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The methods of statistical physics have become increasingly important in recent years for the treatment of a variety of diverse physical problems. Of principal interest is the microscopic description of the dynamics of dissipative systems. Although a unified theoretical description has at present not yet been achieved, we have assumed the task of writing a textbook which summarizes those of the most important methods which are self-contained and complete in themselves. We cannot, of course, claim to have treated the field exhaustively. A microscopic description of physical phenomena must necessarily be based upon quantum theory, and we have therefore carried out the treatment of dynamic processes strictly within a quantum-theoretical framework. For this reason alone it was necessary to omit a number of extremely important theories which have up to now been formulated only in terms of classical statistics. The goal of this book is, on the one hand, to give an introduction to the general principles of the quantum statistics of dynamical processes, and, on the other, to provide readers who are interested in the treatment of particular phenomena with methods for solving specific problems. The theory is for the most part formulated within the calculational frame work of Liouville space, which, together with projector formalism, has become an expedient mathematical tool in statistical physics.
List of contents
1 General Aspects.- 1. The Concept of Statistical Physics.- 2. Summary of Quantum Theory.- 3. Quantum Theory in Liouville Space.- 4. Systems of Many Particles.- 5. Information-Theoretical Construction of the Statistical Operator.- 6. The Significance of Generalized Canonical Statistical Operators for Dynamic Processes.- 2 Response to Time-Dependent External Fields.- 7. The Quantum-Statistical Formulation of Response Theory.- 8. A Scalar Product in the Liouville Space for Linear Response Theory.- 9. Linear Response Theory.- 10. Quadratic Response Theory.- 3 Equations of Motion for Observables in the Case of Small Deviations from Equilibrium.- 11. Exact Integro-Dilferential Equations for Relaxation Processes.- 12. Perturbation-Theoretical Treatment of the Frequency and Memory Matrix.- 13. The Transition to Differential Equations with Damping.- 14. Time Derivatives as a Special Set of Observables.- 15. Dynamic Onsager-Casimir Coefficients as Linear Response Functions for Generalized Forces.- 16. Physical Examples.- 4 Equations of Motion of the Relevant Parts of the Statistical Operator.- 17. Mappings of the Statistical Operator onto a Relevant Part.- 18. The Generalized Canonical Statistical Operator ?(t) as ?rel (t).- A. Equivalence of the Nakajima-Zwanzig Equation and the Generalized-Operator Langevin Equation.- B. Symmetries.- B.1.1 Properties of D(g).- B.1.2 Selection Rules.- B.2.2 Symmetry Properties Resulting from Time-Reversal Invariance.- Solutions to the Exercises.
