Quantum Dissipative Systems

Quantum-statistical mechanics is a very rich and checkered field. It is the theory dealing with the dynamical behavior of spontaneous quantal fluctuations…

The following sections are included:

• Preface

• Preface to the Third Edition

• Preface to the Second Edition

• Preface to the First Edition

• Contents

The following sections are included:

• Diverse limited approaches: a brief survey
  • Langevin equation for a damped classical system
  • New schemes of quantization
  • Traditional system-plus-reservoir methods
  • Stochastic dynamics in Hilbert space

• System-plus-reservoir models
  • Harmonic oscillator bath with linear coupling
  • Ergodicity
  • The spin-boson model
  • Microscopic models
  • Charging and environmental effects in tunnel junctions
  • Nonlinear quantum environments

• Imaginary-time approach and equilibrium dynamics
  • General concepts
  • Effective action and equilibrium density matrix
  • Partition Function of the Open System
  • Quantum statistical expectation values in phase space

• Real-time path integrals and nonequilibrium dynamics
  • Statement of the problem and general concepts
  • Feynman-Vernon method for a product initial state
  • Decoherence and friction
  • General initial states and preparation function
  • Complex-time path integral for the propagating function
  • Real-time path integral for the propagating function
  • Closed time contour representation
  • Semiclassical regime
  • Stochastic unraveling of influence functional
  • Non-Markovian dissipative dynamics in the semiclassical limit
  • Brief summary and outlook

So far I have employed functional integral methods in order to set up exact formal expressions which describe the thermodynamics and dynamics of damped quantum systems. Now we move to new grounds and consider the physical properties of exactly solvable damped linear systems, i.e. the damped quantum oscillator and quantum Brownian particle. Subsequently, I discuss a variational method which makes it possible for us to treat nonlinear damped quantum systems in much the same way as linear systems. I conclude this part with a brief general discussion of quantum decoherence.

In the second part, I considered the exactly solvable case of linear dissipative quantum systems, the thermodynamic variational approach useful for nonlinear quantum systems, and issues of quantum decoherence. Now I turn to a study of the frequent situation in which a metastable state is separated from the outside region by a free energy barrier. The decay of a metastable state plays a central role in many scientific areas including low-temperature physics, nuclear physics, chemical kinetics and transport in biomolecules. At high temperatures, the system escapes from the metastable well predominantly over the barrier by thermal activation. At zero temperature on the other hand, the system is in the localized ground state of the metastable well and can escape only by quantum mechanical tunneling through the barrier. I shall focus the discussion on the influence of friction on the decay process. The treatment will be based on an effective method which allows to study this problem in a unified manner for temperatures ranging from T = 0 up to the classical regime.

One of the most interesting aspects of quantum theory is the phenomenon of constructive and destructive interference. The phase coherence between different quantum mechanical states may lead to clockwise motion. The simplest model involving quantum coherence is a two-state system. The problem of a quantum system whose state is effectively confined to a twodimensional Hilbert space is often encountered in physics and chemistry. For instance, imagine a quantum mechanical particle tunneling clockwise forth and back between two different localized states. In reality, such a system is strongly affected by the surroundings. We will see that the coupling can lead to qualitative changes in the behaviors: the environment-induced fluctuations can destroy quantum coherence and can even lead to a “phase transition” to a state in which quantum tunneling is quenched.

A quantum Brownian particle in a multi-well potential coupled to a dissipative environment is archetypal for many problems in physics and chemistry. Examples include super-ionic conductors, atoms on surfaces, and interstitials in dielectrics and metals. Also the current-voltage characteristics of a Josephson junction, and charge transport in a quantum wire hindered by impurity scattering are described by this model. At high temperature, the particle moves forward or backward from well to well by incoherent tunneling or thermally activated transitions. As the temperature is lowered, coherent tunneling across many wells may become significant, and the competing different tunneling paths may interfere constructively or destructively. The model has a profound and powerful duality symmetry between the weak-binding and strong-binding representation. In view of the broad area of applications, the understanding of quantum transport in multi-well systems is a central issue.

The following sections are included:

• Bibliography

• Index