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 behavior of a system implies going beyond the Born approximation. Additionally, we address with this approach the initial-state problem occurring in non-Markovian master equations.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 behavior of a system implies going beyond the Born approximation. Additionally, we address with this approach the initial-state problem occurring in non-Markovian master equations.

arXiv:1402.6205Physical Review BSep 4, 201430 citations

Master equations for coupled systems

Fumio Shibata, Natsuki Hashitsume

The European Physical Journal BJun 1, 197915 citations

Higher-order Corrections to the Redfield Equation with Respect to the System-bath Coupling Based on the Hierarchical Equations of Motion

Anton Sergeevich Trushechkin

The Redfield equation describes the dynamics of a quantum system weakly coupled to one or more reservoirs and is widely used in theory of open quantum system. However, the assumption of weak system-reservoir coupling is often not fully adequate and higher-order corrections to the Redfield equation with respect to the system-bath coupling is required. Here we propose a general method of derivation of higher-order corrections to the Redfield quantum master equation based on the hierarchical equations of motion (HEOM). Also we derive conditions of validity of the Redfield equation as well as the additional secular approximation for it.The Redfield equation describes the dynamics of a quantum system weakly coupled to one or more reservoirs and is widely used in theory of open quantum system. However, the assumption of weak system-reservoir coupling is often not fully adequate and higher-order corrections to the Redfield equation with respect to the system-bath coupling is required. Here we propose a general method of derivation of higher-order corrections to the Redfield quantum master equation based on the hierarchical equations of motion (HEOM). Also we derive conditions of validity of the Redfield equation as well as the additional secular approximation for it.

arXiv:1905.05068Lobachevskii Journal of MathematicsOct 1, 201920 citations

A master equation description of coupled systems. I

P. Schwendimann

The European Physical Journal BMar 1, 19776 citations

Weak-Coupling Master Equation

Bassano Vacchini

Graduate texts in physicsJan 1, 20240 citations

Minimal two-body quantum absorption refrigerator

Bibek Bhandari, Andrew N. Jordan

We study the phenomenon of absorption refrigeration, where refrigeration is achieved by heating instead of work, in two different setups: a minimal set up based on coupled qubits and two nonlinearly coupled resonators. Considering $ZZ$ interaction between the two qubits, we outline the basic ingredients required to achieve cooling. Using local as well as global master equations, we observe that inclusion of an $XX$ type term in the qubit-qubit coupling is detrimental to cooling. We compare the cooling effect obtained in the qubit case with that of nonlinearly coupled resonators (multilevel system) where the $ZZ$ interaction translates to a Kerr-type nonlinearity. For small to intermediate strengths of nonlinearity, we observe that multilevel quantum systems, for example qutrits, give better cooling effect compared to the qubits. Using Keldysh nonequilibrium Green's function formalism, we go beyond first order sequential tunneling processes and study the effect of higher order processes on refrigeration. We find a reduced cooling effect compared to the master equation calculations.We study the phenomenon of absorption refrigeration, where refrigeration is achieved by heating instead of work, in two different setups: a minimal set up based on coupled qubits and two nonlinearly coupled resonators. Considering $ZZ$ interaction between the two qubits, we outline the basic ingredients required to achieve cooling. Using local as well as global master equations, we observe that inclusion of an $XX$ type term in the qubit-qubit coupling is detrimental to cooling. We compare the cooling effect obtained in the qubit case with that of nonlinearly coupled resonators (multilevel system) where the $ZZ$ interaction translates to a Kerr-type nonlinearity. For small to intermediate strengths of nonlinearity, we observe that multilevel quantum systems, for example qutrits, give better cooling effect compared to the qubits. Using Keldysh nonequilibrium Green's function formalism, we go beyond first order sequential tunneling processes and study the effect of higher order processes on refrigeration. We find a reduced cooling effect compared to the master equation calculations.

arXiv:2105.05835Physical review. B./Physical review. BAug 23, 202124 citations

ZZ

interaction between the two qubits, we outline the basic ingredients required to achieve cooling. Using local as well as global master equations, we observe that inclusion of an

XX

type term in the qubit-qubit coupling is detrimental to cooling. We compare the cooling effect obtained in the qubit case with that of nonlinearly coupled resonators (multilevel system) where the

ZZ

interaction translates to a Kerr-type nonlinearity. For small to intermediate strengths of nonlinearity, we observe that multilevel quantum systems, for example qutrits, give better cooling effect compared to the qubits. Using Keldysh nonequilibrium Green's function formalism, we go beyond first order sequential tunneling processes and study the effect of higher order processes on refrigeration. We find a reduced cooling effect compared to the master equation calculations.