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Quantum chaos; billiards; nodal domains; probability distribution functions.

Zeros of a function encode significant information about the patterns they represent. Owing to nonseparable or/and non-integrable nature of the classical system, the nodal curves display a complex morphology. As they must avoid to cross, the domains of positive or negative sign they enclose look very complex and intriguing. Probability distribution functions of the normalized-domain number will be presented for simple billiards. For some of these systems, the amplitude distribution functions are found. Several open problems will be discussed.

SUDHIR RANJAN JAIN^{1 2 3}

1. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
2. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400 094, India
3. UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Vidyanagari Campus, Mumbai 400 098, India

Published

16 September 2019