Loschmidt Echo for Deformed Wigner Matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929535760465920 |
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| author | Erdős, László Henheik, Joscha Kolupaiev, Oleksii |
| author_facet | Erdős, László Henheik, Joscha Kolupaiev, Oleksii |
| contents | We consider two Hamiltonians that are close to each other, $H_1 \approx H_2 $, and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle ψ_0, \mathrm{e}^{\mathrm{i} t H_2} \mathrm{e}^{-\mathrm{i} t H_1} ψ_0 \rangle|^2$ that expresses the effect of an imperfect time reversal on the initial state $ψ_0$. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such $H_1$ and $H_2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_08108 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loschmidt Echo for Deformed Wigner Matrices Erdős, László Henheik, Joscha Kolupaiev, Oleksii Mathematical Physics Probability Quantum Physics 60B20, 82C10 We consider two Hamiltonians that are close to each other, $H_1 \approx H_2 $, and analyze the time-decay of the corresponding Loschmidt echo $\mathfrak{M}(t) := |\langle ψ_0, \mathrm{e}^{\mathrm{i} t H_2} \mathrm{e}^{-\mathrm{i} t H_1} ψ_0 \rangle|^2$ that expresses the effect of an imperfect time reversal on the initial state $ψ_0$. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools for our results are two-resolvent laws for such $H_1$ and $H_2$. |
| title | Loschmidt Echo for Deformed Wigner Matrices |
| topic | Mathematical Physics Probability Quantum Physics 60B20, 82C10 |
| url | https://arxiv.org/abs/2410.08108 |