Non-Markovian non-stationary completely positive open quantum system dynamics
arXiv:0908.0769 · doi:10.1103/PhysRevA.80.022103
Abstract
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is defined by a set of disruptive events, consisting in the action of a completely positive superoperator over the system density matrix. The random time intervals between events are described by an arbitrary waiting-time distribution. We show that, in contrast to the Markovian case, if one performs a system-preparation (measurement) at an arbitrary time, the subsequent evolution of the density matrix evolution is modified. The non-stationary character refers to the absence of an asymptotic master equation even when the preparation is performed at arbitrary long times. In spite of this property, we demonstrate that operator expectation values and operators correlations have the same dynamical structure, establishing the validity of a non-stationary quantum regression hypothesis. The non-stationary property of the dynamic is also analyzed through the response of the system to an external weak perturbation.
13 pages, 3 figures
References in corpus (34)
- Universal emission intermittency in quantum dots, nanorods, and nanowires
- Statistical Aging and Non Ergodicity in the Fluorescence of Single Nanocrystals
- Non-Markovian generalization of the Lindblad theory of open quantum systems
- Completely positive maps with memory
- Non-Markovian dynamics of a qubit
- Completely Positive Post-Markovian Master Equation via a Measurement Approach
- Finding the Kraus decomposition from a master equation and vice versa
- Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging
- Quantum Semi-Markov Processes
- Stochastic Representation of a Class of Non-Markovian Completely Positive Evolutions
- Staying positive: going beyond Lindblad with perturbative master equations
- Lindblad rate equations
- Weakly non-ergodic Statistical Physics
- Nonergodisity of a time series obeying Lévy statistics
- Correlated projection operator approach to non-Markovian dynamics in spin baths
- Random Lindblad equations from complex environments
- Breakdown of the Onsager principle as a sign of aging
- Multiple-time correlation functions for non-Markovian interaction: Beyond the Quantum Regression Theorem
- Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations
- Fluorescence intermittency in blinking quantum dots: renewal or slow modulation?
- Linear response to perturbation of non-exponential renewal processes
- Renewal, Modulation and Superstatistics
- Correlation function and generalized master equation of arbitrary age
- Limits in the characteristic function description of non-Lindblad-type open quantum systems
- Non-Markovian dynamics for bipartite systems
- Linear Response and Fluctuation Dissipation Theorem for non-Poissonian Renewal Processes
- Aging and Rejuvenation with Fractional Derivatives
- Absorption and Emission in the non-Poisson case
- Open quantum system approach to single-molecule spectroscopy
- Quantum master equation for the microcanonical ensemble
- Nonexponential decoherence and momentum subdiffusion in a quantum Lévy kicked rotator
- Non-Markovian master equations from entanglement with stationary unobserved degrees of freedom
- Controlled decoherence in a quantum Lévy kicked rotator
- Quantum regression theorem for non-Markovian Lindblad equations
Cited by in corpus (18)
- Universal spectra of random Lindblad operators
- Transmission of Information between Complex Networks: 1/f-Resonance
- Quantum non-Markovian processes break conditional past-future independence
- Stochastic Quantum Zeno by Large Deviation Theory
- Markovian embedding of non-Markovian quantum collisional models
- Maximally non-Markovian quantum dynamics without environment backflow of information
- Post-Markovian quantum master equations from classical environment fluctuations
- Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
- Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches
- Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation
- Quantum renewal processes
- Detection of Bidirectional System-Environment Information Exchanges
- A solvable class of non-Markovian quantum multipartite dynamics
- Quantifying environment non-classicality in dissipative open quantum dynamics
- Two-Time Correlation Functions in Dissipative and Interacting Bose-Hubbard Chains
- Reconstruction of the environmental correlation function from single emitter photon statistics: a non-Markovian approach
- Open system approach to the internal dynamics of a model multilevel molecule
- Optimally chosen Nakajima-Zwanzig master equation for mean field approximation