Synopses & Reviews
This volume presents a mathematical theory of the Feynman integral based on probabilistic methods, which is applied to controllable approximations to Hamiltonian and dissipative quantum dynamics. A wide range of methods of random dynamical systems is discussed for models of quantum physics. The probabilistic method is considered an efficient tool for analytic and numerical approximations of the dynamics of large complex quantum systems. Audience: This book will be of interest to specialists in mathematical physics, quantum mechanics, quantum field theory, stochastic processes, dynamical systems and computational physics. It can also be recommended as an introduction to problems of mathematical physics for graduate students of mathematics and theoretical physics.
Synopsis
This volume presents a mathematical theory of the Feynman integral based on probabilistic methods, which is applied to controllable approximations to Hamiltonian and dissipative quantum dynamics. A wide range of methods of random dynamical systems is discussed for models of quantum physics. The probabilistic method is considered an efficient tool for analytic and numerical approximations of the dynamics of large complex quantum systems. Audience: This book will be of interest to specialists in mathematical physics, quantum mechanics, quantum field theory, stochastic processes, dynamical systems and computational physics. It can also be recommended as an introduction to problems of mathematical physics for graduate students of mathematics and theoretical physics.
Description
Includes bibliographical references (p. [353]-362) and index.
Table of Contents
Foreword. Introduction. Basic Notation. 1. Preliminaries. 2. Markov chains. 3. Stochastic differential equations. 4. Semi-groups and the Trotter product formula. 5. The Feynman integral. 6. Feynman integral and stochastic differential equations. 7. Random perturbations of the classical mechanics. 8. Complex dynamics and coherent states. 9. Quantum non-linear oscillations. 10. Feynman integral on analytic submanifolds. 11. Interaction with the environment. 12. Lindblad equation and stochastic Schrödinger equation. 13. Hamiltonian time evolution of the density matrix. 14. Stochastic representation of the Lindblad time evolution. 15. Decoherence and estimates on dissipative dynamics. 16. Diffusive behaviour of the Wigner function and decoherence. 17. Scattering and tunnelling in an environment. 18. The Feynman integral in quantum field theory. 19. The phase space methods in QFT. 20. Computer simulations of quantum random dynamics. Bibliography. Index.