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Dissipation in Wigner–Poisson systems (1994)

Lange, Horst ; Zweifel, P. F.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 35 (1994), S. 1513-1521

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: 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 Schrödinger–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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.530887

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