Princeton University Library Catalog

Quantum statistical mechanics : equilibrium and non-equilbrium theory from first principles / Phil Attard.

Author:
Attard, Phil [Browse]
Format:
Book
Language:
English
Published/​Created:
  • Bristol, UK : IOP Publishing, [2015]
  • ©2015
Description:
1 volume (various pagings) : illustrations ; 27 cm.
Series:
Summary note:
This book provides a clear and self-contained exposition of quantum statistical mechanics, focussing on the foundations. The unifying theme is the statistical entropy, as modified for quantum systems. From this is derived the conventional expressions for equilibrium quantum statistical mechanics, and, most exciting, their extension to non-equilibrium, time-dependent systems. A unified treatment of the equilibrium and non-equilibrium fields is given based upon the conservation laws, time symmetries, and the second law of thermodynamics. One theme of the book is the collapse of the wave function of an open quantum system, which leads to the Maxwell-Boltzmann probability operator, its relationship to the density matrix, and the von Neumann trace expression for a statistical average. A second theme is the development of the appropriate entropy for quantum systems, which, in conjunction with the second law, gives the stochastic, dissipative Schrdinger equation for an open quantum system and the fluctuation-dissipation theorem for the time propagator. A final theme is the derivation of the probability operator for non-equilibrium systems and irreversible processes, which lies at the cutting edge of modern research.
Notes:
"Version 20151001"--Title page verso.
Bibliographic references:
Includes bibliographical references.
Contents:
Machine generated contents note: 1.1. Expectation, density operator and averages -- 1.1.1. Expectation value -- 1.1.2. Density operator -- 1.1.3. Statistical average -- 1.2. Uniform weight density of wave space -- 1.2.1. Probability flux and trajectory uniformity -- 1.2.2. Time average on the hypersurface -- 1.3. Canonical equilibrium system -- 1.3.1. Entropy of energy states -- 1.3.2. Wave function entanglement -- 1.3.3. Expectation values and wave function collapse -- 1.3.4. Statistical average and probability operator -- 1.4. Environmental selection -- 1.5. Wave function collapse and the classical universe -- 1.5.1. Mechanism of statistical collapse -- 1.5.2. Probabilistic nature of the wave function -- 1.5.3. Quantum interference is uniquely non-classical -- 1.5.4. Classical phase space and Hamilton's equations -- References -- 2.1. Bosons, fermions and wave function symmetry -- 2.2. Ideal quantum gas -- 2.2.1. Leading classical term -- 2.2.2. First quantum correction -- 2.2.3. Quantum correction as a potential of mean force -- 2.3. State occupancy by ideal particles -- 2.3.1. Bosons -- 2.3.2. Fermions -- 2.3.3. Classical particles -- 2.4. Thermodynamics and statistical mechanics of ideal particles -- 2.5. Classical ideal gas -- 2.6. Ideal Bose gas -- 2.6.1. Black body radiation -- 2.6.2. Heat capacity of solids -- 2.7. Ideal Fermi gas -- 2.8. Simple harmonic oscillator -- References -- 3.1. Formulation of probability -- 3.1.1. States -- 3.1.2. Weight -- 3.1.3. Probability -- 3.1.4. Entropy -- 3.1.5. Averages -- 3.2. Transitions -- 3.2.1. Transition weight operator -- 3.2.2. Time correlation function -- 3.2.3. First reduction condition -- 3.2.4. Second reduction condition -- 3.2.5. Parity and reversibility -- 3.3. Non-equilibrium probability -- References -- 4.1. Adiabatic time propagator -- 4.1.1. Constant Hamiltonian operator -- 4.1.2. Time-varying Hamiltonian operator -- 4.1.3. Adiabatic Heisenberg picture -- 4.1.4. Adiabatic Liouville operator -- 4.1.5. Adiabatic Pauli master equation -- 4.2. Stochastic time propagator -- 4.2.1. General features -- 4.2.2. Variance of the stochastic operator -- 4.2.3. A quantum fluctuation-dissipation theorem -- 4.2.4. Properties of the stochastic time propagator -- 4.2.5. Heisenberg picture -- 4.2.6. Stochastic Liouville super-operator -- 4.2.7. Kubo cumulant expansion -- 4.2.8. Liouville equation -- 4.3. Kraus representation and Lindblad equation -- 4.3.1. Kraus operators for a sub-system and reservoir -- 4.3.2. Lindblad equation -- 4.4. Caldeira-Leggett model -- 4.4.1. Fundamentals -- 4.4.2. Generalised Langevin equation -- 4.5. Time correlation function -- 4.5.1. Equilibrium time correlation function -- 4.5.2. Unitary and evolution conditions -- 4.6. Transition probability -- 4.6.1. Unconditional transition probability operator -- 4.6.2. Conditional transition probability operator -- 4.7. Microscopic reversibility -- References -- 5.1. Transitions between entropy states -- 5.1.1. Random phase for transitions -- 5.1.2. Mean and stochastic parts of the state transition -- 5.1.3. Form of the time propagator 1 -- 5.1.4. Time correlation function -- 5.1.5. Stochastic and dissipative operators -- 5.2. Second entropy for transitions -- 5.2.1. Fluctuation form -- 5.2.2. Small time expansion for most likely transition -- 5.2.3. Stochastic, dissipative equation of motion -- 5.2.4. Stationarity of the state probability -- 5.2.5. Form of the time propagator 2 -- 5.3. Trajectory in wave space -- 5.3.1. Stochastic dissipative Schrodinger equation -- 5.3.2. Average on the trajectory -- 5.4. Time derivative of entropy operator -- References -- 6.1. Entropy operator for a trajectory -- 6.1.1. Wave space formulation -- 6.1.2. Propagator formulation -- 6.2. Point entropy operator -- 6.2.1. Reduction of the trajectory entropy -- 6.2.2. Form and interpretation of the point entropy -- 6.2.3. Propagator formulation -- 6.3. Non-equilibrium probability operator -- 6.3.1. Operator and average -- 6.3.2. Time derivative -- 6.4. Approximations for the dynamic entropy operator -- 6.4.1. Odd projection of the dynamic entropy operator -- 6.4.2. Adiabatic approximation for steady state thermodynamic systems -- 6.5. Perturbation of the non-equilibrium probability operator -- 6.6. Linear response theory -- 6.6.1. Unitary transformations -- 6.6.2. Interaction picture -- 6.6.3. Probability operator -- 6.6.4. Susceptibility -- 6.6.5. Dissipation -- References -- A. Probability densities and the statistical average -- B. Stochastic state transitions for a non-equilibrium system.
Subject(s):
ISBN:
  • 9780750311892 ((print))
  • 0750311894 ((print))
  • ((ebook))
  • ((mobi))
OCLC:
  • 962846330
  • 954083973
Issuing body:
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