Annales Henri Poincaré

, Volume 10, Issue 7, pp 1223–1249 | Cite as

Dynamical Phase Transition for a Quantum Particle Source



We analyze the time evolution describing a quantum source for non-interacting particles, either bosons or fermions. The growth behavior of the particle number (trace of the density matrix) is investigated, leading to spectral criteria for sublinear or linear growth in the fermionic case, but also establishing the possibility of exponential growth for bosons. We further study the local convergence of the density matrix in the long time limit and prove the semi-classical limit.


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  1. 1.
    Alicki R., Fannes M., Haegeman B., Vanpeteghem D.: Coherent transport and dynamical entropy for fermionic systems. J. Stat. Phys. 113, 549–574 (2003)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alicki, R., Lendi, K.: Quantum dynamical semigroups and applications, Lecture Notes in Physics, vol. 717. Springer, Berlin (2007)Google Scholar
  3. 3.
    Attal, S., Joye, A., Pillet, C.-A.: Open Quantum Systems III: Recent Developments. Lecture Notes in Mathematics, vol. 1882. Springer, Berlin (2006)Google Scholar
  4. 4.
    Damoen B., Vanheuverzwijn P., Verbeure A.: Completely positive maps on the CCR. Lett. Math. Phys. 2, 161–166 (1978)CrossRefADSGoogle Scholar
  5. 5.
    Davies E.B.: Quantum Theory of Open Systems. Academic Press, London (1976)MATHGoogle Scholar
  6. 6.
    Kato T.: Perturbation Theory for Linear Operators, 2nd edn. Springer, Berlin (1976)MATHGoogle Scholar
  7. 7.
    Martinez A.: An Introduction to Semiclassical and Microlocal Analysis. Springer, New York (2002)MATHGoogle Scholar
  8. 8.
    Nier F.: Asymptotic analysis of a scaled Wigner equation and quantum scattering. Transp. Theory Stat. Phys. 24, 591–628 (1995)MATHCrossRefMathSciNetADSGoogle Scholar
  9. 9.
    Perry P.A.: Scattering Theory by the Enss Method. Harwood Academic Publishers, New York (1983)MATHGoogle Scholar
  10. 10.
    Reed M., Simon B.: Methods of Modern Mathematical Physics II. Academic Press, London (1975)MATHGoogle Scholar
  11. 11.
    Reed M., Simon B.: Methods of Modern Mathematical Physics III. Academic Press, London (1979)MATHGoogle Scholar

Copyright information

© Birkhäuser Verlag AG, Basel/Switzerland 2010

Authors and Affiliations

  1. 1.Technische Universität München Zentrum MathematikGarchingGermany

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