| Title: | Fluctuating number of energy levels in mixed-type lemon billiards |
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| Authors: | ID Lozej, Črt (Author)
ID Lukman, Dragan (Author)
ID Robnik, Marko (Author) |
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| Files: |  Fluctuating_number_of_energy_levels_Lozej_2021.pdf (1,40 MB)
MD5: A880A454D0D72B679F8EDC5EC14D172E
 https://www.mdpi.com/2624-8174/3/4/55
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UM - University of Maribor
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| Abstract: | In this paper, the fluctuation properties of the number of energy levels (mode fluctuation) are studied in the mixed-type lemon billiards at high lying energies. The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between the centers, as introduced by Heller and Tomsovic. In this paper, the case of two billiards, defined by B = 0.1953, 0.083, is studied. It is shown that the fluctuation of the number of energy levels follows the Gaussian distribution quite accurately, even though the relative fraction of the chaotic part of the phase space is only 0.28 and 0.16, respectively. The theoretical description of spectral fluctuations in the Berry-Robnik picture is discussed. Also, the (golden mean) integrable rectangular billiard is studied and an almost Gaussian distribution is obtained, in contrast to theory expectations. However, the variance as a function of energy, E, behaves as - E, in agreement with the theoretical prediction by Steiner. |
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| Keywords: | nonlinear dynamics, quantum chaos, mixed-type systems, energy level statistics, lemon billiards, billiards |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 15.07.2021 |
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| Article acceptance date: | 16.08.2021 |
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| Publication date: | 02.10.2021 |
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| Publisher: | MDPI |
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| Year of publishing: | 2021 |
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| Number of pages: | Str. 888-902 |
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| Numbering: | Letn. 3, Št. 4 |
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| PID: | 20.500.12556/DKUM-86152  |
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| UDC: | 530.145 |
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| ISSN on article: | 2624-8174 |
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| COBISS.SI-ID: | 78873347 |
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| DOI: | 10.3390/physics3040055 |
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| Publication date in DKUM: | 13.10.2023 |
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| Views: | 518 |
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| Downloads: | 20 |
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| Metadata: |    |
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| Categories: | Misc.
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