Regensburg 2019 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 46: Quantum Dots, Quantum Wires, Point Contacts

TT 46.11: Talk

Wednesday, April 3, 2019, 17:45–18:00, H22

Feynman-Vernon approach to transport in interacting quantum dots beyond the weak tunneling regime — •Luca Magazzù and Milena Grifoni — Universität Regensburg, Regensburg, Germany

Quantum transport setups based on quantum dots display a rich variety of transport regimes, also involving exquisitely many-body phenomena (e.g. the Kondo effect), that arise by varying the relative magnitude of intra-dot interactions and tunnel coupling to the electronic reservoirs (leads). Despite the large variety of available approximation schemes, a unique framework enabling one to satisfactorily address this complexity is still missing.

In this work we discuss a path integral approach to transport where the trace over the leads degrees of freedom is performed exactly. As a result, formally exact expressions for the dot dynamics and the current are obtained, where the effect of the coupling to the leads is encapsulated in the Feynman-Vernon influence functional, a functional of the Grassmann-valued paths of the dot variables. In the presence of interactions, the path integral is not exactly solvable. Nevertheless, expansion of the influence functional in the number of tunneling events, in conjunction with a convenient parametrization of the paths allowed by properties of the Grassmann variables, provides a diagrammatic representation of the dynamics and offers an efficient means to systematically sum diagram classes. We propose a resummation which recovers results known from the nonperturbative resonant tunneling and second order von Neumann approximations and beyond.