A phase space sampling approach to equilibrium semiclassical statistical mechanics

Semiclassical Statistical Mechanics ∗

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema...

Semiclassical Statistical Mechanics

Typicality and the Approach to Equilibrium in Boltzmannian Statistical Mechanics

Systems prepared in a non-equilibrium state approach, and eventually reach, equilibrium. Why do they do so? An important contemporary version of the Boltzmannian approach to statistical mechanics answers this question in terms of typicality. The problem with this approach is that it comes in different versions, which are, however, not recognised as such and not clearly distinguished. The aim of...

Equilibrium Statistical Mechanics

Classical Statistical Mechanics studies properties of macroscopic aggregates of particles, atoms and molecules, based on the assumption that they are point masses subject to the laws of classical mechanics. Distinction between macroscopic and microscopic is evanescent and in fact the foundations of statistical mechanics have been laid on properties, proved or assumed, of few particles systems. ...

Non equilibrium statistical mechanics

In part I of these lecture notes, I introduce the basic tools of non equilibrium statistical mechanics: linear response, Brownian motion, Langevin equation, (Pauli) master equation. Part II is devoted to a derivation of quantum master equations from the Schrödinger equation, and to some of their applications to quantum optics and to Brownian motion. Finally, in part III, I examine more recent d...