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| Main Author: | |
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| Format: | Preprint |
| Published: |
2001
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0101029 |
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| _version_ | 1866911217165008896 |
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| author | Chebotarev, Alexander M. |
| author_facet | Chebotarev, Alexander M. |
| contents | Mean values of some observables describing quantum interaction between the Bose field in a cavity and a movable mirror can be represented as expectations of rapidly oscillating functions w.r.t. the Poisson measure with a large mean value ($N\approx 10^{23}$) corresponding to the average number of photons in laser beam. Straightforward summation of the series is impossible because over $2\sqrt N$ summands make a significant contribution. We derive an analytical expression approximating this sum with the error $O(N^{-1})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0101029 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | Asymptotic Summation of Slow Converging and Rapidly Oscillating Series Chebotarev, Alexander M. Numerical Analysis Mean values of some observables describing quantum interaction between the Bose field in a cavity and a movable mirror can be represented as expectations of rapidly oscillating functions w.r.t. the Poisson measure with a large mean value ($N\approx 10^{23}$) corresponding to the average number of photons in laser beam. Straightforward summation of the series is impossible because over $2\sqrt N$ summands make a significant contribution. We derive an analytical expression approximating this sum with the error $O(N^{-1})$. |
| title | Asymptotic Summation of Slow Converging and Rapidly Oscillating Series |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/math/0101029 |