Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System
arXiv:1812.04266 · doi:10.1088/1367-2630/ab20d7
Abstract
In the non-Markovian regime, the bath has the memory about the past behavior of the open quantum system. This memory has slowly-decaying power-law tails. Such a long-range character of the memory complicates the description of the resulting real-time dynamics on large time scales. In a numerical simulation, this problem manifests itself in a `revival', a spurious reflected signal which appears after a finite time thus invalidating the simulation. In the present work, we approach this problem and develop a numerical discretization of the bath without revivals. We find that a crucial role is played by the singularities of the bath spectral density (e.g. edges of bands): the memory about the (spectral) behaviour of the open system in the remote past is completely averaged out (forgotten), except an increasingly small vicinity of these singular frequencies. Therefore, we introduce the concept of memory channel, to denote such an irreversible information loss process around a particular singular frequency. On a technical side, we begin the treatment by noting that with respect to the memory loss, the quantum field of the bath should be divided into the following two different parts: the observable and the virtual quanta. Information about the former is never lost: they contribute to the trace over the bath degrees of freedom. The only way to avoid the revival from the observable quanta is to calculate their dynamics exactly. We do this by employing a stochastic sampling of the Husimi function of the bath. The other part, the virtual quanta, are always annihilated after a certain delay time. We construct a dedicated quantum representation for the virtual states by assigning amplitudes to the delay times before annihilation. It is in this representation we rigorously define the concept of memory channels.
arXiv comment15 pages; 4 figures
References in corpus (54)
- Decoherence, einselection, and the quantum origins of the classical
- Decoherence, the measurement problem, and interpretations of quantum mechanics
- Non-Markovian dynamics in open quantum systems
- Quantum trajectories and open many-body quantum systems
- Nonequilibrium dynamical mean-field theory and its applications
- Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
- Efficient simulation of strong system-environment interactions
- Non-Markovian Quantum State Diffusion
- Anomalous Normal-State Properties of High-T Superconductors -- Intrinsic Properties of Strongly Correlated Electron Systems?
- Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
- Concepts of quantum non-Markovianity: a hierarchy
- Nonequilibrium dynamical mean-field theory
- Quantum feedback: theory, experiments, and applications
- Quantum Trajectories and Quantum Measurement Theory
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Hierarchy of stochastic pure states for open quantum system dynamics
- Non-Markovian generalization of the Lindblad theory of open quantum systems
- Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
- Pseudomodes as an effective description of memory: Non-Markovian dynamics of two-state systems in structured reservoirs
- Mappings of open quantum systems onto chain representations and Markovian embeddings
- Auxiliary master equation approach to non-equilibrium correlated impurities
- Quantum Darwinism in quantum Brownian motion: the vacuum as a witness
- How to discretize a quantum bath for real-time evolution
- Non-Markovian stochastic Schrödinger equations: Generalization to real-valued noise using quantum measurement theory
- Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
- Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
- Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
- Numerically exact full counting statistics of the nonequilibrium Anderson impurity model
- The interpretation of non-Markovian stochastic Schrödinger equations as a hidden-variable theory
- Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
- Redundant Information from Thermal Illumination: Quantum Darwinism in Scattered Photons
- Feedback Control of Quantum Transport
- Dissipative Universal Lindbladian Simulation
- Strong suppression of shot noise in a feedback-controlled single-electron transistor
- Monitoring of the process of system information broadcasting in time
- Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models
- Error-transparent quantum gates for small logical qubit architectures
- Quantum Trajectories for Realistic Photodetection I: General Formalism
- Generic emergence of objectivity of observables in infinite dimensions
- Spikes in quantum trajectories
- Non-Markovian Open Quantum Systems: Input-Output Fields, Memory, Monitoring
- Generic appearance of objective results in quantum measurements
- Input and output in damped quantum systems III: Formulation of damped systems driven by Fermion fields
- Quantum Trajectories for Realistic Photodetection II: Application and Analysis
- Quantum trajectories for the realistic measurement of a solid-state charge qubit
- Resonance fluorescence in a band gap material: Direct numerical simulation of non-Markovian evolution
- Computing the Rates of Measurement-Induced Quantum Jumps
- Non-Markovian quantum jumps from measurements in bipartite Markovian dynamics
- Reverse quantum state engineering using electronic feedback loops
- Feedback Network Models for Quantum Transport
- A non-Markovian quantum trajectory approach to radiation into structured continuum
- Feedback Control of Waiting Times
- Stochastic dressed wavefunction: a numerically exact solver for bosonic impurity model dynamics within wide time interval
- Stochastic Wave-Function Simulation of Irreversible Emission Processes for Open Quantum Systems in a Non-Markovian Environment