LIMIT DISTRIBUTION OF THE NODAL DOMAIN NUMBER FOR THE RIGHT-ISOSCELES TRIANGLE BILLIARD

被引：0

作者：

Jain, M. ^{[1
,2
]}

Bamal, B. ^{[3
]}

Jain, S. R. ^{[4
,5
,6
]}

机构：

[1] Univ Firenze, Dipartimento Fis & Astron, Sesto Fiorentino, FI, Italy

[2] INFN, LENS, Sez Firenze, Sesto Fiorentino, FI, Italy

[3] Malaviya Natl Inst Technol, Jaipur, Rajasthan, India

[4] Bhabha Atom Res Ctr, Nucl Phys Div, Mumbai, Maharashtra, India

[5] Homi Bhabha Natl Inst, Mumbai, Maharashtra, India

[6] Univ Mumbai, UM DAE Ctr Excellence Basic Sci, Mumbai, Maharashtra, India

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2021年 / 207卷 / 01期

关键词：

billiard; limit distribution; integrable system;

D O I：

10.1134/S0040577921040061

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 root 2/pi. The only exact results previously known in this direction correspond to integrable billiards that are separable.

引用

页码：483 / 486

页数：4

共 17 条

[1] Nodal domains of a non-separable problem-the right-angled isosceles triangle [J].

Aronovitch, Amit ;

Band, Ram ;

Fajman, David ;

Gnutzmann, Sven .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (08)

[2] A class of N-body problems with nearest- and next-to-nearest-neighbour interactions [J].

Auberson, G ;

Jain, SR ;

Khare, A .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (04) :695-724

[3]

Berry M. V., 1978, AIP Conference Proceedings, P16, DOI 10.1063/1.31417

[4] QUANTUM DESCRIPTION OF A PSEUDOINTEGRABLE SYSTEM - THE PI-3-RHOMBUS BILLIARD [J].

BISWAS, D ;

JAIN, SR .

PHYSICAL REVIEW A, 1990, 42 (06) :3170-3185

[5]

Courant R., 1923, NACHR GES WISS GOTTI, V1923, P81

[6] Spacing distributions for rhombus billiards [J].

Gremaud, B ;

Jain, SR .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (37) :L637-L643

[7] ARITHMETICAL DEGENERACIES IN SIMPLE QUANTUM-SYSTEMS [J].

ITZYKSON, C ;

LUCK, JM .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1986, 19 (02) :211-239

[8]

Itzykson C., 1985, INT J MODERN PHYS A, V1, P65, DOI [10.1142/S0217751X86000046, DOI 10.1142/S0217751X86000046]

[9]

Jain S. R., 1995, Proceedings of the Indian National Science Academy, Part A, V61, P275

[10] Ground state of an arbitrary triangle with a Calogero-Sutherland-Moser potential [J].

Jain, Sudhir R. .

PRAMANA-JOURNAL OF PHYSICS, 2009, 72 (03) :611-615

← 1 2 →