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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2401.15512 |
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| _version_ | 1866929226192519168 |
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| author | Loomis, Alex Sethuraman, Sunder |
| author_facet | Loomis, Alex Sethuraman, Sunder |
| contents | In the `Many Interacting Worlds' (MIW) discrete Hamiltonian system approximation of Schrödinger's wave equation, introduced in \cite{hall_2014}, convergence of ground states to the Normal ground state of the quantum harmonic oscillator, via Stein's method, in Wasserstein-$1$ distance with rate $\mathcal{O}(\sqrt{\log N}/N)$ has been shown in McKeague-Levin (2016), Chen-Thanh (2023), McKeague-Swan (2023). In this context, we construct approximate higher energy states of the MIW system, and show their convergence with the same rate in Wasserstein-$1$ distance to higher energy states of the quantum harmonic oscillator. In terms of techniques, we apply the `differential equation' approach to Stein's method, which allows to handle behavior near zeros of the higher energy states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher energy state approximations in the `Many Interacting Worlds' model Loomis, Alex Sethuraman, Sunder Mathematical Physics Probability 60F05, 81Q65 In the `Many Interacting Worlds' (MIW) discrete Hamiltonian system approximation of Schrödinger's wave equation, introduced in \cite{hall_2014}, convergence of ground states to the Normal ground state of the quantum harmonic oscillator, via Stein's method, in Wasserstein-$1$ distance with rate $\mathcal{O}(\sqrt{\log N}/N)$ has been shown in McKeague-Levin (2016), Chen-Thanh (2023), McKeague-Swan (2023). In this context, we construct approximate higher energy states of the MIW system, and show their convergence with the same rate in Wasserstein-$1$ distance to higher energy states of the quantum harmonic oscillator. In terms of techniques, we apply the `differential equation' approach to Stein's method, which allows to handle behavior near zeros of the higher energy states. |
| title | Higher energy state approximations in the `Many Interacting Worlds' model |
| topic | Mathematical Physics Probability 60F05, 81Q65 |
| url | https://arxiv.org/abs/2401.15512 |