Quantum Ergodicity

Dear Colleagues,

Ergodicity of classical stochastic processes can be viewed from several different perspectives, such as ergodicity in mean, ergodicity in correlations, ergodicity in mean-squared increments, or ergodicity in distribution. Physically, a general question is: Can we deduce from statistical properties of an ensemble of identical non-interacting physical systems, e.g., molecules, the statistical behavior of each separate system entering the ensemble from its individual dynamics, and vice versa? It becomes especially important in the context of single-molecular research, such as studies of fluctuating ion currents through single biological ion channels undergoing open-shut gating dynamics (mostly classical objects) or intermittency of fluorescence blinking of single nanocrystals or single organic molecules (quantum objects). Another important issue relates to micro-canonical thermalization of quantum mechanical or semi-classical systems with a few degrees of freedom, like hydrogen atom in a strong magnetic field, or a few body system of cold atoms, or vibrational relaxation in molecules. A generalization of the classical concept of ergodicity on quantum mechanical systems is a delicate issue, which is still in its infancy. This Special Issue is devoted to different aspects of quantum ergodicity and its breaking: From micro-canonical thermalization in quantum-mechanical systems with a few degrees of freedom to statistical properties of quantum jumps in single-molecular systems.

Prof. Dr. Igor Goychuk
Guest Editor

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