Reduced Dynamics of Full Counting Statistics
arXiv:2111.08525 · doi:10.21468/SciPostPhys.13.2.027
Abstract
We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they can be difficult to formulate for observables spanning the system and its environment, such as those characterizing transport properties. A large variety of mixed system--environment observables, as well as their statistical properties, can be evaluated by considering counting fields. Given a numerical method able to simulate the field-modified dynamics over the memory timescale, we show that the long-lived full counting statistics can be efficiently obtained from the reduced dynamics. We demonstrate the utility of the technique by computing the long-time current in the nonequilibrium Anderson impurity model from short-time Monte Carlo simulations.
References in corpus (74)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- Electron transport through double quantum dots
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- The numerical renormalization group method for quantum impurity systems
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Kondo physics in carbon nanotubes
- Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
- Fermionic transport in a homogeneous Hubbard model: Out-of-equilibrium dynamics with ultracold atoms
- Real-time path integral approach to nonequilibrium many-body quantum system
- Advances and challenges in single-molecule electron transport
- Conduction of Ultracold Fermions Through a Mesoscopic Channel
- Diagrammatic Monte Carlo simulation of non-equilibrium systems
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
- Completely positive maps with memory
- Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems
- Quantum stochastic processes and quantum non-Markovian phenomena
- Quantum transport in ultracold atoms
- Real-Time Diagrammatic Monte Carlo for Nonequilibrium Quantum Transport
- Memory Effects In Nonequilibrium Quantum Impurity Models
- Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model
- Decoherence and lead induced inter-dot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
- Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
- Observation of the SU(4) Kondo state in a double quantum dot
- Tunable Quantum Criticality and Super-ballistic Transport in a `Charge' Kondo Circuit
- Solving nonequilibrium dynamical mean-field theory using matrix product states
- Quantum Semi-Markov Processes
- Multiple steady-states in nonequilibrium quantum systems with electron-phonon interactions
- Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics
- Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model
- Observation of the Kondo Screening Cloud of Micron Lengths
- Nonequilibrium quantum systems with electron-phonon interactions: Transient dynamics and approach to steady state
- Non-Markovian Quantum Process Tomography
- Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
- Efficient DMFT impurity solver using real-time dynamics with Matrix Product States
- Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win?
- Quantum process tomography via completely positive and trace-preserving projection
- Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States
- Transport through an Anderson impurity: Current ringing, non-linear magnetization and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations
- Green's functions from real-time bold-line Monte Carlo
- An introduction to operational quantum dynamics
- Numerically Exact Long Time Behavior of Nonequilibrium Quantum Impurity Models
- Generalized master equations leading to completely positive dynamics
- Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
- Real-Time Dynamics in Quantum Impurity Models with Diagrammatic Monte Carlo
- Inelastic Interaction Corrections and Universal Relations for Full Counting Statistics
- Generalized projected dynamics for non-system observables of non-equilibrium quantum impurity models
- Numerically exact full counting statistics of the nonequilibrium Anderson impurity model
- Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach
- Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo
- Green's function methods for single molecule junctions
- Quantum heat statistics with time-evolving matrix product operators
- Sufficient conditions for memory kernel master equation
- Tomographically reconstructed master equations for any open quantum dynamics
- Dynamics of Kondo voltage splitting after a quantum quench
- Sub-Ohmic to super-Ohmic crossover behavior in nonequilibrium quantum systems with electron-phonon interactions
- Periodically refreshed baths to simulate open quantum many-body dynamics
- Full counting statistics in the self-dual interacting resonant level model
- Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach
- Exact Calculation of the Time Convolutionless Master Equation Generator: Application to the Nonequilibrium Resonant Level Model
- A Quantum Monte Carlo algorithm for out-of-equilibrium Green's functions at long times
- Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
- Transport measurement of the orbital Kondo effect with ultracold atoms
- Renormalized Lindblad Driving: A Numerically-Exact Nonequilibrium Quantum Impurity Solver
- Numerically exact counting statistics of energy current in the Kondo regime
- Shot noise in the self-dual Interacting Resonant Level Model
- Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach
- Lead Geometry and Transport Statistics in Molecular Junctions
- Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times
- Pseudogap Anderson impurity model out of equilibrium: A master equation tensor network approach
- Phonon dynamics in correlated quantum systems driven away from equilibrium
- Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements
- Full counting statistics in the not-so-long-time limit
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- Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
- Photon-resolved Floquet theory approach to spectroscopic quantum sensing