Time local master equation connecting the Born and Markov approximations

Abstract

We present an exact expansion of the master equation for an open quantum system. The resulting equation is time local and enables us to calculate clearly defined higher order corrections to the Born-Markov approximation. In particular, we show that non-Markovian terms are of the same order of magnitude as higher order terms in the system-bath coupling. As a result we emphasize that analyzing non-Markovian behaviour of a system implies going beyond Born approximation. Additionally, we address with this approach the initial state problem occurring in non-Markovian master equations.

arXiv comment9 pages. 2 figure, published in Phys. Rev. B

References in corpus (30)

• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Franck-Condon blockade and giant Fano factors in transport through single molecules
• Phonon effects in molecular transistors: Quantum and classical treatment
• Mesoscopic quantum transport: Resonant tunneling in the presence of strong Coulomb interaction
• General non-Markovian dynamics of open quantum systems
• Zero-bias anomalies and boson-assisted tunneling through quantum dots
• Quantum Dot Cavity-QED in the Presence of Strong Electron-Phonon Interactions
• Tunneling through molecules and quantum dots: master-equation approaches
• Switching via quantum activation: A parametrically modulated oscillator
• Cotunneling at resonance for the single-electron transistor
• Rigorous Born Approximation and beyond for the Spin-Boson Model
• Transport through a double quantum dot in the sequential- and co- tunneling regimes
• Dynamics of the spin-boson model with a structured environment
• Shot noise in tunneling transport through molecules and quantum dots
• Adiabatic pumping through a quantum dot with coulomb interactions: A perturbation expansion in the tunnel coupling
• Non-perturbative stochastic method for driven spin-boson model
• Non-Markovian qubit dynamics in the presence of 1/f noise
• Cotunneling and non-equilibrium magnetization in magnetic molecular monolayers
• Reduced density matrix for nonequilibrium steady states: A modified Redfield solution approach
• Lasing without Inversion in Circuit Quantum Electrodynamics
• Dissipation in Josephson qubits
• Vibrational absorption sidebands in the Coulomb blockade regime of single-molecule transistors
• Circuit-QED analogue of a single-atom injection maser: Lasing, trapping states and multistability
• Spin-boson dynamics beyond conventional perturbation theories
• The quench dynamics of a dissipative quantum system: a renormalization group study
• Dynamical Steady-States in Driven Quantum Systems
• Spin pumping through quantum dots
• Quantum critical temperature of a modulated oscillator
• Solid-State Spin-Photon Quantum Interface without Spin-Orbit Coupling

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