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 iβ∂tαu=−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 language | English |
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Article number | 109033 |
Journal | Applied Mathematics Letters |
Volume | 152 |
DOIs | |
State | Published - Jun 2024 |
Bibliographical note
Publisher Copyright:© 2024 Elsevier Ltd
Keywords
- Quantum diffusion
- Schrödinger equation
- Time-fractional derivative
ASJC Scopus subject areas
- Applied Mathematics