The nuclear shell model as a testing ground for many-body quantum chaos

Physics Report

Volumn 276, Issue 2-3, 1996, Pages 85-176

  Zelevinsky, Vladimir ^a,b   Brown, B Alex ^a   Frazier, Njema ^a   Horoi, Mihai ^a,c,d  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b BUDKER INSTITUTE OF NUCLEAR PHYSICS   (Russian Federation)

^c CENTRAL MICHIGAN UNIVERSITY   (United States)

^d INSTITUTE OF ATOMIC PHYSICS   (Romania)

Author keywords

Entropy; Level statistics; Nuclear shell model; Pairing; Quantum chaos; Spreading width

Indexed keywords

EID: 0030295787     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(96)00007-5     Document Type: Review

References (136)

1. [1] A.J. Lichtenberg and M.A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).
2. [2] H.G. Schuster, Deterministic Chaos (VCH Verlagsgesellschaft, Weinheim, 1989).
3. [3] F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).
4. [4] P.V. Elyutin, Usp. Fiz. Nauk 155 (1988) 397 [Sov. Phys. Usp. 31 (1988) 597].
5. [4] P.V. Elyutin, Usp. Fiz. Nauk 155 (1988) 397 [Sov. Phys. Usp. 31 (1988) 597].
6. [5] F.M. Izrailev, Phys. Rep. 196 (1990) 299.
7. [6] Statistical Theories of Spectra: Fluctuations, ed. C.E. Porter (Academic Press, New York, 1965).
8. [7] T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey and S.S.M. Wong, Rev. Mod. Phys. 53 (1981) 385.
9. [8] R. Haq, A. Pandey and O. Bohigas, Phys. Rev. Lett. 48 (1982) 1986.
10. [9] H.-J. Stöckmann and J. Stein, Phys. Rev. Lett. 64 (1990) 2215.
11. [10] H.-D. Gräf, H.L. Harney, H. Lengeler, C.H. Lewenkopf, C. Rangacharyulu, A. Richter, P. Schardt and H.A. Weidenmüller, Phys. Rev. Lett. 69 (1992) 1296.
12. [11] C. Ellegaard, T. Guhr, K. Lindemann, H.Q. Lorensen, J. Nygård and M. Oxborrow, Phys. Rev. Lett. 75 (1995) 1546.
13. [12] R. Arvieu, F. Brut, J. Carbonell and J. Touchard, Phys. Rev. A35 (1987) 2389.
14. [13] B. Milek, W. Nörenberg and P. Rozmej, Z. Phys. A334 (1989) 233.
15. [14] W.D. Heiss, R.G. Nazmitdinov and S. Radu, Phys. Rev. Lett. 72 (1994) 2351.
16. [15] L.P. Gor'kov and G.M. Eliashberg, Zh. Eksp. Teor. Fiz. 48 (1965) 1407 [Sov. Phys. JETP 21 (1965) 940].
17. [15] L.P. Gor'kov and G.M. Eliashberg, Zh. Eksp. Teor. Fiz. 48 (1965) 1407 [Sov. Phys. JETP 21 (1965) 940].
18. [16] C.M. Marcus et al., Phys. Rev. Lett. 69 (1992) 506.
19. [17] Y. Alhassid and A. Novoselsky, Phys. Rev. C45 (1992) 1677.
20. [18] V. Lopac, S. Brant and V. Paar, Z. Phys. A337 (1990) 131.
21. [19] H. Frisk and R. Arvieu, J. Phys. A22 (1989) 1765.
22. [20] I.I. Gurevich, Zh. Eksp. Teor. Phys. 9 (1939) 1283.
23. [21] A. Bohr and B. Mottelson, Nuclear Structure, Vol. 1 (Benjamin, New York, 1969).
24. [22] M. Berry and M. Robnik, J. Phys. A17 (1984) 2413; M. Berry, Proc. R. Soc. A400 (1985) 229.
25. [22] M. Berry and M. Robnik, J. Phys. A17 (1984) 2413; M. Berry, Proc. R. Soc. A400 (1985) 229.
26. [23] J.B. French et al. Phys. Rev. Lett. 54 (1985) 2313; 58 (1987) 2400.
27. [23] J.B. French et al. Phys. Rev. Lett. 54 (1985) 2313; 58 (1987) 2400.
28. [24] G.E. Mitchell et al., Phys. Rev. Lett. 61 (1988) 1473; J.F. Shriner, Jr. et al., Z. Phys. A335 (1990) 393.
29. [24] G.E. Mitchell et al., Phys. Rev. Lett. 61 (1988) 1473; J.F. Shriner, Jr. et al., Z. Phys. A335 (1990) 393.
30. [25] S. Raman et al., Phys. Rev. C43 (1991) 521.
31. [26] S. Drozdz, S. Nishizaki, J. Speth and J. Wambach, Phys. Rev. C49 (1994) 867.
32. [27] J.D. Garrett et al., Future Directions with 4π Gamma Detection Systems of the New Generation, ed. J. Dudek and B. Haas (AIP, 1991) p. 345.
33. [28] R.J. Blin-Stoyle, Phys. Rev. 120 (1960) 181.
34. [29] O.P. Sushkov and V.V. Flambaum, Pis'ma Zh. Eksp. Teor. Fiz. 32 (1980) 377 [JETP Lett. 32 (1980) 353]; Usp. Fiz. Nauk 136 (1982) 3 [Sov. Phys. Usp. 25 (1982) 1].
35. [29] O.P. Sushkov and V.V. Flambaum, Pis'ma Zh. Eksp. Teor. Fiz. 32 (1980) 377 [JETP Lett. 32 (1980) 353]; Usp. Fiz. Nauk 136 (1982) 3 [Sov. Phys. Usp. 25 (1982) 1].
36. [29] O.P. Sushkov and V.V. Flambaum, Pis'ma Zh. Eksp. Teor. Fiz. 32 (1980) 377 [JETP Lett. 32 (1980) 353]; Usp. Fiz. Nauk 136 (1982) 3 [Sov. Phys. Usp. 25 (1982) 1].
37. [29] O.P. Sushkov and V.V. Flambaum, Pis'ma Zh. Eksp. Teor. Fiz. 32 (1980) 377 [JETP Lett. 32 (1980) 353]; Usp. Fiz. Nauk 136 (1982) 3 [Sov. Phys. Usp. 25 (1982) 1].
38. [30] V.G. Zelevinsky, Nucl. Phys. A553 (1993) 125c; A570 (1994) 411c.
39. [30] V.G. Zelevinsky, Nucl. Phys. A553 (1993) 125c; A570 (1994) 411c.
40. [31] N. Bohr, Nature 137 (1936) 344.
41. [32] V.V. Sokolov and V.G. Zelevinsky, Phys. Lett. B202 (1988) 10; Nucl. Phys. A504 (1989) 562; Ann. Phys. 216 (1992) 323.
42. [32] V.V. Sokolov and V.G. Zelevinsky, Phys. Lett. B202 (1988) 10; Nucl. Phys. A504 (1989) 562; Ann. Phys. 216 (1992) 323.
43. [32] V.V. Sokolov and V.G. Zelevinsky, Phys. Lett. B202 (1988) 10; Nucl. Phys. A504 (1989) 562; Ann. Phys. 216 (1992) 323.
44. [33] G. Montambaux et al., Phys. Rev. Lett. 70 (1993) 497.
45. [34] N. Rosenzweig and C.E. Porter, Phys. Rev. 120 (1960) 1698.
46. [35] V.V. Flambaum, A.A. Gribakina, G.F. Gribakin and M.G. Kozlov, Phys. Rev. A50 (1994) 267.
47. [36] I.C. Percival, J. Phys. B6 (1973) L229.
48. [37] E.J. Heller, Phys. Rev. Lett. 53 (1984) 1515.
49. [38] R. Aurich and F. Steiner, Physica D48 (1991) 445.
50. [39] W. Bauer, D. McGrew, V. Zelevinsky and P. Schuck, Phys. Rev. Lett. 72 (1994) 3771; Nucl. Phys. A583 (1995) 93.
51. [39] W. Bauer, D. McGrew, V. Zelevinsky and P. Schuck, Phys. Rev. Lett. 72 (1994) 3771; Nucl. Phys. A583 (1995) 93.
52. [40] V.G. Zelevinsky, Nucl. Phys. A555 (1993) 109.
53. [41] G. Mantzouranis and H.C. Pauli, Z. Phys. A278 (1976) 373.
54. [42] V.G. Zelevinsky, P.F. Bortignon and R.A. Broglia, preprint NBI-93-45.
55. [43] V.V. Flambaum and O.P. Sushkov, Nucl. Phys. A412 (1984) 13.
56. [44] B. Lauritzen, P.F. Bortignon, R.A. Broglia and V.G. Zelevinsky, Phys. Rev. Lett. 74 (1995) 5190.
57. [45] J.J. Gaardhøje, Annu. Rev. Nucl. Part. Sci. 42 (1992) 483.
58. [46] H.L. Harney, A. Richter and H.A. Weidenmüller, Rev. Mod. Phys. 58 (1986) 607.
59. [47] V.G. Zelevinsky and P. von Brentano, Nucl. Phys. A529 (1991) 141.
60. [48] J. Reiter and H.L. Harney, Z. Phys. A337 (1990) 121.
61. [49] D.C. Meredith, S.E. Koonin and M.R. Zirnbauer, Phys. Rev. A37 (1988) 3499.
62. [50] D.C. Meredith, Phys. Rev. E47 (1993) 2405.
63. [51] B.A. Brown and G. Bertsch, Phys. Lett. 148B (1984) 5.
64. [52] W.E. Ormand and R.A. Broglia, Phys. Rev. C46 (1992) 1710.
65. [53] J.B. French and K.F. Ratcliff, Phys. Rev. C3 (1971) 94; K.F. Ratcliff, Phys. Rev. C3 (1971) 117.
66. [53] J.B. French and K.F. Ratcliff, Phys. Rev. C3 (1971) 94; K.F. Ratcliff, Phys. Rev. C3 (1971) 117.
67. [54] F.S. Chang and J.B. French, Phys. Lett. 44B (1973) 131.
68. [55] J.P. Draayer, J.B. French and S.S.M. Wong, Ann. Phys. 106 (1977) 472, 503.
69. [56] J.J.M. Verbaarschot and P.J. Brussard, Phys. Lett. 87B (1979) 155.
70. [57] V.V. Flambaum, Phys. Scr. T46 (1993) 198.
71. [58] C.A. Bertulani and V.G. Zelevinsky, Nucl. Phys. A568 (1994) 931.
72. [59] C.H. Lewenkopf and V.G. Zelevinsky, Nucl. Phys. A569 (1994) 183.
73. [60] B. Lauritzen, T. Døssing and R.A. Broglia, Nucl. Phys. A457 (1986) 61.
74. [61] S. Åberg, Prog. Part. Nucl. Phys. 28 (1992) 11.
75. [62] T. Ericson, Adv. Phys. 9 (1960) 425.
76. [63] S.T. Belyaev and V.G. Zelevinsky, Yad. Fiz. 2 (1965) 615 [Sov. J. Nucl. Phys. 2 (1966) 442].
77. [63] S.T. Belyaev and V.G. Zelevinsky, Yad. Fiz. 2 (1965) 615 [Sov. J. Nucl. Phys. 2 (1966) 442].
78. [64] V.V. Samoilov and M.H. Urin, Nucl. Phys. A567 (1994) 237.
79. [65] B.A. Brown and B.H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38 (1988) 29.
80. [66] B.A. Brown et al., OXBASH code, MSUNSCL Report 524 (1988).
81. [67] W.E. Ormand and B.A. Brown, Nucl. Phys. A491 (1989) 1.
82. [68] E.P. Wigner, Ann. Math. 62 (1955) 548.
83. [69] M. Horoi, B.A. Brown and V. Zelevinsky, Phys. Rev. C50 (1994) R2274.
84. [70] M. Feingold, D.M. Leitner and M. Wilkinson, Phys. Rev. Lett. 66 (1991) 986.
85. [71] J. Casati et al., Phys. Rev. Lett. 64 (1990) 1; M. Kuś, M. Lewenstein and F. Haake, Phys. Rev. A44 (1991) 2800.
86. [71] J. Casati et al., Phys. Rev. Lett. 64 (1990) 1; M. Kuś, M. Lewenstein and F. Haake, Phys. Rev. A44 (1991) 2800.
87. [72] Y.V. Fyodorov and A.D. Mirlin, Phys. Rev. Lett. 67 (1991) 2405.
88. [73] J. Wambach, private communication.
89. [74] D. Kusnezov, private communication.
90. [75] J.B. French and S.S.M. Wong, Phys. Lett. B35 (1971) 5; K.K. Mon and J.B. French, Ann. Phys. 95 (1975) 90.
91. [75] J.B. French and S.S.M. Wong, Phys. Lett. B35 (1971) 5; K.K. Mon and J.B. French, Ann. Phys. 95 (1975) 90.
92. [76] I.I. Gurevich and M.I. Pevsner, Nucl. Phys. 2 (1957) 575.
93. [77] T. Prosen and M. Robnik, J. Phys. A26 (1993) 2371.
94. [78] S. Mizutori and V.G. Zelevinsky, Z. Phys. A346 (1993) 1.
95. [79] L. Molinari and V.V. Sokolov, J. Phys. A22 (1989) L999.
96. [80] A. Altland and D. Fuchs, Phys. Rev. Lett. 74 (1995) 4269.
97. [81] O. Bohigas, M.J. Giannoni and C. Schmit, Phys. Rev. Lett. 52 (1984) 1.
98. [82] M.V. Berry, Proc. R. Soc. London, Ser. A 400 (1985) 229.
99. [83] D. Wintgen and H. Marxer, Phys. Rev. Lett. 60 (1988) 971.
100. [84] P. Arve, Phys. Rev. A44 (1991) 6920.
101. [85] B. Mottelson, unpublished.
102. [86] P. Pechukas, Phys. Rev. Lett. 51 (1983) 943.
103. [87] D.W. Noid, M.L. Koszykowski, M. Tabor and R.A. Marcus, J. Chem. Phys. 72 (1980) 6169.
104. [88] M. Wilkinson, J. Phys. A22 (1989) 2795.
105. [89] A. Szafer and B.L. Altshuler, Phys. Rev. Lett. 70 (1993) 587.
106. [90] P. Gaspard, S.A. Rice, H.J. Mikeska and K. Nakamura, Phys. Rev. A42 (1990) 4015.
107. [91] J. Zakrzewski and D. Delande, Phys. Rev. E47 (1993) 1650.
108. [92] F. von Oppen, Phys. Rev. Lett. 73 (1994) 798.
109. [93] D. Kusnezov, B.A. Brown and V. Zelevinsky, in preparation.
110. [94] N. Ullah and C.E. Porter, Phys. Lett. 6 (1963) 301; N. Ullah, Int. Nucl. Phys. Conf., ed. R.L. Becker (Academic, New York, 1967) p. 812.
111. [94] N. Ullah and C.E. Porter, Phys. Lett. 6 (1963) 301; N. Ullah, Int. Nucl. Phys. Conf., ed. R.L. Becker (Academic, New York, 1967) p. 812.
112. [95] M.V. Berry, J. Phys. A10 (1977) 2083.
113. [96] V. Zelevinsky, M. Horoi and B.A. Brown, Phys. Lett. B350 (1995) 141.
114. [97] F.J. Yonezawa, Non-Cryst. Solids 35 & 36 (1980) 29.
115. [98] J. Reichl, Europhys. Lett. 6 (1988) 669.
116. [99] E.K. Warburton and B.A. Brown, Phys. Rev. C46 (1992) 923.
117. [100] J.P. Elliott, Proc. R. Soc. A245 (1958) 128, 562.
118. [101] M. Feingold, A. Gioletta, F.M. Izrailev and L. Molinari, to be published.
119. [102] M. Horoi, V. Zelevinsky and B.A. Brown, Phys. Rev. Lett. 74 (1995) 5194.
120. [103] L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon Press, Oxford, 1958).
121. [104] D.J. Morrissey, W. Benenson and W.A. Friedman, Annu. Rev. Nucl. Part. Sci. 44 (1994) 27.
122. [105] V.V. Flambaum and O.K. Vorov, Phys. Rev. Lett. 70 (1993) 4051.
123. [106] J. Ford and G.H. Lunsford, Phys. Rev. A1 (1970) 59.
124. [107] M.V. Berry, Les Mouches XXXVI, Chaotic Behavior of Deterministic Systems, eds. G. Iooss, R.H.G. Helleman and R. Stora (North Holland, Amsterdam, 1983); Les Mouches LII, Chaos and Quantum Physics, eds. M.-J. Giannoni, A. Voros and J. Zinn-Justin (North Holland, Amsterdam, 1991).
125. [107] M.V. Berry, Les Mouches XXXVI, Chaotic Behavior of Deterministic Systems, eds. G. Iooss, R.H.G. Helleman and R. Stora (North Holland, Amsterdam, 1983); Les Mouches LII, Chaos and Quantum Physics, eds. M.-J. Giannoni, A. Voros and J. Zinn-Justin (North Holland, Amsterdam, 1991).
126. [108] M. Srednicki, Phys. Rev. E50 (1994) 888.
127. [109] Ya.G. Sinai, Usp. Mat. Nauk 25 (1970) 137 [Russ. Math. Surv. 25 (1970) 137].
128. [109] Ya.G. Sinai, Usp. Mat. Nauk 25 (1970) 137 [Russ. Math. Surv. 25 (1970) 137].
129. [110] L. van Hove, Physica 21 (1955) 517; 23 (1957) 441; 25 (1959) 268.
130. [110] L. van Hove, Physica 21 (1955) 517; 23 (1957) 441; 25 (1959) 268.
131. [110] L. van Hove, Physica 21 (1955) 517; 23 (1957) 441; 25 (1959) 268.
132. [111] H.-T. Elze and P.A. Carruthers, preprint CERN-TH.7431/94.
133. [112] T. Døssing et al., Phys. Rev. Lett. 75 (1995) 1276.
134. [113] K.T. Hecht, Phys. Rev. 139 (1995) B794; J.P. Elliott and J.A. Evans, Phys. Lett. 31B (1970) 157.
135. [113] K.T. Hecht, Phys. Rev. 139 (1995) B794; J.P. Elliott and J.A. Evans, Phys. Lett. 31B (1970) 157.
136. [114] G. Racah, Phys. Rev. 76 (1949) 1352.