Classical and Quantum Dissipative Systems

Dissipative forces play an important role in problems of classical as well as quantum mechanics. Since these forces are not among the basic forces of nature, it is essential to consider whether they should be treated as phenomenological interactions used in the equations of motion, or they should be derived from other conservative forces. In this book we discuss both approaches in detail starting with the Stoke's law of motion in a viscous fluid and ending with a rather detailed review of the recent attempts to understand the nature of the drag forces originating from the motion of a plane or a sphere in vacuum caused by the variations in the zero-point energy. In the classical formulation, mathematical techniques for construction of Lagrangian and Hamiltonian for the variational formulation of non-conservative systems are discussed at length. Various physical systems of interest including the problem of radiating electron, theory of natural line width, spin-boson problem, scattering and trapping of heavy ions and optical potential models of nuclear reactions are considered and solved.

Contents:

• Phenomenological Equations of Motion for Dissipative Systems
• Lagrangian Formulation
• Hamiltonian Formulation
• Hamilton-Jacobi Formulation
• Motion of a Charged Damped Particle in an External Electromagnetic Field
• Noether and Non-Noether Symmetries and Conservation Laws
• Dissipative Forces Derived from Many-Body Problems
• The Equation of Motion for an Oscillator Coupled to a Field
• Damped Motion of the Central Particle
• Classical Microscopic Models of Dissipation and Minimal Coupling Rule
• Quantization of Dissipative Systems
• Quantization of Explicitly Time-Dependent Hamiltonians
• Coherent State Formulation of Damped Systems
• Density Matrix and the Wigner Distribution Function
• Path Integral Formulation of a Damped Harmonic Oscillator
• Quantization of the Motion of an Infinite Chain
• The Heisenberg Equations of Motion for a Particle Coupled
• Quantum Mechanical Models of Dissipative Systems
• Dissipation Arising from the Motion of the Boundaries
• The Optical Potential

Readership: Researchers and graduate students in applied mathematics and theoretical physics.