Pushing the limits of the reaction-coordinate mapping
arXiv:1905.13673 · doi:10.1063/1.5114690
Abstract
The reaction-coordinate mapping is a useful technique to study complex quantum dissipative dynamics into structured environments. In essence, it aims to mimic the original problem by means of an 'augmented system', which includes a suitably chosen collective environmental coordinate---the 'reaction coordinate'. This composite then couples to a simpler 'residual reservoir' with short-lived correlations. If, in addition, the residual coupling is weak, a simple quantum master equation can be rigorously applied to the augmented system, and the solution of the original problem just follows from tracing out the reaction coordinate. But, what if the residual dissipation is strong? Here we consider an exactly solvable model for heat transport---a two-node linear "quantum wire" connecting two baths at different temperatures. We allow for a structured spectral density at the interface with one of the reservoirs and perform the reaction-coordinate mapping, writing a perturbative master equation for the augmented system. We find that: (a) strikingly, the stationary state of the original problem can be reproduced accurately by a weak-coupling treatment even when the residual dissipation on the augmented system is very strong; (b) the agreement holds throughout the entire dynamics under large residual dissipation in the overdamped regime; (c) and that such master equation can grossly overestimate the stationary heat current across the wire, even when its non-equilibrium steady state is captured faithfully. These observations can be crucial when using the reaction-coordinate mapping to study the largely unexplored strong-coupling regime in quantum thermodynamics.
arXiv comment12 pages, 4 figures; comments welcome; references updated
References in corpus (49)
- Quantum heat engines and refrigerators: Continuous devices
- On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
- Quantum fidelity for arbitrary Gaussian states
- Exact c-number Representation of Non-Markovian Quantum Dissipation
- Non-perturbative treatment of non-Markovian dynamics of open quantum systems
- Reconciliation of quantum local master equations with thermodynamics
- Modeling heat transport through completely positive maps
- Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems
- Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping
- Testing the validity of the local and global GKLS master equations on an exactly solvable model
- Quantum dot Rabi rotations beyond the weak exciton-phonon coupling regime
- Performance of a quantum heat engine at strong reservoir coupling
- The thermodynamic cost of driving quantum systems by their boundaries
- Universal Markovian reduction of Brownian particle dynamics
- Perturbative treatment of inter-site couplings in the local description of open quantum networks
- Locality of temperature
- Mappings of open quantum systems onto chain representations and Markovian embeddings
- Energy transfer in structured and unstructured environments: master equations beyond the Born-Markov approximations
- Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions
- Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong coupling regime
- Low-temperature thermometry can be enhanced by strong coupling
- Entanglement of mechanical oscillators coupled to a non-equilibrium environment
- Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
- Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse-graining
- Dynamics and thermodynamics of linear quantum open systems
- The equilibrium states of open quantum systems in the strong coupling regime
- Adding dynamical generators in quantum master equations
- Multiple-time correlation functions for non-Markovian interaction: Beyond the Quantum Regression Theorem
- Fundamental limits for cooling of linear quantum refrigerators
- Optimal strategy for a single-qubit gate and trade-off between opposite types of decoherence
- Thermodynamic deficiencies of some simple Lindblad operators
- From quantum heat engines to laser cooling: Floquet theory beyond the Born-Markov approximation
- Optimizing co-operative multi-environment dynamics in a dark-state-enhanced photosynthetic heat engine
- An electronic Maxwell demon in the coherent strong-coupling regime
- Asymptotic Discord and Entanglement of Non-Resonant Harmonic Oscillators in an Equilibrium Environment
- Markovian evolution of strongly coupled harmonic oscillators
- New analytic solution for the heat flow through a general harmonic network
- Quantum thermometry using the ac Stark shift within the Rabi model
- Electron pumping in the strong coupling and non-Markovian regime: A reaction coordinate mapping approach
- Rectification of heat currents across nonlinear quantum chains: A versatile approach beyond weak thermal contact
- Local temperature in quantum thermal states
- Intensive temperature and quantum correlations for refined quantum measurements
- Locality of temperature in spin chains
- The smallest absorption refrigerator: the thermodynamics of a system with quantum local detailed balance
- Electron Counting Statistics for Non-Additive Environments
- Gaussian tripartite entanglement out of equilibrium
- Spin-boson model as a simulator of non-Markovian multiphoton Jaynes-Cummings models
- Transmission from reverse reaction coordinate mappings
- Currents and fluctuations of quantum heat transport in harmonic chains
Cited by in corpus (19)
- QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
- Quantum Brownian Motion for Magnets
- Strong coupling effects in quantum thermal transport with the reaction coordinate method
- Capturing non-Markovian dynamics with the reaction coordinate method
- Measurability of nonequilibrium thermodynamics in terms of the Hamiltonian of mean force
- Quantum Thermal Transport Beyond Second Order with the Reaction Coordinate Mapping
- Steady state in strong system-bath coupling: mean force Gibbs state versus reaction coordinate
- von Neumann entropy and the entropy production of a damped harmonic oscillator
- Steady state in ultrastrong coupling regime: perturbative expansion and first orders
- Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach
- Quantum thermalization and vanishing thermal entanglement in the open Jaynes-Cummings model
- Enhanced entanglement in multi-bath spin-boson models
- On the Role of Non-Diagonal System-Environment Interactions in Bridge-Mediated Electron Transfer
- Quantum thermalization and thermal entanglement in the open quantum Rabi model
- Non-equilibrium boundary driven quantum systems: models, methods and properties
- Potential renormalisation, Lamb shift and mean-force Gibbs state -- to shift or not to shift?
- Nonequilibrium quantum heat transport between structured environments
- Optimal qubit-mediated quantum heat transfer via noncommuting operators and strong coupling effects
- Subtleties in the pseudomodes formalism