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Author: Neidhardt, Hagen × Author: Zagrebnov, Valentin A. × End date: 2019 × Start date: 2018 × End date: 2009 × Start date: 2000 × Has files: Yes × Type: Text ×

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    Linear non-autonomous Cauchy problems and evolution semigroups
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Neidhardt, Hagen; Zagrebnov, Valentin A.
    The paper is devoted to the problem of existence of propagators for an abstract linear non-autonomous evolution Cauchy problem of hyperbolic type in separable Banach spaces. The problem is solved using the so-called evolution semigroup approach which reduces the existence problem for propagators to a perturbation problem of semigroup generators. The results are specified to abstract linear non-autonomous evolution equations in Hilbert spaces where the assumption is made that the domains of the quadratic forms associated with the generators are independent of time. Finally, these results are applied to time-dependent Schrödinger operators with moving point interactions in 1D.
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    The effect of time-dependent coupling on non-equilibirum steady states
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Cornean, Horia D.; Neidhardt, Hagen; Zagrebnov, Valentin A.
    Consider (for simplicity) two one-dimensional semi-infinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and each of its components is at thermal equilibrium. In the remote future the system is fully coupled. We define and compute the non equilibrium steady state (NESS) generated by this evolution. We show that when restricted to the subspace of absolute continuity of the fully coupled system, the state does not depend at all on the switching. Moreover, we show that the stationary charge current has the same invariant property, and derive the Landau-Lifschitz and Landauer-Büttiker formulas.