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Article Dans Une Revue Journal of Mathematical Physics Année : 2019

TRANSPORT OF A QUANTUM PARTICLE IN A TIME-DEPENDENT WHITE-NOISE POTENTIAL

Peter D. Hislop
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Jeffrey Schenker
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Résumé

We show that a quantum particle in R d , for d 1, subject to a white-noise potential, moves superballistically in the sense that the mean square displacement x 2 ρ(x, x, t) dx grows like t 3 in any dimension. The white noise potential is Gaussian distributed with an arbitrary spatial correlation function and a delta correlation function in time. This is a known result in one dimension [7, 15]. The energy of the system is also shown to increase linearly in time. We also prove that for the same white-noise potential model on the lattice Z d , for d 1, the mean square displacement is diffusive growing like t 1. This behavior on the lattice is consistent with the diffusive behavior observed for similar models in the lattice Z d with a time-dependent Markovian potential [17].
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Dates et versions

hal-01847857 , version 1 (24-07-2018)
hal-01847857 , version 2 (29-04-2019)

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Peter D. Hislop, Kay Kirkpatrick, Stefano Olla, Jeffrey Schenker. TRANSPORT OF A QUANTUM PARTICLE IN A TIME-DEPENDENT WHITE-NOISE POTENTIAL. Journal of Mathematical Physics, 2019, 60 (8), pp.083303. ⟨10.1063/1.5054017⟩. ⟨hal-01847857v2⟩
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