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Diffusion for a Quantum Particle Coupled to Phonons in d ≥ 3

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Abstract

We prove diffusion for a quantum particle coupled to a field of bosons (phonons or photons). The importance of this result lies in the fact that our model is fully Hamiltonian and randomness enters only via the initial (thermal) state of the bosons. This model is closely related to the one considered in (De Roeck, Fröhlich, Commun Math Phys 303:613–707, 2011) but various restrictive assumptions of the latter have been eliminated. In particular, depending on the dispersion relation of the bosons, the present result holds in dimension d ≥ 3 and no severe infrared conditions on the coupling are necessary.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120, Heidelberg, Germany

    W. De Roeck

  2. Department of Mathematics, University of Helsinki, P.O. Box 68, 00014, Helsinki, Finland

    A. Kupiainen

Authors
  1. W. De Roeck
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  2. A. Kupiainen
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Correspondence to W. De Roeck.

Additional information

Communicated by H.-T. Yau

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De Roeck, W., Kupiainen, A. Diffusion for a Quantum Particle Coupled to Phonons in d ≥ 3. Commun. Math. Phys. 323, 889–973 (2013). https://doi.org/10.1007/s00220-013-1794-y

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  • DOI: https://doi.org/10.1007/s00220-013-1794-y

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