Asymptotic analysis of time-fractional quantum diffusion

Peter D. Hislop, Éric Soccorsi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study the large-time asymptotics of the mean-square displacement for the time-fractional Schrödinger equation in Rd. We define the time-fractional derivative by the Caputo derivative. We consider the initial-value problem for the free evolution of wave packets in Rd governed by the time-fractional Schrödinger equation iβtαu=−Δu, with initial condition u(t=0)=u0, parameterized by two indices α,β∈(0,1]. We show distinctly different long-time evolution of the mean square displacement according to the relation between α and β. In particular, asymptotically ballistic motion occurs only for α=β.

Original languageEnglish
Article number109033
JournalApplied Mathematics Letters
Volume152
DOIs
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Ltd

Keywords

  • Quantum diffusion
  • Schrödinger equation
  • Time-fractional derivative

ASJC Scopus subject areas

  • Applied Mathematics

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