Optimal Transport of a Free Quantum Particle and its Shape Space Interpretation
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914185790619648 |
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| author | Lessel, Bernadette |
| author_facet | Lessel, Bernadette |
| contents | A solution of the free Schrödinger equation is investigated by means of Optimal transport. The curve of probability measures $μ_t$ this solution defines is shown to be an absolutely continuous curve in the Wasserstein space $W_2(\mathbb{R}^3)$. The optimal transport map from $μ_t$ to $μ_s$, the cost for this transport (i.e. the Wasserstein distance) and the value of the Fisher information along $μ_t$ are being calculated. It is finally shown that this solution of the free Schrödinger equation can naturally be interpreted as a curve in so-called Shape space, which forgets any positioning in space but only describes properties of shapes. In Shape space, $μ_t$ continues to be a shortest path geodesic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Transport of a Free Quantum Particle and its Shape Space Interpretation Lessel, Bernadette Quantum Physics Mathematical Physics Functional Analysis A solution of the free Schrödinger equation is investigated by means of Optimal transport. The curve of probability measures $μ_t$ this solution defines is shown to be an absolutely continuous curve in the Wasserstein space $W_2(\mathbb{R}^3)$. The optimal transport map from $μ_t$ to $μ_s$, the cost for this transport (i.e. the Wasserstein distance) and the value of the Fisher information along $μ_t$ are being calculated. It is finally shown that this solution of the free Schrödinger equation can naturally be interpreted as a curve in so-called Shape space, which forgets any positioning in space but only describes properties of shapes. In Shape space, $μ_t$ continues to be a shortest path geodesic. |
| title | Optimal Transport of a Free Quantum Particle and its Shape Space Interpretation |
| topic | Quantum Physics Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2512.06940 |