Perturbative treatment of inter-site couplings in the local description of open quantum networks

Abstract

The problem of construction of a quantum master equation for a system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. Microscopic derivation of a quantum master equation requires a diagonalization of the Hamiltonian of the network, which can be a difficult task. When the inter-site couplings are weak, the local approach, which neglects the influence of the inter-site couplings on the system-reservoir couplings, is often used. Recently, some doubts were cast to the consistency of the local approach. We develop a systematic perturbation expansion to derive corrections to the local approach and establish its range of validity. Using this extension of the local approach, we derive an expression for the heat flux for a particular model and show that it does not violate the second law of thermodynamics.

5 pages

References in corpus (11)

• Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
• Laser cooling of a nanomechanical resonator mode to its quantum ground state
• On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
• Modeling heat transport through completely positive maps
• Origin of long-lived oscillations in 2D-spectra of a Quantum Vibronic Model: Electronic vs Vibrational coherence
• On apparent breaking the second law of thermodynamics in quantum transport studies
• Perturbative treatment of intercenter coupling in Redfield theory
• Quantum Multipole Noise and Generalized Quantum Stochastic Equations
• Quantum optical master equation for solid-state quantum emitters
• Non-equilibrium quantum systems: Divergence between global and local descriptions
• Spintronics-based mesoscopic heat engine

Cited by in corpus (85)

• Markovian master equations for quantum thermal machines: local vs global approach
• Reconciliation of quantum local master equations with thermodynamics
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Quantum thermal absorption machines: refrigerators, engines and clocks
• Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
• Unified Gorini-Kossakowski-Lindblad-Sudarshan quantum master equation beyond the secular approximation
• Non-additive dissipation in open quantum networks out of equilibrium
• Coherence-enhanced constancy of a quantum thermoelectric generator
• Quantum correlations and thermodynamic performances of two-qubit engines with local and collective baths
• Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths
• Autonomous Rotor Heat Engine
• A thermodynamically consistent Markovian master equation beyond the secular approximation
• Quantum coherence, many-body correlations, and non-thermal effects for autonomous thermal machines
• An operational approach to quantum stochastic thermodynamics
• Quantum thermodynamics in strong coupling: heat transport and refrigeration
• Quantum thermodynamically consistent local master equations
• Boosting the performance of small autonomous refrigerators via common environmental effects
• Two coupled qubits interacting with a thermal bath: A comparative study of different models
• Irreversible quantum evolution with quadratic generator: Review
• Symmetry and block structure of the Liouvillian superoperator in partial secular approximation
• Local master equations bypass the secular approximation
• Many-body open quantum systems beyond Lindblad master equations
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems
• Nonequilibrium quantum absorption refrigerator
• Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations
• Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
• Pushing the limits of the reaction-coordinate mapping
• Searching for Lindbladians obeying local conservation laws and showing thermalization
• Lyapunov equation in open quantum systems and non-Hermitian physics
• A brief journey through collision models for multipartite open quantum dynamics
• Pseudomode approach and vibronic non-Markovian phenomena in light harvesting complexes
• Dark states and delocalization: competing effects of quantum coherence on the efficiency of light harvesting systems
• Going beyond Local and Global approaches for localized thermal dissipation
• The smallest absorption refrigerator: the thermodynamics of a system with quantum local detailed balance
• Wigner entropy production and heat transport in linear quantum lattices
• Classical emulation of quantum-coherent thermal machines
• Necessarily transient quantum refrigerator
• Response theory for nonequilibrium steady-states of open quantum systems
• Flows in nonequilibrium quantum systems and quantum photosynthesis
• Local master equations may fail to describe dissipative critical behavior
• Higher-order corrections to the Redfield equation with respect to the system-bath coupling based on the hierarchical equations of motion
• Bath assisted transport in a three-site spin chain: global {\sl vs} local approach
• Sub-diffusive phases in open clean long-range systems
• Non-Markovian evolution of multi-level system interacting with several reservoirs. Exact and approximate
• Thermodynamics of a continuously monitored double quantum dot heat engine in the repeated interactions framework
• Quantum-enhanced performance in superconducting Andreev-reflection engines
• Sudden death of entanglement induced by a minimal thermal environment
• Learning the best thermoelectric nanoscale heat engines through evolving network topology
• Notes on the SYK model in real time
• Active beam splitting attack applied to differential phase shift quantum key distribution protocol
• Exact steady state of the open XX-spin chain: entanglement and transport properties
• Quantum Models of Consciousness from a Quantum Information Science Perspective
• On extrema of the objective functional for short-time generation of single qubit quantum gates
• Quantum master equation for many-body systems: Derivation based on the Lieb-Robinson bound
• Entropy production in the mesoscopic-leads formulation of quantum thermodynamics
• Time dependent Markovian master equation beyond the adiabatic limit
• Conditional fluctuation theorems and entropy production for monitored quantum systems under imperfect detection
• Effective Gibbs state for averaged observables
• Does canonical quantization lead to GKSL dynamics?
• Certifying quantum enhancements in thermal machines beyond the Thermodynamic Uncertainty Relation
• Exact non-Markovian evolution with multiple reservoirs
• Kraus operators for a pair of interacting qubits: a case study
• Effect of inter-system coupling on heat transport in a microscopic collision model
• Complete Positivity and Thermal Relaxation in Quadratic Quantum Master Equations
• Holographic control of information and dynamical topology change for composite open quantum systems
• Thermodynamically consistent master equation based on subsystem eigenstates
• Bounds on skewness and kurtosis of steady state currents
• Analytical solution of the open dispersive Jaynes-Cummings model and perturbative analytical solution of the open quantum Rabi model
• On analysis in differential algebras and modules
• A Thermodynamic Framework for Coherently Driven Systems
• Leveraging collective effects for thermometry in waveguide quantum electrodynamics
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• Perturbative treatment for stationary state of local master equation
• Numerical implementation of the partial secular approximation and unified master equation in structured open quantum systems
• Simultaneous photon and phonon lasing in a two-tone driven optomechanical system
• Dynamics of a dispersively coupled transmon qubit in the presence of a noise source embedded in the control line
• Model of vibrones in quantum photosynthesis as an analog of model of laser
• Davies equation without the secular approximation: Reconciling locality with quantum thermodynamics for open quadratic systems
• Dual effects of Lamb Shift in Quantum Thermodynamical Systems
• Evolution of the holographic entanglement entropy quantities for composite quantum systems
• Quantum reservoir computing in Jaynes-Cummings models: Nonlinear memory and time-series prediction
• Self-adjoint approximations of degenerate Schrodinger operator
• Open harmonic chain without secular approximation
• Semidefinite programming for understanding the limitations of Lindblad equations
• Nonadiabatic evolution and thermodynamics for a boundary-driven system with a weak intrasubsystem interaction