Generic features of the dynamics of complex open quantum systems: Statistical approach based on averages over the unitary group

Abstract

We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of complex open quantum systems, employing arguments from ensemble theory. We further generalize these results to arbitrary eigenvalue distributions, allowing a detailed comparison of typical regular and chaotic systems with the help of concepts from random matrix theory. To illustrate the physical relevance and the general applicability of our results we present a series of examples related to the fields of open quantum systems and nonequilibrium quantum thermodynamics. These include the effect of initial correlations, the average quantum dynamical maps, the generic dynamics of system-environment pure state entanglement and, finally, the equilibration of generic open and closed quantum systems.

15 pages, 10 figures, 4 tables

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• Local Detection of Quantum Correlations with a Single Trapped Ion
• Localization with random time-periodic quantum circuits
• Extreme Decoherence and Quantum Chaos
• Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling
• Effective dynamics of disordered quantum systems
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Generating and protecting correlated quantum states under collective dephasing
• Decoherence rate in random Lindblad dynamics
• Quantum noise generated by local random Hamiltonians
• Quantum ergodicity for a class of non-generic systems
• Average of uncertainty-product for bounded observables
• Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion
• Average entropy of a subsystem over a global unitary orbit of a mixed bipartite state
• The local detection method: Dynamical detection of quantum discord with local operations
• Revealing correlations between a system and an inaccessible environment