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Rate of Decoherence for an Electron Weakly Coupled to a Phonon Gas

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Abstract

We study the dynamics of an electron weakly coupled to a phonon gas. The initial state of the electron is the superposition of two spatially localized distant bumps moving towards each other, and the phonons are in a thermal state. We investigate the dynamics of the system in the kinetic regime and show that the time evolution makes the non-diagonal terms of the density matrix of the electron decay, destroying the interference between the two bumps. We show that such a damping effect is exponential in time, and the related decay rate is proportional to the total scattering cross section of the electron-phonon interaction.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via R. Cozzi 53, 20125, Milan, Italy

    Riccardo Adami

  2. Mathematisches Institut der Ludwig-Maximilians-Universität München, 39 Theresienstr., 80333, Munich, Germany

    László Erdős

Authors
  1. Riccardo Adami
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  2. László Erdős
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Correspondence to Riccardo Adami.

Additional information

R.A. is grateful to the Mathematisches Institut der Ludwig-Maximilians-Universität München for the kind hospitality, and to the Istituto Nazionale di Alta Matematica for providing financial support through the “Borsa per l’Estero INdAM” fellowship.

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Adami, R., Erdős, L. Rate of Decoherence for an Electron Weakly Coupled to a Phonon Gas. J Stat Phys 132, 301–328 (2008). https://doi.org/10.1007/s10955-008-9561-8

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  • DOI: https://doi.org/10.1007/s10955-008-9561-8

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