SELBERG ZETA-FUNCTION AND THE QUANTIZATION OF CHAOS

被引：35

作者：

MATTHIES, C

STEINER, F

机构：

[1] II. Institut für Theoretische Physik, Universität Hamburg, 2000 Hamburg 50

来源：

PHYSICAL REVIEW A | 1991年 / 44卷 / 12期

关键词：

D O I：

10.1103/PhysRevA.44.R7877

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

We study Artin's billiard, an extremely chaotic system defined on the fundamental domain of the modular group PSL(2,Z), and show that its quantum energy levels are given exactly by the nontrivial zeros of a certain Selberg zeta function expressed as an Euler product over the classical periodic orbits. We demonstrate that at least the first 73 energy levels can be determined by using only a finite number of periodic orbits.

引用

页码：R7877 / R7880

页数：4

共 16 条

[1]

[Anonymous], 1924, ABH MATH SEM HAMBURG, DOI [10.1007/BF02954622, DOI 10.1007/BF02954622]

[2] A RULE FOR QUANTIZING CHAOS [J].

BERRY, MV ;

KEATING, JP .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (21) :4839-4849

[3]

BOLTE J, 1990, DESY90082 REP

[4] PERIODIC ORBITS AND CLASSICAL QUANTIZATION CONDITIONS [J].

GUTZWILL.MC .

JOURNAL OF MATHEMATICAL PHYSICS, 1971, 12 (03) :343-&

[5]

HASEGAWA H, 1989, PROG THEOR PHYS SUPP, P198, DOI 10.1143/PTPS.98.198

[6]

HEJHAL DA, 1983, SELBERG TRACE FORM 2, V1001

[7]

HEJHAL DA, 1989, UMSI8921 U MINN SUP

[8] SELBERGS TRACE FORMULA AS APPLIED TO A COMPACT RIEMANN SURFACE [J].

MCKEAN, HP .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1972, 25 (03) :225-&

[9]

Selberg A., 1956, J INDIAN MATH SOC, V20, P47

[10] QUANTIZATION OF CHAOS [J].

SIEBER, M ;

STEINER, F .

PHYSICAL REVIEW LETTERS, 1991, 67 (15) :1941-1944

← 1 2 →