1. Introduction -- 1.1. Why phase space? -- 1.2. Why not direct quantum methods? -- 1.3. Advantages and challenges of phase space -- 1.4. Old applications, new perspectives 2. Wave packet formulation -- 2.1. Introduction -- 2.2. Wave packets as eigenfunctions in the classical limit -- 2.3. Wave packet symmetrization and overlap -- 2.4. Statistical averages in phase space 3. Symmetrization factor and permutation loop expansion -- 3.1. Introduction -- 3.2. Partition function -- 3.3. Symmetrization and occupancy for multi-particle states -- 3.4. Symmetrization expansion of the partition function 4. Applications with single-particle states -- 4.1. Ideal gas -- 4.2. Independent harmonic oscillators -- 4.3. Occupancy of single-particle states -- 4.4. Ideal fermions 5. The [lambda]-transition and superfluidity in liquid helium -- 5.1. Introduction -- 5.2. Ideal gas approach to the [lambda]-transition -- 5.3. Ideal gas : exact enumeration -- 5.4. The [lambda]-transition for interacting bosons -- 5.5. Interactions on the far side -- 5.6. Permutation loops, the [lambda]-transition, and superfluidity 6. Further applications -- 6.1. Vibrational heat capacity of solids -- 6.2. One-dimensional harmonic crystal -- 6.3. Loop Markov superposition approximation -- 6.4. Symmetrization for spin-position factorization 7. Phase space formalism for the partition function and averages -- 7.1. Partition function in classical phase space -- 7.2. Loop expansion, grand potential and average energy -- 7.3. Multi-particle density -- 7.4. Virial pressure 8. High temperature expansions for the commutation function -- 8.1. Preliminary definitions -- 8.2. Expansion 1 -- 8.3. Expansion 2 -- 8.4. Expansion 3 -- 8.5. Fluctuation expansion -- 8.6. Numerical results 9. Nested commutator expansion for the commutation function -- 9.1. Introduction -- 9.2. Commutator factorization of exponentials -- 9.3. Maxwell-Boltzmann operator factorized -- 9.4. Temperature derivative of the commutation function operator -- 9.5. Evaluation of the commutation function -- 9.6. Results for the one-dimensional harmonic crystal 10. Local state expansion for the commutation function -- 10.1. Effective local field and operator -- 10.2. Higher order local fields -- 10.3. Harmonic local field -- 10.4. Gross-Pitaevskii mean field Schr�odinger equation -- 10.5. Numerical results in one-dimension 11. Many-body expansion for the commutation function -- 11.1. Commutation function -- 11.2. Symmetrization function -- 11.3. Generalized Mayer f-function -- 11.4. Numerical analysis -- 11.5. Ursell clusters, Lee-Yang theory, classical phase space 12. Density matrix and partition function -- 12.1. Introduction -- 12.2. Quantum statistical average -- 12.3. Uniform weight density of wave space -- 12.4. Canonical equilibrium system.
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.
Lecturers, and scientific researchers in the fields of thermodynamics, statistical mechanics, condensed matter physics, theoretical chemistry, dynamics, many-body systems, or quantum mechanics.
Mode of access: World Wide Web. System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
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.