Phenomenological position and energy resolving Lindblad approach to quantum kinetics

Abstract

A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular approximation. This allows for the treatment of systems, where coherences are generated by the bath couplings while avoiding the negative occupations occurring in the Bloch-Wangsness-Redfield kinetic equations. The versatility and accuracy of the approach is verified by its application to three entirely different physical systems: (i) electric transport through a double-dot system coupled to electronic reservoirs, (ii) exciton kinetics in coupled chromophores in the presence of a heat bath, and (iii) the simulation of quantum cascade lasers, where the coherent electron transport is established by scattering with phonons and impurities.

Double quantum-dot engine fueled by entanglement between electron spins

“…Equation (5) is solved using the time-dependent Lindblad equation solver included in the Python package QuTiP. 41,42 The jump operators A i,σ for the different spin flip processes, expressed in the time-dependent eigenbasis |a t of H DQD (t), are given by A i,σ = a,a |a t γν(|E a a (t)|) · (n(|E a a (t)|) + θ(E a a (t))) × a t |c † i,σ c i,σ |a t a t |, 43 where E a a = E a − E a and θ denotes the Heaviside step-function. In order to solve Eq.…”

Electron extraction from excited quantum dots with higher order coulomb scattering

“…The Lindblad jump operators in equations (8) and (9) do not carry energetic information about the interactions between the system and bath. A scheme to incorporate these aspects is the Position and Energy Resolving Lindblad approach (PERLind) [39]. Let the states ñ ñ a b , , | | etc be an eigenbasis of Ĥ with E E , , a b etc as the corresponding eigenenergies.…”

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

“…We also shortly describe a particular form of the Lindblad equation in Appendix F, which takes first-order processes into consideration. It is similar to the first-order Redfield or first-order von Neumann methods, but additionally preserves positivity of the reduced density matrix [32]. In Appendix G we give suggestions in which cases which approach to use.…”

“…where the matrix elements of the jump operators are defined as [32] L cb,α = 2πν F f (+x α cb )T bc,α , L bc,α = 2πν F f (−x α cb )T bc,α . + Equation (F.1) is of the first-order type in the rates Γ and can describe the sequential tunneling in the presence of coherences.…”

“…In particular, we address the so-called Pauli master equation [6,26,27], the first-order Redfield approach [6,28,29], the first/second-order von Neumann approaches [19,30], and a particular form of the Lindblad equation [31,32], and apply these methods for tunneling models, where the quantum dots can have arbitrary Coulomb interactions [33]. Even though there is a lot of literature on such methods, there is no publicly-available, well-documented package, which is easy to apply for quantum dot model systems.…”