Dissipative Properties of Quantum Systems

AUTOR(ES)

Grecos, A. P.

RESUMO

We consider the dissipative properties of large quantum systems from the point of view of kinetic theory. The existence of a nontrivial collision operator imposes restrictions on the possible collisional invariants of the system. We consider a model in which a discrete level is coupled to a set of quantum states and which, in the limit of a large “volume,” becomes the Friedrichs model. Because of its simplicity this model allows a direct calculation of the collision operator as well as of related operators and the constants of the motion. For a degenerate spectrum the calculations become more involved but the conclusions remain simple. The special role played by the invariants that are functions of the Hamiltonion is shown to be a direct consequence of the existence of a nonvanishing collision operator. For a class of observables we obtain ergodic behavior, and this reformulation of the ergodic problem may be used in statistical mechanics to study the ergodicity of large quantum systems containing a small physical parameter such as the coupling constant or the concentration.

Documentos Relacionados

• The second law as a selection principle: The microscopic theory of dissipative processes in quantum systems
• DISSIPATIVE PROCESSES, QUANTUM STATES, AND ENTROPY
• Review of Marek and Schreiber: Chaotic Behaviour of Deterministic Dissipative Systems
• Dynamical properties in quantum many body systems
• Integrable systems and quantum groups