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| Home > Publications database > Fermionic superoperator formalism for reduced density operator dynamics:new insights into the non-equilibrium Anderson model |
| Poster (Other) | FZJ-2012-00223 |
;
2012
Abstract: Recently we introduced a new formalism of fermionic superoperators in Liouville-Fock space to enable for the first time a real-time renormalization group analysis cite{Saptsov12a} of the non-equilibrium Anderson model in the stationary state. Here we show that this approach also sheds new light on physics of the relaxation of a quantum dot to the stationary state. With help of superoperators possessing a fermionic statistics we obtain new, general properties of an effective dot Liouvillian of a quantum dot which are not at all obvious in other formulations. In particular we elegantly explain a recent theoretical observation cite{Contreras12} on a relaxation of an Anderson quantum to the equilibrium state and generalize this to arbitrary order in a coupling constant $Gamma$. We furthermore, consider the non-interacting and weakly interacting quantum dots and show their generalization to "beyond of wide band limit" and "beyond of factorisable initial conditions" limits. The solution for the non-interacting case turns out to be very illustrative and intuitive: perturbation series in $Gamma$ truncates at a finite (second) order due to anti-commutation algebra of the superoperators. For the weakly interacting case in the wide band limit we show relations between perturbative series in the coupling constant $Gamma$ and interaction $U$. Finally we present a new Liouville space path-integral representation in terms of fermionic superfields and indicate useful applications of this formalism in non-equilibrium physics.
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