Research in Statistical Physics

统计力学领域中最基本的问题之一是根据组成粒子的潜在微观动力学来解释在不可逆过程中观察到的系统熵的增加。动力系统理论（通常称为“混沌”理论）最近的工作已经在这个方向上取得了相当大的进展，并且可以对描述系统不可逆行为的量（如输运系数）以及描述系统混沌行为的量（如李雅普诺夫指数和动态“熵”）进行定量预测。本研究的目的是应用统计力学技术来计算具有物理意义的系统的输运量和动量值，并将它们相互联系起来，在某些情况下，还将它们与系统的热力学性质联系起来。这将导致对第二定律和微观动力学之间的联系有更深的理解。对于量子系统，这也将导致对一些当前相当感兴趣的固态器件的行为的进一步理解。

One of the most fundamental questions in the field of statistical mechanics is to explain the observed increase of a system's entropy in an irreversible process in terms of the underlying microscopic dynamics of the constituent particles. Recent work in dynamical systems theory (often called `chaos` theory) has allowed for considerable progress in this direction and for quantitative predictions to be made for both the quantities that describe the irreversible behavior of the system, such as transport coefficients, as well as the quantities that describe the system's chaotic behavior, such as Lyapunov exponents and dynamical `entropies`. The purpose of this research is to apply techniques of statistical mechanics to calculate both transport and dynamical quantities for systems of physical interest, and to relate them to each other and, in some cases, to the thermodynamic properties of the system. This will lead to a deeper understanding of the connections between the Second Law and microscopic dynamics. For quantum systems, this will also lead to further understanding of the behavior of some solid state devices of considerable current interest.