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Author: Neidhardt, Hagen × Author: Wilhelm, Lukas × End date: 2019 × Start date: 2010 × Version: publishedVersion × WGL Institute: WIAS ×

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    The Cayley transform applied to non-interacting quantum transport : dedicated to the memory of Markus Büttiker (1950-2013)
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Cornean, Horia D.; Neidhardt, Hagen; Wilhelm, Lukas; Zagrebnov, Valentin A.
    We extend the Landauer-Büttiker formalism in order to accommodate both unitary and self-adjoint operators which are not bounded from below. We also prove that the pure point and singular continuous subspaces of the decoupled Hamiltonian do not contribute to the steady current. One of the physical applications is a stationary charge current formula for a system with four pseudo-relativistic semi-infinite leads and with an inner sample which is described by a Schrödinger operator defined on a bounded interval with dissipative boundary conditions. Another application is a current formula for electrons described by a one dimensional Dirac operator; here the system consists of two semi-infinite leads coupled through a point interaction at zero.
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    A new model for quantum dot light emitting-absorbing devices : dedicated to the memory of Pierre Duclos
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Neidhardt, Hagen; Wilhelm, Lukas; Zagrebnov, Valentin A.; Duclos, Pierre
    Motivated by the Jaynes-Cummings (JC) model, we consider here a quantum dot coupled simultaneously to a reservoir of photons and to two electric leads (free-fermion reservoirs). This Jaynes-Cummings-Leads (JCL) model makes possible that the fermion current through the dot creates a photon flux, which describes a light-emitting device. The same model also describes a transformation of the photon flux into a fermion current, i.e. a quantum dot light-absorbing device. The key tool to obtain these results is an abstract Landauer-Büttiker formula.