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Browsing by Author "Lange, Horst"

Now showing 1 - 4 of 4
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    A discrete-velocity, stationary Wigner equation
    Arnold, Anton; Lange, Horst; Zweifel, Paul F. (AIP Publishing, 2000-11)
    This paper is concerned with the one-dimensional stationary linear Wigner equation, a kinetic formulation of quantum mechanics. Specifically, we analyze the well-posedness of the boundary value problem on a slab of the phase space with given inflow data for a discrete-velocity model. We find that the problem is uniquely solvable if zero is not a discrete velocity. Otherwise one obtains a differential-algebraic equation of index 2 and, hence, the inflow data make the system overdetermined. (C) 2000 American Institute of Physics. [S0022-2488(00)00112-2].
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    Dissipation in Wigner-Poisson systems
    Lange, Horst; Zweifel, Paul F. (AIP Publishing, 1994-04)
    The Wigner-Poisson (WP) system (or quantum Vlasov-Poisson system) is modified to include dissipative terms in the Hamiltonian. By utilizing the equivalence of the WP system to the Schrodinger-Poisson system, global existence and uniqueness are proved and regularity properties are deduced. The proof differs somewhat from that for the nondissipative case treated previously by Brezzi-Markowich and Illner et al.; in particular the Hille-Yosida Theorem is used since the linear evolution is not unitary, and a Liapunov function is introduced to replace the energy, which is not conserved.
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    Inflow boundary conditions in quantum transport theory
    Lange, Horst; Toomire, Bruce V.; Zweifel, Paul F. (Hindawi Publishing Corporation, 1999)
    A linear (given potential) steady-state Wigner equation is considered in conjunction with inflow boundary conditions and relaxation-time terms. A brief review of the use of inflow conditions in the classical case is also discussed. An analytic expansion of solutions is shown and a recursion relation derived for the given problem under certain regularity assumptions on the given inflow data. The uniqueness of the physical current of the solutions is shown and a brief discussion of the lack of charge conservation associated with the relaxation-time is given.
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    Time-dependent dissipation in nonlinear Schrodinger systems
    Lange, Horst; Toomire, Bruce V.; Zweifel, Paul F. (AIP Publishing, 1995-03)
    A coupled nonlinear Schrödinger–Poisson equation is considered which contains a time‐dependent dissipation function as a specific model of dissipation effects in nonlinear quantum transport theory and other areas. The Wigner–Poisson equation associated with this system is derived. Using conservation and quasiconservation laws and certain growth assumptions for the nonlinearities and the dissipation function, global existence of solutions to the Cauchy problem of the time‐dependent Schrödinger–Poisson system is shown both for small (attractive case) or arbitrary data (repulsive case).