Quantum Statistical Mechanics in Classical Phase Space

Quantum and classical results are often presented as being dependent upon separate postulates as if the two are distinct and unrelated, and there is little attempt to show how the quantum implies the classical. The transformation to classical phase space gives researchers access to a range of algorithms derived from classical statistical mechanics that promise results on much more favourable numerical terms. Quantum Statistical Mechanics in Classical Phase Space offers not just a new computational approach to condensed matter systems, but also a unique conceptual framework for understanding the quantum world and collective molecular behaviour. A formally exact transformation, this revolutionary approach goes beyond the quantum perturbation of classical condensed matter to applications that lie deep in the quantum regime. It offers scalable computational algorithms and tractable approximations tailored to specific systems. Concrete examples serve to validate the general approach and demonstrate new insights. For example, the computer simulations and analysis of the λ-transition in liquid helium provide a new molecular-level explanation of Bose-Einstein condensation and a quantitative theory for superfluid flow. The intriguing classical phase space formulation in this book offers students and researchers a range of new computational algorithms and analytic approaches. It offers not just an efficient computational approach to quantum condensed matter systems, but also an exciting perspective on how the classical world that we observe emerges from the quantum mechanics that govern the behaviour of atoms and molecules. The applications, examples, and physical insights foreshadow new discoveries in quantum condensed matter systems.

Author Biography

1 Introduction

2 Wave Packet Formulation

3 Symmetrization Factor and Permutation Loop Expansion

4 Applications with Single Particle States

5 The λ-Transition and Superfluidity in Liquid Helium

6 Further Applications

7 Phase Space Formalism for the Partition Function and Averages

8 High-Temperature Expansions for the Commutation Function

9 Nested Commutator Expansion for the Commutation Function

10 Local State Expansion for the Commutation Function

11 Many-Body Expansion for the Commutation Function

12 Density Matrix and Partition Function