Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables
arXiv:1903.04195 · doi:10.1063/1.5094412
Abstract
To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local (TCL) and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily \emph{increase} significantly in order to reach a stationary state with \emph{smaller} occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely-positive divisibility is more subtly signaled by the \emph{prohibition} of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy and coherent information.
arXiv commentSubmitted to The Journal of Chemical Physics, 19 pages + 14 pages of appendices with 13 figures. Significantly extended introduction and discussion, no results changed
References in corpus (85)
- Introduction to Quantum Noise, Measurement and Amplification
- Non-Markovian dynamics in open quantum systems
- Entanglement and non-Markovianity of quantum evolutions
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Quantum trajectories and open many-body quantum systems
- Quantum data processing and error correction
- Quantum information can be negative
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Microscopic derivation of rate equations for quantum transport
- Measurements with a noninvasive detector and dephasing mechanism
- Resonant tunneling through ultrasmall quantum dots: zero-bias anomalies, magnetic field dependence, and boson-assisted transport
- Input-output theory for waveguide QED with an ensemble of inhomogeneous atoms
- On measures of non-Markovianity: divisibility vs. backflow of information
- Quantum state merging and negative information
- Zero-bias anomalies and boson-assisted tunneling through quantum dots
- Tunneling through molecules and quantum dots: master-equation approaches
- Kinetic Equations for Transport Through Single-Molecule Transistors
- Quantum channels and their entropic characteristics
- A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
- Memory Effects In Nonequilibrium Quantum Impurity Models
- Spectral theorem for the Lindblad equation for quadratic open fermionic systems
- Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model
- Exact master equations for the non-Markovian decay of a qubit
- Optimal control of a qubit coupled to a non-Markovian environment
- Finding the Kraus decomposition from a master equation and vice versa
- Comparative study of non-Markovianity measures in exactly solvable one and two qubit models
- Decoherence and lead induced inter-dot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
- Microscopic derivation of the Jaynes-Cummings model with cavity losses
- Cotunneling at resonance for the single-electron transistor
- Tunneling through nanosystems: Combining broadening with many-particle states
- Super-fermion representation of the Lindblad master equation for the electron transport problem
- Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions
- Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state
- Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory
- Charge transport through single molecules, quantum dots, and quantum wires
- Staying positive: going beyond Lindblad with perturbative master equations
- Superoperator nonequilibrium Green's function theory of many-body systems; Applications to charge transfer and transport in open junctions
- Eternal non-Markovianity: from random unitary to Markov chain realisations
- Operational approach to open dynamics and quantifying initial correlations
- Nonequilibrium Kondo model: Crossover from weak to strong coupling
- Exact master equation for a spin interacting with a spin bath: Non-Markovianity and negative entropy production rate
- Probing level renormalization by sequential transport through double quantum dots
- Exact closed master equation for Gaussian non-Markovian dynamics
- An introduction to operational quantum dynamics
- Nonequilibrium Kondo Effect in a Quantum Dot Coupled to Ferromagnetic Leads
- Coherent Transport through an interacting double quantum dot: Beyond sequential tunneling
- Fermionic superoperators for zero-temperature non-linear transport: real-time perturbation theory and renormalization group for Anderson quantum dots
- A renormalization-group analysis of the interacting resonant level model at finite bias: Generic analytic study of static properties and quench dynamics
- Time-convolutionless master equation for quantum dots: Perturbative expansion to arbitrary order
- Time scales in the dynamics of an interacting quantum dot
- Quantum-fluctuation effects on the thermopower of a single-electron transistor
- Detecting non-Markovianity of quantum evolution via spectra of dynamical maps
- Sufficient conditions for memory kernel master equation
- Resonant Tunneling and Coulomb Oscillations
- Exact Calculation of the Time Convolutionless Master Equation Generator: Application to the Nonequilibrium Resonant Level Model
- Note: On the memory kernel and the reduced system propagator
- Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states
- Nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport
- Application of a semiclassical model for the second-quantized many-electron Hamiltonian to nonequilibrium quantum transport: The resonant level model
- Fermion-parity duality and energy relaxation in interacting open systems
- Feshbach projection formalism for open quantum systems
- Transport mirages in single-molecule devices
- Tensor power of dynamical maps and P- vs. CP-divisibility
- Exact Non-Markovian master equation for the Spin-Boson and Jaynes-Cummings models
- Eternal non-Markovianity is generic for the spin-boson model
- Kondo model in nonequilibrium: Interplay between voltage, temperature, and crossover from weak to strong coupling
- Exact correspondence between Renyi entropy flows and physical flows
- The quench dynamics of a dissipative quantum system: a renormalization group study
- Strong quantum memory at resonant Fermi edges revealed by shot noise
- Non-Adiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density Functional Theory
- Detection of the relaxation rates of an interacting quantum dot by a capacitively coupled sensor dot
- A diagrammatic description of the equations of motion, current, and noise within the second-order von Neumann approach
- Nonequilibrium Fock space for the electron transport problem
- Out-of-equilibrium Anderson model at high and low bias voltages
- Transport across an Anderson quantum dot in the intermediate coupling regime
- Recursive approach for non-Markovian time-convolutionless master equations
- Relaxation of quantum dots in a magnetic field at finite bias -- charge, spin and heat currents
- Duality for open fermion systems: energy-dependent weak coupling and quantum master equations
- Dissipative quantum mechanics beyond Bloch-Redfield: A consistent weak-coupling expansion of the ohmic spin boson model at arbitrary bias
- Full counting statistics of information content in the presence of Coulomb interaction
- Non-adiabatic effects in periodically driven-dissipative open quantum systems
- Time-dependent i-DFT exchange-correlation potentials with memory: Applications to the out-of-equilibrium Anderson model
- Non-Markovian effects at the Fermi-edge singularity in quantum dots
- Continued-fraction representation of the Kraus map for non-Markovian reservoir damping
- Analytical Continuation Approaches to Electronic Transport: The Resonant Level Model
Cited by in corpus (19)
- Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
- Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
- Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
- Green's function methods for single molecule junctions
- Non-Markovian Quantum Mpemba effect
- Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation
- The Tilt of the Local Velocity Ellipsoid as Seen by Gaia
- How quantum evolution with memory is generated in a time-local way
- Field-theoretical approach to open quantum systems and the Lindblad equation
- Density-operator evolution: Complete positivity and the Keldysh real-time expansion
- Feynman-Vernon influence functional approach to quantum transport in interacting nanojunctions: An analytical hierarchical study
- Quantum renewal processes
- The connection between time-local and time-nonlocal perturbation expansions
- Construction of propagators for divisible dynamical maps
- Renormalization group for open quantum systems using environment temperature as flow parameter
- Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
- Illusory cracks in the second law of thermodynamics in quantum nanoelectronics
- Fermionic duality: General symmetry of open systems with strong dissipation and memory
- Adapted projection operator technique for the treatment of initial correlations