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In this paper we study the fractal dimensions of wave function for the periodically kicked free top. We find that when kicking strength coefficient is less than or equal to 1 (≤ 1), the motion in classical phase space is regular, the fractal dimension is about 1, and as kicking strength increases, the motion in classical phase space becomes chaotic and the fractal dimension also increases. And we also find that when kicking strength is greater than or equal to 6 (≥ 6), the phase space becomes completely chaotic, the fractal dimension reaches its maximum value 1.5 and will keep this value.
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Keywords:
- top /
- wave function /
- fractal dimension /
- phase space
[1] Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer) pp254-281
[2] Hönig A, Wintgen D 1989 Phys. Rev. A 39 5642
[3] Yang S B, Liu D K 2013 J. Nanjing Normal Univ. (Natural Science Edition) 36 1 (in Chinese) [杨双波, 刘达可 2013 南京师范大学报 (自然科学版) 36 1]
[4] Bohigas O, Haq R U, Pandey A 1985 Phys. Rev. Lett. 54 1645
[5] Huang L, Lai Y C, Celso G 2011 Chaos 21 013102
[6] Seligman T H, Verbaarschot J M, Zirnbauer M R 1984 Phys. Rev. Lett. 53 215
[7] Davis M J, Heller E J 1981 J. Chem. Phys. 75 3916
[8] Lin W A, Ballentine L E 1992 Phys. Rev. A 45 3637
[9] Liu D K, Yang S B 2014 J. Nanjing Normal Univ. (Natural Science Edition) 37 2 (in Chinese) [刘达可, 杨双波 2014 南京师范大学报 (自然科学版) 37 2]
[10] Tomsovic S, Heller E J 1991 Phys. Rev. Lett. 67 664
[11] Stratt R M, Handy N C, Miller W H 1979 J. Chem. Phys. 71 3311
[12] McDonald S W 1983 Ph. D. Dissertation (Berkeley: University of California)
[13] Heller E J 1984 Phys. Rev. Lett. 53 1515
[14] Qin C C, Yang S B 2014 Acta Phys. Sin. 63 140507 (in Chinese) [秦陈陈, 杨双波 2014 物理学报 63 140507]
[15] Mandelbrot B B 1983 the Fractal Geometry of Nature (New York: Freeman)
[16] Zhang J Z 1997 Fractal (Beijing: Qinghua University Press)
[17] Harper P G 1955 Proc. Phys. Soc. London Sect. A 68 874
[18] Hofstadter D R 1976 Phys. Rev. B 14 2239
[19] Anderson P W 1958 Phys. Rev. 109 1492
[20] Evers F, Mirlin A D 2008 Rev. Mod. Phys. 80 1355
[21] Wang J, Gong J B 2009 Phys. Rev. Lett. 102 244102
[22] Wang J, Gong J B 2010 Phys. Rev. E 81 026204
[23] Bandyopadhyay J N, Wang J, Gong J B 2010 Phys. Rev. E 81 066212
[24] Martin J, Giraud O, Georgeot B 2008 Phys. Rev. E 77 035201
[25] Deng S H, Gao S, Li Y P, Xu X Y, Lin S L 2010 Chin. Phys. B 19 040511
[26] Ren X C, Guo L X 2008 Chin. Phys. B 17 2956
[27] Yang Q N, Zhang Y H, Cai X J, Jiang G H, Xu X Y 2013 Acta Phys. Sin. 62 080505 (in Chinese) [杨秦男, 张延惠, 蔡祥吉, 蒋国辉, 徐学友 2013 物理学报 62 080505]
[28] Nakamura K, Okazaki Y, Bishop A R 1986 Phys. Rev. Lett. 57 5
[29] Haak F, Kus M, Scharf R 1987 Z.Phys. B: Condens. Matter 65 381
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[1] Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer) pp254-281
[2] Hönig A, Wintgen D 1989 Phys. Rev. A 39 5642
[3] Yang S B, Liu D K 2013 J. Nanjing Normal Univ. (Natural Science Edition) 36 1 (in Chinese) [杨双波, 刘达可 2013 南京师范大学报 (自然科学版) 36 1]
[4] Bohigas O, Haq R U, Pandey A 1985 Phys. Rev. Lett. 54 1645
[5] Huang L, Lai Y C, Celso G 2011 Chaos 21 013102
[6] Seligman T H, Verbaarschot J M, Zirnbauer M R 1984 Phys. Rev. Lett. 53 215
[7] Davis M J, Heller E J 1981 J. Chem. Phys. 75 3916
[8] Lin W A, Ballentine L E 1992 Phys. Rev. A 45 3637
[9] Liu D K, Yang S B 2014 J. Nanjing Normal Univ. (Natural Science Edition) 37 2 (in Chinese) [刘达可, 杨双波 2014 南京师范大学报 (自然科学版) 37 2]
[10] Tomsovic S, Heller E J 1991 Phys. Rev. Lett. 67 664
[11] Stratt R M, Handy N C, Miller W H 1979 J. Chem. Phys. 71 3311
[12] McDonald S W 1983 Ph. D. Dissertation (Berkeley: University of California)
[13] Heller E J 1984 Phys. Rev. Lett. 53 1515
[14] Qin C C, Yang S B 2014 Acta Phys. Sin. 63 140507 (in Chinese) [秦陈陈, 杨双波 2014 物理学报 63 140507]
[15] Mandelbrot B B 1983 the Fractal Geometry of Nature (New York: Freeman)
[16] Zhang J Z 1997 Fractal (Beijing: Qinghua University Press)
[17] Harper P G 1955 Proc. Phys. Soc. London Sect. A 68 874
[18] Hofstadter D R 1976 Phys. Rev. B 14 2239
[19] Anderson P W 1958 Phys. Rev. 109 1492
[20] Evers F, Mirlin A D 2008 Rev. Mod. Phys. 80 1355
[21] Wang J, Gong J B 2009 Phys. Rev. Lett. 102 244102
[22] Wang J, Gong J B 2010 Phys. Rev. E 81 026204
[23] Bandyopadhyay J N, Wang J, Gong J B 2010 Phys. Rev. E 81 066212
[24] Martin J, Giraud O, Georgeot B 2008 Phys. Rev. E 77 035201
[25] Deng S H, Gao S, Li Y P, Xu X Y, Lin S L 2010 Chin. Phys. B 19 040511
[26] Ren X C, Guo L X 2008 Chin. Phys. B 17 2956
[27] Yang Q N, Zhang Y H, Cai X J, Jiang G H, Xu X Y 2013 Acta Phys. Sin. 62 080505 (in Chinese) [杨秦男, 张延惠, 蔡祥吉, 蒋国辉, 徐学友 2013 物理学报 62 080505]
[28] Nakamura K, Okazaki Y, Bishop A R 1986 Phys. Rev. Lett. 57 5
[29] Haak F, Kus M, Scharf R 1987 Z.Phys. B: Condens. Matter 65 381
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