Recurrence Time for Finite Quantum Systems
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910173973446656 |
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| author | Gupta, Chaitanya Short, Anthony J. |
| author_facet | Gupta, Chaitanya Short, Anthony J. |
| contents | We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states are close to their initial configuration, and at least one state has deviated significantly during this interval. Considering finite-dimensional quantum systems evolving unitarily, we find bounds on this notion of recurrence time, for continuous time and discrete time, by using Dirichlet's approximation theorem. We show how the problem of finding a bound on recurrence time can be related to approximating the difference of real numbers by rationals. We present a mathematical result on the latter, which we then use to obtain tighter bounds on recurrence time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14995 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recurrence Time for Finite Quantum Systems Gupta, Chaitanya Short, Anthony J. Quantum Physics Number Theory 11J13 (secondary) We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states are close to their initial configuration, and at least one state has deviated significantly during this interval. Considering finite-dimensional quantum systems evolving unitarily, we find bounds on this notion of recurrence time, for continuous time and discrete time, by using Dirichlet's approximation theorem. We show how the problem of finding a bound on recurrence time can be related to approximating the difference of real numbers by rationals. We present a mathematical result on the latter, which we then use to obtain tighter bounds on recurrence time. |
| title | Recurrence Time for Finite Quantum Systems |
| topic | Quantum Physics Number Theory 11J13 (secondary) |
| url | https://arxiv.org/abs/2604.14995 |