Semiclassical asymptotics of the Bloch--Torrey operator in two dimensions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911777405534208 |
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| author | Hérau, Frédéric Krejcirik, David Raymond, Nicolas |
| author_facet | Hérau, Frédéric Krejcirik, David Raymond, Nicolas |
| contents | The Bloch--Torrey operator $-h^2Δ+e^{iα}x_1$ on a bounded smooth planar domain, subject to Dirichlet boundary conditions, is analyzed. Assuming $α\in\left[0,\frac{3π}{5}\right)$ and a non-degeneracy assumption on the left-hand side of the domain, asymptotics of the eigenvalues with the smallest real part in the limit $h \to 0$ are derived. The strategy is a backward complex scaling and the reduction to a tensorized operator involving a real Airy operator and a complex harmonic oscillator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semiclassical asymptotics of the Bloch--Torrey operator in two dimensions Hérau, Frédéric Krejcirik, David Raymond, Nicolas Spectral Theory Mathematical Physics Analysis of PDEs The Bloch--Torrey operator $-h^2Δ+e^{iα}x_1$ on a bounded smooth planar domain, subject to Dirichlet boundary conditions, is analyzed. Assuming $α\in\left[0,\frac{3π}{5}\right)$ and a non-degeneracy assumption on the left-hand side of the domain, asymptotics of the eigenvalues with the smallest real part in the limit $h \to 0$ are derived. The strategy is a backward complex scaling and the reduction to a tensorized operator involving a real Airy operator and a complex harmonic oscillator. |
| title | Semiclassical asymptotics of the Bloch--Torrey operator in two dimensions |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2402.08574 |