Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems

Abstract

We provide a rigorous construction of Markovian master equations for a wide class of quantum systems that encompass quadratic models of finite size, linearly coupled to an environment modeled by a set of independent thermal baths. Our theory can be applied for both fermionic and bosonic models in any number of physical dimensions, and does not require any particular spatial symmetry of the global system. We show that, for non-degenerate systems under a full secular approximation, the effective Lindblad operators are the normal modes of the system, with coupling constants that explicitly depend on the transformation matrices that diagonalize the Hamiltonian. Both the dynamics and the steady-state (guaranteed to be unique) properties can be obtained with a polynomial amount of resources in the system size. We also address the particle and energy current flowing through the system in a minimal two-bath scheme and find that they hold the structure of Landauer's formula, being thermodynamically consistent.

arXiv comment17 pages, 2 figures. Final version

References in corpus (74)

• Unpaired Majorana fermions in quantum wires
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• An Open-System Quantum Simulator with Trapped Ions
• Open Quantum Systems. An Introduction
• Quantum Thermodynamic Cycles and quantum heat engines
• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Keldysh Field Theory for Driven Open Quantum Systems
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Dissipation and Ultrastrong Coupling in Circuit QED
• A Dissipatively Stabilized Mott Insulator of Photons
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Quantum many-body dynamics in optomechanical arrays
• Conduction of Ultracold Fermions Through a Mesoscopic Channel
• The power of a critical heat engine
• Experimental signature of programmable quantum annealing
• Quantum and Information Thermodynamics: A Unifying Framework based on Repeated Interactions
• Open-System Dynamics of Entanglement
• On the Local and Global Approaches to Quantum Transport and Violation of the Second-law of Thermodynamics
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Markovian master equations for quantum thermal machines: local vs global approach
• Markovian Master Equations: A Critical Study
• Reconciliation of quantum local master equations with thermodynamics
• Quantum master equation for electron transport through quantum dots and single molecules
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Modeling heat transport through completely positive maps
• Observation of Quantized Conductance in Neutral Matter
• Antiferromagnetic phase transition in a nonequilibrium lattice of Rydberg atoms
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Constructing neural stationary states for open quantum many-body systems
• A positive tensor network approach for simulating open quantum many-body systems
• Testing the validity of the local and global GKLS master equations on an exactly solvable model
• Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
• The thermodynamic cost of driving quantum systems by their boundaries
• Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
• Observation of a Dissipation-Induced Classical to Quantum Transition
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Perturbative treatment of inter-site couplings in the local description of open quantum networks
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Out of equilibrium open quantum systems: a comparison of approximate Quantum Master Equation approaches with exact results
• Majorana Fermions: The race continues
• Topological phase transitions and chiral inelastic transport induced by the squeezing of light
• Non-additive dissipation in open quantum networks out of equilibrium
• Dynamics and thermodynamics of linear quantum open systems
• Cooling and Autonomous Feedback in a Bose-Hubbard chain with Attractive Interactions
• On the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan equation
• Quantum thermodynamics in strong coupling: heat transport and refrigeration
• Quantum thermodynamically consistent local master equations
• A solvable family of driven-dissipative many-body systems
• Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model
• Thermodynamic consistency of the optomechanical master equation
• A matrix product solution for a nonequilibrium steady state of an XX chain
• Thermodynamic deficiencies of some simple Lindblad operators
• Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions
• Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability
• Non-equilibrium quantum chains under multi-site Lindblad baths
• Two coupled qubits interacting with a thermal bath: A comparative study of different models
• Generic transport formula for a system driven by Markovian reservoirs
• Symmetry and block structure of the Liouvillian superoperator in partial secular approximation
• Microscopic theory of a non-equilibrium open bosonic chain
• Theory of transformation for the diagonalization of quadratic Hamiltonians
• Competing coherent and dissipative dynamics close to quantum criticality
• Going beyond Local and Global approaches for localized thermal dissipation
• Bath assisted transport in a three-site spin chain: global {\sl vs} local approach
• Local master equations may fail to describe dissipative critical behavior
• Engineered Open Systems and Quantum Simulations with Atoms and Ions
• Nonreciprocal Quantum Transport at Junctions of Structured Leads
• Diverging conductance at the contact between random and pure quantum XX spin chains
• Number-resolved master equation approach to quantum measurement and quantum transport

Cited by in corpus (25)

• Coherent and dissipative dynamics at quantum phase transitions
• The Ising critical quantum Otto engine
• Quantum heat engine with long-range advantages
• Quantum critical systems with dissipative boundaries
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Logarithmic entanglement scaling in dissipative free-fermion systems
• Poor man's approach to thermalization in Luttinger liquid
• Many-body quantum heat engines based on free-fermion systems
• Kibble-Zurek scaling due to environment temperature quench in the transverse field Ising model
• Universal cooling dynamics toward a quantum critical point
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Multiparticle Quantum Heat Engine: Exploring the Impact of Criticality on Efficiency
• Thermal-bath effects in quantum quenches within quantum critical regimes
• Impossibility of bosonic autonomous entanglement engines in the weak-coupling limit
• Universal Quench Dynamics of an Open Quantum System
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Long-range Kitaev chain in a thermal bath: Analytic techniques for time-dependent systems and environments
• Dissipation and non-thermal states in cryogenic cavities
• Inelastic tunneling through normal and superconducting junctions in the presence of photonic bath within Lindbladian formalism
• Exact non-Markovian master equations: a generalized derivation for Gaussian systems
• Exceptional point in self-consistent Markovian master equations
• Topological signatures in a weakly dissipative Kitaev chain of finite length
• Diffusion coefficients preserving long-time correlations: Consequences on the Einstein relation and on entanglement in a bosonic Bogoliubov system
• Dual effects of Lamb Shift in Quantum Thermodynamical Systems