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Classical and Quantum Dissipative Systems

General Information
Type.................: Ebook
Part Size............: 11,584,162 bytes
Post Information
Posted by............: ~tqw~

Release Notes
This book discusses issues associated with the quantum mechanical formulation of
dissipative systems. It begins with an introductory review of phenomenological
damping forces, and the construction of the Lagrangian and Hamiltonian for the
damped motion. It is shown, in addition to these methods, that classical
dissipative forces can also be derived from solvable many-body problems. A
detailed discussion of these derived forces and their dependence on dynamical
variables is also presented. The second part of this book investigates the use
of classical formulation in the quantization of dynamical systems under the
influence of dissipative forces. The results show that, while a satisfactory
solution to the problem cannot be found, different formulations represent
different approximations to the complete solution of two interacting systems.
The third and final part of the book focuses on the problem of dissipation in
interacting quantum mechanical systems, as well as the connection of some of
these models to their classical counterparts. A number of important
applications, such as the theory of heavy-ion scattering and the motion of a
radiating electron, are also discussed.

Table Of Contents

1 Introduction 1
2 Phenomenological equations of motion for dissipative systems 5
3 Lagrangian formulations 15
4 Hamiltonian formulation 33
5 Hamilton-Jacobi formulation 63
6 Motion of a charge particle in an external electromagnetic field in the
presence of damping 71
7 Noether and non-noether symmetries and conservation laws 77
8 Dissipative forces derived from many-body problems 91
9 A particle coupled to a field 107
10 Damped motion of the central particle 117
11 Classical microscopic models of dissipation and minimal coupling rule
12 Quantization of dissipative systems 129
13 Quantization of explicitly time-dependent Hamiltonian 157
14 Density matrix and the Wigner distribution function 201
15 Path integral formulation of a damped harmonic oscillator 223
16 Quantization of the motion of an infinite chain 239
17 The Heisenberg equations of motion for a particle coupled to a heat bath
18 Quantum mechanical models of dissipative systems 279
19 More on the concept of optical potential 315

Product Details

* ISBN: 1860945252
* ISBN-13: 9781860945250
* Format: Hardcover, 334pp
* Publisher: Imperial College Press
* Pub. Date: March 2006

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