Quantum Kinetic Equations of Many-Particle Systems in Condensed States

Interacting particle systems with long-range interactions: scaling limits and kinetic equations

The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential and scaling limit. Our focus in this paper is on particle systems with long-range interactions. The derivation here is formal, but it provides an interpretation of particle systems as the motion of a particle in a random force field with a friction term which is due to the interaction with the surrounding particles. Some of the technical details of this meth…

活性软物质开放系统的动力学方程探索

Towards kinetic equations of open systems of active soft matter

本章提出基于可观测量演化方程的新方法，在标度近似下构建含初始关联的开放活性软物质系统动力学方程，并探讨由多实体动力学严格推导非马尔可夫方程以描述记忆效应。

Kinetic SIR equations and particle limits

We present and analyze two simple $N$-particle particle systems for the spread of an infection, respectively with binary and with multi-body interactions. We establish a convergence result, as $N \to \infty$, to a set of kinetic equations, providing a mathematical justification of related numerical schemes. We analyze rigorously the time asymptotics of these equations, and compare the models numerically.

Eigenvalue asymptotics for the one-particle kinetic energy density operator

The kinetic energy of a multi-particle system is described by the one-particle kinetic energy density matrix $τ(x, y)$. Alongside the one-particle density matrix $γ(x, y)$, it is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula $λ_k \sim (Bk)^{-2}$, $B \ge 0$, as $k\to\infty$, for the eigenvalues $λ_k$ of the self-adjoint operator $\boldsymbol{\sf T}\ge 0$ with kernel $τ(x, y)$.

Exotic galilean symmetry and non-commutative mechanics in mathematical & in condensed matter physics

The ``exotic'' particle model with non-commuting position coordinates, associated with the two-parameter central extension of the planar Galilei group, can be used to derive the ground states of the Fractional Quantum Hall Effect. The relation to other NC models is discussed. Anomalous coupling is presented. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.

浸没在粘性流体中的球形颗粒的可控性与动力学极限

Controllability and kinetic limit of spherical particles immersed in a viscous fluid

本文研究粘性流体中球形颗粒系统的可控性与动力学极限，分别利用几何控制理论和Boltzmann型表述分析少颗粒可控性及颗粒数趋于无穷时的极限行为。