Phys. Rev. Lett. 77, 1198–1201 (1996)Long Time Asymptotics for Quantum Particles in a Periodic PotentialReceived 21 March 1996; published in the issue dated 12 August 1996 We study a quantum particle in a periodic potential and subject to slowly varying electromagnetic potentials. It is proved that, in the Heisenberg picture, the scaled position operator εx(ε-1t) has a limit as ε→0. The limit operator is determined by the semiclassical equations of motion, which implies that for long times the wave packet is well approximated by the semiclassical evolution. From our result we infer the hydrodynamic limit, q→0,t→∞,qt = const, of the structure function S(q,t) of a fluid of noninteracting fermions in a crystal potential. © 1996 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.77.1198
DOI:
10.1103/PhysRevLett.77.1198
PACS:
03.65.Sq, 02.30.Sa, 05.30.Fk
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