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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.20488 |
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| _version_ | 1866908730550910976 |
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| author | Breteaux, Sébastien Faupin, Jérémy Grasselli, Viviana |
| author_facet | Breteaux, Sébastien Faupin, Jérémy Grasselli, Viviana |
| contents | We establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle, starting in a convex set $X\subset\mathbb{R}^d$ at $t=0$, to reach a convex set $Y\subset\mathbb{R}^d$ at a time $t>0$, is bounded by $e^{-2δ}$ where $δ$ is the distance from $Y$ to the section at time $t$ of the light cone generated by $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Decay outside of the Light Cone for the Pseudo-Relativistic Non-Autonomous Schrödinger Equation Breteaux, Sébastien Faupin, Jérémy Grasselli, Viviana Mathematical Physics Analysis of PDEs We establish a maximal velocity bound for a pseudo-relativistic quantum particle in an external time-dependent potential. Our estimate shows that the probability for the particle, starting in a convex set $X\subset\mathbb{R}^d$ at $t=0$, to reach a convex set $Y\subset\mathbb{R}^d$ at a time $t>0$, is bounded by $e^{-2δ}$ where $δ$ is the distance from $Y$ to the section at time $t$ of the light cone generated by $X$. |
| title | Exponential Decay outside of the Light Cone for the Pseudo-Relativistic Non-Autonomous Schrödinger Equation |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2512.20488 |