Weak-Coupling Master Equation

Anton Sergeevich Trushechkin, Igor Vasil'evich Volovich

A system of sites weakly coupled to each other and to one or more reservoirs (open quantum network) is considered. A new quantum master equation which improves shortcomings of the master equation known in the so-called local approach is derived. The usual quantum master equation describing the weak coupling of the system with reservoir requires the knowledge of eigenvalues and eigenvectors of the Hamiltonian of the system, so it often becomes impractical. By this reason, 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. However, recently, it was reported that the local approach master equation leads to the violation of the second law of thermodynamics. We develop a systematic perturbation expansion to derive corrections to the local approach master equation. Using this improvement 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.

Gang Ren, Jian-ming Du

Chien-Chang Chen, Thomas M. Stace, Hsi‐Sheng Goan

We apply a full-polaron master equation and a weak-coupling non-Markovian master equation to describe the steady-state time-averaged properties of a driven two-level system, an electron coherently tunneling between double quantum dots (DQDs), interacting with a bosonic phonon bath. Comparing the results obtained using these two master equations with those from a recent DQD experiment and its corresponding weak-coupling theoretical method, we find that the original parameter set used in the experiment and theoretical method is not in the weak-coupling parameter regime. By using the full-polaron master equation with a slight adjustment on only the value of the interdot separation in the original experimental parameter set, we find that a reasonable fit to the experimentally measured time-averaged steady-state population data can be achieved. The adjusted interdot separation is within the possible values allowed by the geometry of the surface gates that define the DQD in the experiment. Our full-polaron equation approach does not require the special renormalization scheme employed in their weak-coupling theoretical method, and can still describe the experimental results of driving-induced phonon-enhanced steplike shoulder behaviors in the experiment. This demonstrates that the full-polaron master equation approach is a correct and efficient tool to describe the steady-state properties of a driven spin-boson model in the case of strong system-environment coupling.

Fumio Shibata, Natsuki Hashitsume

Johannes Agerskov, Frederik Nathan

We consider the evolution of open quantum systems coupled to one or more Gaussian environments. We demonstrate that such systems can be described by a Markovian quantum master equation (MQME) up to a correction that decreases exponentially with the inverse system-bath coupling strength. We provide an explicit expression for this MQME, along with rigorous bounds on its residual correction, and numerically benchmark it for an exactly solvable model. The MQME is obtained via a generalized Born-Markov approximation that can be iterated to arbitrary orders in the system-bath coupling; our error bound converges asymptotically to zero with the iteration order. Our results thus demonstrate that the non-Markovian component in the evolution of an open quantum system, while possibly inevitable, can be exponentially suppressed at weak coupling.

A. Fuliński, W. J. Kramarczyk