Fredholm method for scars

被引:39
作者
Fishman, S [1 ]
Georgeot, B [1 ]
Prange, RE [1 ]
机构
[1] TECHNION ISRAEL INST TECHNOL, DEPT PHYS, IL-32000 HAIFA, ISRAEL
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1996年 / 29卷 / 04期
关键词
D O I
10.1088/0305-4470/29/4/019
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A new quasiclassical formula for scars is obtained by using the Fredholm method. We show that it can be expanded into a formula obtained earlier by Agam and Fishman. The derivation is simple and direct. It is also more rigorous and more general than that of Agam and Fishman. It also clarifies the remarkable process of resurgence, relating the high-order terms based on long orbits to the Weyl term whose origin is the zero length orbits.
引用
收藏
页码:919 / 937
页数:19
相关论文
共 42 条
[1]   QUANTUM EIGENFUNCTIONS IN TERMS OF PERIODIC-ORBITS OF CHAOTIC SYSTEMS [J].
AGAM, O ;
FISHMAN, S .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (09) :2113-2137
[2]  
AGAM O, 1993, J PHYS A-MATH GEN, V26, P6595
[3]   SEMICLASSICAL CRITERION FOR SCARS IN WAVE-FUNCTIONS OF CHAOTIC SYSTEMS [J].
AGAM, O ;
FISHMAN, S .
PHYSICAL REVIEW LETTERS, 1994, 73 (06) :806-809
[4]  
AGAM O, COMMUNICATION
[5]   ASYMPTOTIC EVALUATION OF GREENS FUNCTION FOR LARGE QUANTUM NUMBERS [J].
BALIAN, R ;
BLOCH, C .
ANNALS OF PHYSICS, 1971, 63 (02) :592-&
[6]   DISTRIBUTION OF EIGENFREQUENCIES FOR WAVE EQUATION IN A FINITE DOMAIN .2. ELECTROMAGNETIC FIELD - RIEMANNIAN SPACES [J].
BALIAN, R ;
BLOCH, C .
ANNALS OF PHYSICS, 1971, 64 (01) :271-&
[7]   DISTRIBUTION OF EIGENFREQUENCIES FOR WAVE EQUATION IN A FINITE DOMAIN .1. 3-DIMENSIONAL PROBLEM WITH SMOOTH BOUNDARY SURFACE [J].
BALIAN, R ;
BLOCH, C .
ANNALS OF PHYSICS, 1970, 60 (02) :401-&
[8]   SOLUTION OF SCHRODINGER EQUATION IN TERMS OF CLASSICAL PATHS [J].
BALIAN, R ;
BLOCH, C .
ANNALS OF PHYSICS, 1974, 85 (02) :514-545
[9]   DISTRIBUTION OF EIGENFREQUENCIES FOR WAVE-EQUATION IN A FINITE DOMAIN .3. EIGENFREQUENCY DENSITY OSCILLATIONS [J].
BALIAN, R ;
BLOCH, C .
ANNALS OF PHYSICS, 1972, 69 (01) :76-&
[10]   A NEW ASYMPTOTIC REPRESENTATION FOR ZETA(1/2 + IT) AND QUANTUM SPECTRAL DETERMINANTS [J].
BERRY, MV ;
KEATING, JP .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1992, 437 (1899) :151-173