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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 1, Pages 99–103
DOI: https://doi.org/10.4213/tmf10008 (Mi tmf10008) 		 
Limit distribution of the nodal domain number for the right-isosceles triangle billiard

M. Jainab, B. Bamalc, S. R. Jaindef

a Dipartimento di Fisica e Astronomia, Università di Firenze and LENS, Firenze, Italy
b INFN Sezione di Firenze, Sesto Fiorentino (FI), Firenze, Italy
c Malaviya National Institute of Technology, Jaipur, Rajasthan, India
d Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai, India
e Homi Bhabha National Institute, Mumbai, India
f UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Mumbai, India
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DOI: https://doi.org/10.4213/tmf10008
Abstract: We present the probability distribution function of the nodal domain number for the right-isosceles triangle billiard. This is the first explicit result for a nonseparable plane polygonal billiard. The distribution function has a peak at $2/\pi$ (the same as for integrable billiards) and also at $2\sqrt{2}/\pi$. The only exact results previously known in this direction correspond to integrable billiards that are separable.
Keywords: billiard, limit distribution, integrable system.
Received: 10.11.2020
Revised: 10.11.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 1, Pages 483–486
DOI: https://doi.org/10.1134/S0040577921040061
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Jain, B. Bamal, S. R. Jain, “Limit distribution of the nodal domain number for the right-isosceles triangle billiard”, TMF, 207:1 (2021), 99–103; Theoret. and Math. Phys., 207:1 (2021), 483–486
Citation in format AMSBIB
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