Quantum Ergodicity
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A topical collection in Entropy (ISSN 1099-4300).
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Editor
Prof. Dr. Igor Goychuk
Prof. Dr. Igor Goychuk
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Collection Editor
1. Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany
2. Institute for Multiscale Simulation, Friedrich-Alexander University, Erlangen–Nuremberg, Germany
Interests: theoretical condensed matter, statistical physics and nonlinear stochastic dynamics, biophysics, chemical physics
Topical Collection Information
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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Keywords
- Quantum ergodicity in mean and correlations
- quantum ergodicity and foundations of statistical mechanics
- quantum ergodicity and vibrational relaxation in isolated molecules
- quantum ergodicity and microcanonical thermalization versus Anderson localization
- ergodicity in quantum wave functions and semi-classical chaos
- quantum jumps intermittency and ergodicity
- ergodicity of continuous time quantum walks
Published Papers (1 paper)
2018
Open AccessFeature PaperReview
Molecules and the Eigenstate Thermalization Hypothesis
by
David M. Leitner
Cited by 9 | Viewed by 4039
Abstract
We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of
N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization
[...] Read more.
We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of
N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as
N3, in marked contrast to the total density of states, which scales as exp(
aN), where
a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.
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