Abstract
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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Alicki R., Fannes M., Haegeman B., Vanpeteghem D.: Coherent transport and dynamical entropy for fermionic systems. J. Stat. Phys. 113, 549–574 (2003)
Alicki, R., Lendi, K.: Quantum dynamical semigroups and applications, Lecture Notes in Physics, vol. 717. Springer, Berlin (2007)
Attal, S., Joye, A., Pillet, C.-A.: Open Quantum Systems III: Recent Developments. Lecture Notes in Mathematics, vol. 1882. Springer, Berlin (2006)
Damoen B., Vanheuverzwijn P., Verbeure A.: Completely positive maps on the CCR. Lett. Math. Phys. 2, 161–166 (1978)
Davies E.B.: Quantum Theory of Open Systems. Academic Press, London (1976)
Kato T.: Perturbation Theory for Linear Operators, 2nd edn. Springer, Berlin (1976)
Martinez A.: An Introduction to Semiclassical and Microlocal Analysis. Springer, New York (2002)
Nier F.: Asymptotic analysis of a scaled Wigner equation and quantum scattering. Transp. Theory Stat. Phys. 24, 591–628 (1995)
Perry P.A.: Scattering Theory by the Enss Method. Harwood Academic Publishers, New York (1983)
Reed M., Simon B.: Methods of Modern Mathematical Physics II. Academic Press, London (1975)
Reed M., Simon B.: Methods of Modern Mathematical Physics III. Academic Press, London (1979)
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Communicated by Jean Bellissard.
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Butz, M., Spohn, H. Dynamical Phase Transition for a Quantum Particle Source. Ann. Henri Poincaré 10, 1223–1249 (2010). https://doi.org/10.1007/s00023-010-0021-z
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DOI: https://doi.org/10.1007/s00023-010-0021-z