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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.10880 |
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| _version_ | 1866915594126753792 |
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| author | Kruk, Maciej B. Kulik, Piotr Andersen, Malthe F. Deuar, Piotr Gajda, Mariusz Pawłowski, Krzysztof Witkowska, Emilia Arlt, Jan J. Rzążewski, Kazimierz |
| author_facet | Kruk, Maciej B. Kulik, Piotr Andersen, Malthe F. Deuar, Piotr Gajda, Mariusz Pawłowski, Krzysztof Witkowska, Emilia Arlt, Jan J. Rzążewski, Kazimierz |
| contents | Bose-Einstein condensation represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while the mean number of condensed atoms is independent of the choice of statistical ensemble, the microcanonical, canonical, or grand canonical variances differ significantly among these ensembles. In this paper, we review the progress made over the past 30 years in studying the statistical fluctuations of Bose-Einstein condensates. Focusing primarily on the ideal Bose gas, we emphasize the inequivalence of the Gibbs statistical ensembles and examine various approaches to this problem. These approaches include explicit analytic results for primarily one-dimensional systems, methods based on recurrence relations, asymptotic results for large numbers of particles, techniques derived from laser theory, and methods involving the construction of statistical ensembles via stochastic processes, such as the Metropolis algorithm. We also discuss the less thoroughly resolved problem of the statistical behavior of weakly interacting Bose gases. In particular, we elaborate on our stochastic approach, known as the hybrid sampling method. The experimental aspect of this field has gained renewed interest, especially following groundbreaking recent measurements of condensate fluctuations. These advancements were enabled by unprecedented control over the total number of atoms in each experimental realization. Additionally, we discuss the fluctuations in photonic condensates as an illustrative example of grand canonical fluctuations. Finally, we briefly consider the future directions for research in the field of condensate statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the fluctuations of the number of atoms in the condensate Kruk, Maciej B. Kulik, Piotr Andersen, Malthe F. Deuar, Piotr Gajda, Mariusz Pawłowski, Krzysztof Witkowska, Emilia Arlt, Jan J. Rzążewski, Kazimierz Quantum Gases Bose-Einstein condensation represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while the mean number of condensed atoms is independent of the choice of statistical ensemble, the microcanonical, canonical, or grand canonical variances differ significantly among these ensembles. In this paper, we review the progress made over the past 30 years in studying the statistical fluctuations of Bose-Einstein condensates. Focusing primarily on the ideal Bose gas, we emphasize the inequivalence of the Gibbs statistical ensembles and examine various approaches to this problem. These approaches include explicit analytic results for primarily one-dimensional systems, methods based on recurrence relations, asymptotic results for large numbers of particles, techniques derived from laser theory, and methods involving the construction of statistical ensembles via stochastic processes, such as the Metropolis algorithm. We also discuss the less thoroughly resolved problem of the statistical behavior of weakly interacting Bose gases. In particular, we elaborate on our stochastic approach, known as the hybrid sampling method. The experimental aspect of this field has gained renewed interest, especially following groundbreaking recent measurements of condensate fluctuations. These advancements were enabled by unprecedented control over the total number of atoms in each experimental realization. Additionally, we discuss the fluctuations in photonic condensates as an illustrative example of grand canonical fluctuations. Finally, we briefly consider the future directions for research in the field of condensate statistics. |
| title | On the fluctuations of the number of atoms in the condensate |
| topic | Quantum Gases |
| url | https://arxiv.org/abs/2502.10880 |