Asymptotic analysis of time-fractional quantum diffusion
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arXiv
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| Format: | Preprint |
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2024
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| author | Hislop, Peter D. Soccorsi, Eric |
| author_facet | Hislop, Peter D. Soccorsi, Eric |
| contents | We study the large-time asymptotics of the mean-square displacement for the time-fractional Schrodinger equation in $\mathbb{R}^d$. We define the time-fractional derivative by the Caputo derivative and we consider the initial-value problem for the free evolution of wave packets in $\mathbb{R}^d$ governed by the time-fractional Schrodinger equation $ i^β\partial_t^αu = - Δu, ~~~~u(t=0) = u_0$, parameterized by two indices $α, β\in (0,1]$. 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 $α=β$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_10918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic analysis of time-fractional quantum diffusion Hislop, Peter D. Soccorsi, Eric Analysis of PDEs Mathematical Physics 81Q99 35Q40 35R11 We study the large-time asymptotics of the mean-square displacement for the time-fractional Schrodinger equation in $\mathbb{R}^d$. We define the time-fractional derivative by the Caputo derivative and we consider the initial-value problem for the free evolution of wave packets in $\mathbb{R}^d$ governed by the time-fractional Schrodinger equation $ i^β\partial_t^αu = - Δu, ~~~~u(t=0) = u_0$, parameterized by two indices $α, β\in (0,1]$. 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 $α=β$. |
| title | Asymptotic analysis of time-fractional quantum diffusion |
| topic | Analysis of PDEs Mathematical Physics 81Q99 35Q40 35R11 |
| url | https://arxiv.org/abs/2401.10918 |