Quantum statistical mechanics in classical phase space /

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Attard, Phil (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2021]
Colección:IOP (Series). Release 21.
IOP ebooks. 2021 collection.
Temas:
Quantum statistics.
Phase transformations (Statistical physics)
Quantum physics (quantum mechanics & quantum field theory)
Quantum science.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 Schrödinger 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.

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