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Contributions to Plasma Physics

Localization of Coherent Wave Packets in Plasmas due to Decoherence

Christian Gocke, GERD RÖPKE

Published Jun 6, 2007• 4 citations
Publisher

Abstract

Abstract Localization of electron and ion states in a plasma is considered, applying the picture of a test particle in a dissipative environment. The plasma environment is represented by the dielectric function. For the reduced statistical operator a quantum master equation in Born‐Markov‐approximation can be used to quantify the influence of the dissipative background, which gives rise to decoherence and friction. We compare localization of ions due to collisional decoherence with the electronic part with screened interaction and localization by the thermal radiation field. The usual procedure to treat ions classically and electrons as quantum objects is supported by comparing the width of robust states and the mean distance in plasmas. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/ctpp.200710039

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Abstract A quantitative analysis of the electron decoherence is performed in the case where an electron interacts with an environment consisting of a phonon bath at a given temperature T. In particular we study the decoherence in terms of the entanglement formation between the electron, initially described by a Gaussian wavepacket, and the environment by using the linear entropy written in terms of the Wigner function. In our work we evaluate, in a rigorous fully quantum mechanical approach, the electron‐phonon interaction using the Wigner‐function formalism. The problem is numerically solved for different time steps, up to the lowest order in the Neumann expansion. Our numerical procedure allows to analyze the system in different conditions and to understand the effect of the electron velocity and of the phonon momenta on the entanglement formation. Results are obtained in a one‐dimensional silicon system but they can be considered indicative of a more general behaviour. The Wigner function describing the electron and the phonon bath is evaluated by means of Neumann series, whose terms may be graphically represented by the so‐called Wigner paths. They are orbits in the Wigner phase‐space and are formed by ballistic free flights separated by scattering processes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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