Does statistical mechanics equal one-loop quantum field theory?

Does quantum chaos explain quantum statistical mechanics?

If a many-body quantum system approaches thermal equilibrium from a generic initial state, then the expectation value 〈ψ(t)|Ai|ψ(t)〉, where |ψ(t)〉 is the system’s state vector and Ai is an experimentally accessible observable, should approach a constant value which is independent of the initial state, and equal to a thermal average of Ai at an appropriate temperature. We show that this is the c...

The Connection Between Statistical Mechanics and Quantum Field Theory

A four part series of lectures on the connection of statistical mechanics and quantum field theory. The general principles relating statistical mechanics and the path integral formulation of quantum field theory are presented in the first lecture. These principles are then illustrated in lecture 2 by a presentation of the theory of the Ising model for H = 0, where both the homogeneous and rando...

Algebra versus analysis in statistical mechanics and quantum field theory

I contrast the profound differences in the ways in which algebra and analysis are used in physics. In particular I discuss the fascinating phenomenon that theoretical physicists devote almost all their efforts to algebraic problems even though all problems of experimental interest require some methods of analysis.

Conformal Field Theory and Statistical Mechanics∗

Statistical Mechanics of Vortices from Field Theory

We study with lattice Monte Carlo simulations the interactions and macroscopic behaviour of a large number of vortices in the 3-dimensional U(1) gauge+Higgs field theory, in an external magnetic field. We determine non-perturbatively the (attractive or repelling) interaction energy between two or more vortices, as well as the critical field strength H c , the thermodynamical discontinuities, an...