Transport of a quantum particle in a time-dependent white-noise potential
Hislop, Peter; Kirkpatrick, Kay; Olla, Stefano; Schenker, Jeffrey (2019), Transport of a quantum particle in a time-dependent white-noise potential, Journal of Mathematical Physics, 60, 8. 10.1063/1.5054017
TypeArticle accepté pour publication ou publié
Journal nameJournal of Mathematical Physics
American Institute of Physics
MetadataShow full item record
Department of Mathematics
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Department of Mathematics [Lansing]
Abstract (EN)We show that a quantum particle in ℝd, 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 t3 in any dimension. The white-noise potential is Gaussian distributed with an arbitrary spatial correlation function and a delta correlation function in time. Similar results were established in one dimension by Jayannavar and Kumar [Phys. Rev. Lett. 48(8), 553–556 (1982)], and for any dimension using different methods by Fischer et al. [Phys. Rev. Lett. 73(12), 1578–1581 (1994)]. We also prove that for the same white-noise potential model on the lattice ℤd, for d ⩾ 1, the mean square displacement is diffusive growing like t1. This behavior on the lattice is consistent with the diffusive behavior observed for similar models on the lattice ℤd with a time-dependent Markovian potential by Kang and Schenker [J. Stat. Phys. 134, 1005–1022 (2009)].
Subjects / Keywordssuperballistic motion; Quantum Transport
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