Finite coupling effects in double quantum dots near equilibrium
arXiv:1610.00866 · doi:10.1103/PhysRevB.95.035428
Abstract
A weak coupling quantum master equation provides reliable steady-state results only in the van Hove limit, i.e., when the system-lead coupling approaches zero. Recently, J. Thingna et al. [Phys. Rev. E 88, 052127 (2013)] proposed an alternative approach, based on an analytic continuation of the Redfield solution, to evaluate the reduced density matrix up to second order in the system-bath coupling. The approach provides accurate results for harmonic oscillator and spin-bosonic systems. We apply this approach to study fermionic systems and the calculation on an exactly solvable double quantum dot system shows that the method is rigorously valid only near equilibrium, i.e., linear response regime. We further compare to the Redfield and the secular Redfield (Lindblad-type) master equations that are inaccurate in all parameter regimes. Lastly, we consider the non-trivial problem of strong Coulomb interaction and illustrate the interplay between system-lead coupling, inter-dot tunneling, and Coulomb strength that can be captured only via the analytic continuation method.
8 pages, 4 figures; typos corrected
References in corpus (8)
- A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
- Kondo effect in quantum dots
- Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
- The Accuracy of Perturbative Master Equations
- New method for studying steady states in quantum impurity problems: The interacting resonant level model
- The formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution
- Improved Dyson series expansion for steady-state quantum transport beyond the weak coupling limit - divergences and resolution
- Thermoelectric transport through a quantum nanoelectromechanical system and its backaction