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Methods in statistical mechanics : a modern view
- Author / Creator
- Available as
- Online
- Summary
-
This book presents a variety of techniques for tackling phenomena that are not amenable to the conventional approach based on the concept of probabilities. The methods described rely on the use of ...
This book presents a variety of techniques for tackling phenomena that are not amenable to the conventional approach based on the concept of probabilities. The methods described rely on the use of path integration, thermal Green functions, time-temperature propagators, Liouville operators, second quantization, and field correlators at finite density and temperature. Also exploring the statistical mechanics of unstable quantum systems, the book is intended as a supplementary or reference text for use in one-semester graduate courses on Quantum Mechanics, Thermodynamics, Electromagnetism, and Mathematical Methods in Physics.
Details
- Format
- Books
- Language
- English
- Publication
-
- [Place of publication not identified] : Springer, 2020
- Series
- Physical Details
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- 1 online resource
- data file
- ISBNs
- 9783030536572, 9783030536589, 3030536580, 3030536572, 9783030536596
- OCLC
- on1195923431
- Intro -- Preface -- Contents -- About the Authors -- 1 An Introduction to Statistical Mechanics -- 1.1 Partition Functions -- 1.1.1 Systems with Discrete Spectrum -- 1.2 Partition Function for a Gas of Photons -- 1.2.1 The Blackbody Radiation -- 1.3 The Maxwell Distribution -- 1.4 Classical Statistical Mechanics -- 1.4.1 On the Equipartition Theorem -- 1.5 Systems with a Variable Number of Particles -- 1.5.1 On the Classical Limits of Quantum Statistics -- 1.5.2 The Grand Canonical Partition Function in the Continuum Limit -- 1.6 Some Features of Quantum Distributions -- 1.6.1 Fermions
- 1.6.2 Bosons -- 1.7 Bose-Einstein Condensation -- 1.7.1 Massive Fermions in the Relativistic Limit -- 1.7.2 Massless Relativistic Fermions -- 1.8 Summary -- 2 The Role of Dynamics in Statistical Mechanics -- 2.1 Statistic Distributions -- 2.1.1 The Liouville Theorem -- 2.1.2 The Role of First Integrals -- 2.1.3 The Quantum Case -- 2.2 Averages and Fluctuations -- 2.3 Summary -- 2.3.1 H-Theorem and Approach to Equilibrium -- 2.4 Perturbative Method for the Density Operator -- 2.4.1 The Partition Function -- 2.5 Summary -- 3 Operator Representations of the Statistical Mechanics -- 3.1 Introduction
- 3.2 The Concept of Thermal Propagator -- 3.2.1 Wick Theorem -- 3.3 Some Thermal Averages -- 3.4 Interpretation in Terms of Green's Functions -- 3.4.1 The Truncated Fourier Transform of Green's Function -- 3.4.2 Summary -- 3.5 Grand Partition Function -- 3.5.1 Representation in Terms of Bound States -- 3.5.2 Double Green's Functions -- 3.5.3 Independent Particle Green's Functions -- 3.6 Ferromagnetism -- 4 Path Integrals and Applications -- 4.1 Basic Ideas -- 4.1.1 Interpretation of Results -- 4.2 Path Integrals with Vector Potentials -- 4.3 A Working Example
- 4.4 Applications to Statistical Mechanics -- 4.4.1 Particle Interaction with a Central Potential -- 4.4.2 Representation of the Partition Function Using Coherent States: The Harmonic Oscillator in the Number Representation -- 5 The Liouville Equation -- 5.1 Introduction: Two Points of View -- 5.2 Classical Time Evolution -- 5.2.1 Distribution Probabilities -- 5.2.2 Liouville Equation -- 5.2.3 A Consequence of the Liouville Equation -- 5.2.4 The Liouvillian -- 5.3 Liouville Equations in Quantum Mechanics -- 5.3.1 General Properties of the Statistical Averages
- 5.3.2 Time Evolution of the Statistical Averages -- 5.3.3 The Unitary Operator Ut,t0 -- 5.3.4 Some Comments on mathcalD0 -- 5.4 Symmetry Properties -- 5.5 Mathematical Properties of the Density Operator -- 6 Canonical Distributions and Thermodynamic Functions -- 6.1 Integrals of Motion -- 6.2 Gibbs Distributions -- 6.3 Thermodynamic Construction in Quasi-static Processes -- 6.3.1 Homogeneous Systems -- 6.3.2 Fluctuations -- 6.3.3 Representations -- 6.4 The Grand Canonical Ensemble -- 6.4.1 On the Uniqueness of the Values for µj -- 6.4.2 Thermodynamic Functions