uehling-Uhlenbeck equation from more fundamental quantum many-particle systems is a challenging open problem in mathematics. In this paper, we exam the weak coupling limit of quantum N-particle dynamics. We…
Consider a microscopic system of $N$ hard spheres that are initially independent (modulo the exclusion condition on particle positions) and identically distributed in $\mathbb{R}^3$. When the number $N$ of particles goes to infinity and the…
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a…
In this paper, we rigorously derive a Boltzmann equation for mixtures from the many body dynamics of two types of hard sphere gases. We prove that the microscopic dynamics of two gases with different masses and diameters is well defined,…
We study the Boltzmann equation near vacuum in anisotropic low-regularity Besov spaces. We establish the global existence and uniqueness of strong solutions with the critical regularity index $2/p$ for $p\in[1,\infty)$ in $\mathbb{R}^3$.…
We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation.…
In the paper the possible approaches to the rigorous derivation of the Boltzmann kinetic equation with hard sphere collisions from underlying dynamics are considered. In particular, a formalism for the description of the evolution of…
The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A…
This is the first one of two papers on the global dynamics of the original Boltzmann equations without angular cutoff on the torus. We address the problem for the hard potentials and Maxwellian molecules in the present paper. The case of…
Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an…
We derive the formalism for steady state nonequilibrium dynamical mean-field theory in a real-time formalism along the Kadanoff-Baym contour. The resulting equations of motion are first transformed to Wigner coordinates (average and…
Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions…
The classical limit of quantum mechanics is investigated, by focusing on the study of the center of mass of a many-body system where each particle is described by quantum mechanics. We study how, in the limit when the number of particles…
We consider the spatially inhomogeneous quantum Boltzmann equation for bosons with a singular collision kernel, the weak-coupling limit of a large system of Bose-Einstein particles interacting through inverse power law. Global…
A surprising "duality" of the Newton equation with time-dependent forces and the stationary Schroedinger equation is discussed. Wide classes of exact solutions not known before for few-body Newton equations are generated directly from…
The BBGKY hierarchy of equations for a particle interacting with ideal gas is analyzed in terms of irreducible many-particle correlations between gas atoms and the particle's motion. The transition to the hard-sphere interaction is…
In this paper, we analyze in a mathematically rigorous fashion the validity of the Boltzmann transport equation within quantum field theory. We work within the specific model of a hermitian, scalar field with polynomial self-interaction in…
The hypothesis of molecular chaos plays the central role in kinetic theory, which provides a closure leading to the Boltzmann equation for quantitative description of classic fluids. Yet how to properly extend it to active systems is still…
We give a rigorous, quantitative derivation of the incompressible Euler equation from the many-body problem for $N$ bosons on $\mathbb{T}^d$ with binary Coulomb interactions in the semiclassical regime. The coupling constant of the…
A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The…