Phase space methods for degenerate quantum gases / Bryan J. Dalton, John Jeffers, Stephen M. Barnett.

Format:

• Book

Author/Creator:

• Dalton, Bryan J., author.
• Jeffers, John (Physicist), author.
• Barnett, S. M. (Stephen M.), author.

Series:

• International series of monographs on physics ; 163.
• International Series of Monographs on Physics ; 163

Language:

English

Subjects (All):

• Cold gases.
• Phase transformations (Statistical physics).
• Quantum theory.

Physical Description:

1 online resource (432 p.)

Edition:

First edition.

Place of Publication:

Oxford : Oxford University Press, [2015]

Language Note:

English

Summary:

Recent experimental progress has enabled cold atomic gases to be studied at nanokelvin temperatures, creating new states of matter where quantum degeneracy occurs-Bose-Einstein condensates and degenerate Fermi gases. Such quantum states are of macroscopic dimensions. This title presents the phase space theory approach to treating the physics of degenerate quantum gases, an approach already widely used in quantum optics.

Contents:

• Cover; Preface; Contents; 1 Introduction; 1.1 Bosons and Fermions, Commuting and Anticommuting Numbers; 1.2 Quantum Correlation and Phase Space Distribution Functions; 1.3 Field Operators; 2 States and Operators; 2.1 Physical States; 2.2 Annihilation and Creation Operators; 2.3 Fock States; 2.4 Two-Mode Systems; 2.5 Physical Quantities and Field Operators; 2.6 Dynamical Processes; 2.7 Normally Ordered Forms; 2.8 Vacuum Projector; 2.9 Position Measurements and Quantum Correlation Functions; Exercises; 3 Complex Numbers and Grassmann Numbers; 3.1 Algebra of Grassmann and Complex Numbers
• 3.2 Complex Conjugation3.3 Monomials and Grassmann Functions; Exercises; 4 Grassmann Calculus; 4.1 C-number Calculus in Complex Phase Space; 4.2 Grassmann Differentiation; 4.2.1 Definition; 4.2.2 Differentiation Rules for Grassmann Functions; 4.2.3 Taylor Series; 4.3 Grassmann Integration; 4.3.1 Definition; 4.3.2 Pairs of Grassmann Variables; Exercises; 5 Coherent States; 5.1 Grassmann States and Grassmann Operators; 5.2 Unitary Displacement Operators; 5.3 Boson and Fermion Coherent States; 5.4 Bargmann States; 5.5 Examples of Fermion States
• 5.6 State and Operator Representations via Coherent States5.6.1 State Representation; 5.6.2 Coherent-State Projectors; 5.6.3 Fock-State Projectors; 5.6.4 Representation of Operators; 5.6.5 Equivalence of Operators; 5.7 Canonical Forms for States and Operators; 5.7.1 Fermions; 5.7.2 Bosons; 5.8 Evaluating the Trace of an Operator; 5.8.1 Bosons; 5.8.2 Fermions; 5.8.3 Cyclic Properties of the Fermion Trace; 5.8.4 Differentiating and Multiplying a Fermion Trace; 5.9 Field Operators and Field Functions; 5.9.1 Boson Fields; 5.9.2 Fermion Fields; 5.9.3 Quantum Correlation Functions; Exercises
• 6 Canonical Transformations6.1 Linear Canonical Transformations; 6.2 One- and Two-Mode Transformations; 6.2.1 Bosonic Modes; 6.2.2 Fermionic Modes; 6.3 Two-Mode Interference; 6.4 Particle-Pair Creation; 6.4.1 Squeezed States of Light; 6.4.2 Thermofields; 6.4.3 Bogoliubov Excitations of a Zero-Temperature Bose Gas; Exercises; 7 Phase Space Distributions; 7.1 Quantum Correlation Functions; 7.1.1 Normally Ordered Expectation Values; 7.1.2 Symmetrically Ordered Expectation Values; 7.2 Characteristic Functions; 7.2.1 Bosons; 7.2.2 Fermions; 7.3 Distribution Functions; 7.3.1 Bosons; 7.3.2 Fermions
• 7.4 Existence of Distribution Functions and Canonical Forms for Density Operators7.4.1 Fermions; 7.4.2 Bosons; 7.5 Combined Systems of Bosons and Fermions; 7.6 Hermiticity of the Density Operator; 7.7 Quantum Correlation Functions; 7.7.1 Bosons; 7.7.2 Fermions; 7.7.3 Combined Case; 7.7.4 Uncorrelated Systems; 7.8 Unnormalised Distribution Functions; 7.8.1 Quantum Correlation Functions; 7.8.2 Populations and Coherences; Exercises; 8 Fokker-Planck Equations; 8.1 Correspondence Rules; 8.2 Bosonic Correspondence Rules
• 8.2.1 Standard Correspondence Rules for Bosonic Annihilation and Creation Operators

Notes:

• Description based upon print version of record.
• Includes bibliographical references and index.
• Description based on print version record.
• Description based on publisher supplied metadata and other sources.

ISBN:

• 0-19-174731-9
• 0-19-102863-0

OCLC:

922973294