Hannover 2016 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 15: Quantum Effects: Disorder

Q 15.3: Vortrag

Montag, 29. Februar 2016, 17:30–17:45, f442

Analytical description of wave packet expansion in a one dimensional disordered potential — •Juan Pablo Ramirez Valdes, Andreas Buchleitner, and Thomas Wellens — Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3a, 79104 Freiburg, Germany

We present an analytic description of the asymptotic disorder-averaged probability density of an initially strongly confined wave packet in a one-dimensional weak, random potential with finite correlation length. At long times, the expansion of the wave packet comes to a halt due to destructive interferences leading to Anderson localization, the signature of which is the exponential decay of the energy eigenfunctions. But in the case of a wave packet, there is an additional element in the description: the asymptotic state is determined by the superposition of partial waves with different energies E. Using diagrammatic techniques, it is possible to calculate the asymptotic state at fixed energy E [1]. Combining this result with a self-consistent equation for the spectral density of the wave packet [2], we derive an analytical expression for the asymptotic average density, which is compared with the results of numerical simulations.

[1] V. L. Berezinskii, Sov. Phys. JETP 38, 620 (1974).

[2] Bertrand I. Halperin, Phys. Rev. 139, A104 (1965).