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.
Table of Contents:
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
About the Author :
Phil Attard researches broadly in
statistical mechanics, quantum mechanics, thermodynamics, and colloid science. He
has held academic positions in Australia, Europe, and North America, and he was
a Professorial Research Fellow of the Australian Research Council. He has
authored some 120 papers, 10 review articles, and 4 books, with over 7000
citations. As an internationally recognized researcher, he has made seminal contributions
to the theory of electrolytes and the electric double layer, to measurement
techniques for atomic force microscopy and colloid particle interactions, and
to computer simulation and integral equation algorithms for condensed matter. Attard
is perhaps best known for his discovery of nanobubbles and for establishing
their nature. Recent research has focused on non-equilibrium systems. He has
discovered a new entropy --the second entropy-- as the basis for
non-equilibrium thermodynamics, hydrodynamics, and chemical kinetics, and he
has derived the probability distribution for non-equilibrium statistical
mechanics. The theory provides a coherent approach to non-equilibrium systems and
to irreversible processes, and it has led to the development of stochastic
molecular dynamics and non-equilibrium Monte Carlo computer simulation
algorithms. Attard has formulated quantum statistical mechanics in classical
phase space, for its conceptual insight into quantum mechanics, for its account
of the transition to our classical world, and for its potential for efficient
computational approaches to many-body condensed matter systems. Also, it is
different, which is where discovery is to be found.
