周期受击陀螺系统波函数的分形

周洁; 杨双波

doi:10.7498/aps.63.220507

摘要

研究了周期受击陀螺系统波函数的分形. 发现在打击强度系数较弱时 (即≤ 1时), 相空间是规则的, 分形维接近于1; 随着打击强度系数的增大, 相空间开始变得混沌, 分形维也随之增大; 当打击强度系数达到6时, 相空间完全混沌, 分形维将达到最大值, 此时若继续增大打击强度系数, 分形维保持基本不变.

关键词:

陀螺 /
波函数 /
分形维 /
相空间

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.

Keywords:

作者及机构信息

周洁,
杨双波

1.
南京师范大学物理科学与技术学院, 大规模复杂系统数值模拟江苏省重点实验室, 南京 210023

Authors and contacts

1.
Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China

参考文献

[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

施引文献

[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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