20.500.12556/DKUM-86152 Fluctuating number of energy levels in mixed-type lemon billiards Nihanje števila energijskih nivojev v Lemonovem biljardu mešanega tipa 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. nonlinear dynamics quantum chaos mixed-type systems energy level statistics lemon billiards billiards nelinearna dinamika kvantni kaos sistemi mešanega tipa statistika energijskih nivojev Lemonovi biljardi biljardi true false true MDPI Angleški jezik Slovenski jezik Znanstveno delo 2023-10-13 13:42:41 2023-10-13 13:57:00 2023-10-16 09:16:58 0000-00-00 00:00:00 2021 0 0 Str. 888-902 Št. 4 Letn. 3 2021 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2021-07-15 2021-08-16 2021-10-02 530.145 78873347 10.3390/physics3040055 2624-8174 Fluctuating_number_of_energy_levels_Lozej_2021.pdf Fluctuating_number_of_energy_levels_Lozej_2021.pdf 1 A880A454D0D72B679F8EDC5EC14D172E 1580d8cdc12a818303eaa207a842b08b0ded1ce4fed940a139690579270521a7 16dbff41-69bf-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173555 https://www.mdpi.com/2624-8174/3/4/55 1 a039b123-69bd-11ee-b6cb-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=173554 Univerza v Mariboru 0 0 0