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Starting from time evolution of wave function, quantum dynamics for a periodically kicked free top system is studied in this paper. For an initial spherical coherent state wave packet (localized) we find that 1) as the number of kicking is small, the speed and the direction of the diffusion for a time-evolving wave packet on a periodically kicked free top is related to the kicking strength: the stronger the kicking strength, the more chaotic for the diffusion (which means the more randomized in direction) is and the faster the speed of diffusion is, and then more quickly the full phase space is filled up; 2) as the kicking number is large, the time-evolving wave function will take on fine structure distribution in phase space, and the scope of the distribution for the fine structure will expand with the increase of the kicking strength, and the whole phase space will be filled up finally, and then the wave function will show multifractal property in phase space.#br#We study the multifractal behavior for a time-evolving wave function by partition function method: 1) for different kicking strengths and different q values, we study the scaling properties of partition function X(q), and find the power law relation between the partition function and the scaling L, i.e., X(q)-Lτ(q); 2) at different kicking strength, for a time-evolving wave function we calculate the singularity spectrum f(a)-a, and find that a maximum value of f(a) is 2.0 independent of the kicking strength, but the width of the singularity spectrum becomes narrow with the increase of the kicking strength, which means that the scope of the distribution for a is widest for regular state (localized), and is narrower for transition state from regular to chaotic, and is narrowest for chaotic state; 3) in the time-evolving process, the fluctuation for the width of the singular spectrum is smallest for chaotic state, intermediate for transition state of regular to chaotic, and the largest for regular state; 4) we calculate the generalized fractal dimension Dq-q for different kicking strengths, and find D0 = 2 independent of the kicking strength.#br#We study the mutifractal behaviors for the mean propbability amplitude distribution for a sequence of time-evolving wave functions and find that the result is similar to that of the single wave function type but has the difference: the width of the spectrum is reduced for each kicking strength.
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Keywords:
- top /
- wave function /
- multifractal /
- phase space
[1] Enns R H, McGuire G C 2001 Nonlinear Physics with Mathematica for Scientists and Engineers (Boston: Birkhäuser)
[2] Kono M, Skoric M 2010 Nonlinear Physics of Plasmas (Berlin: Springer)
[3] Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[4] Zhang J Z 1997 Fractal (Beijing: Qing Hua University Press)
[5] Zhou J, Yang S B 2014 Acta Phys Sin. 63 22 (in Chinese) [周洁, 杨双波 2014 63 22]
[6] Heller E J 1984 Phys. Rev. Lett. 53 1515
[7] Nakamura K, Okazaki Y, Bishop A R 1986 Phys. Rev. Lett. 57 5
[8] Halsey T C, Jensen M H, Kadanoff L P, Procaccia I, Shraimant B I 1986 Phys. Rev. A 33 1141
[9] Nakamura K, Bishop A R, Shudo A 1989 Phys. Rev. B 39 12422
[10] Chhabra A, Jensen R V 1989 Phys. Rev. Lett. 62 1328
[11] Martin J, Giraud O, Georgeot B 2008 Phys. Rev. E 77 035201
[12] Goldberger A L, Amaral L A N, Hausdorff J M, Ivanov P C, Peng C K, Stanley H E 2009 Proc. Natl. Acad. Sci. USA 99 2466
[13] Sorensen C M 2001 Aerosol Sci. Tech. 35 648
[14] Evers F, Mirlin A D 2008 Rev. Mod. Phys. 80 1355
[15] Albrecht C, Smet J H, von Klitzing K, Weiss D, Umansky V, Schweizer H 2001 Phys. Rev. Lett. 86 147
[16] Gu G F, Zhou W X 2010 Phys. Rev. E 82 011136
[17] Qiao W, Sun J, Liu S T 2015 Chin. Phys. B 24 050504
[18] Cai J C 2014 Chin. Phys. B 23 044701
[19] Gu G F, Zhou W X 2006 Phys. Rev. E 74 061104
[20] Gutzwiller M C1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
[21] Hönig A, Wintgen D 1989 Phys. Rev. A 39 5642
[22] Huang L, Lai Y C, Grebogi C 2011 Chaos 21 013102
[23] Qin C C, Yang S B 2014 Acta Phys. Sin. 63 140507 (in Chinese) [秦陈陈, 杨双波 2014 63 140507]
[24] Liu D K, Yang S B 2014 J. Nanjing Normal University (Natural Science Edition) 37 2 (in Chinese) [刘达可, 杨双波 2014 南京师大学报(自然科学版) 37 2]
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[1] Enns R H, McGuire G C 2001 Nonlinear Physics with Mathematica for Scientists and Engineers (Boston: Birkhäuser)
[2] Kono M, Skoric M 2010 Nonlinear Physics of Plasmas (Berlin: Springer)
[3] Mandelbrot B B 1983 The Fractal Geometry of Nature (New York: Freeman)
[4] Zhang J Z 1997 Fractal (Beijing: Qing Hua University Press)
[5] Zhou J, Yang S B 2014 Acta Phys Sin. 63 22 (in Chinese) [周洁, 杨双波 2014 63 22]
[6] Heller E J 1984 Phys. Rev. Lett. 53 1515
[7] Nakamura K, Okazaki Y, Bishop A R 1986 Phys. Rev. Lett. 57 5
[8] Halsey T C, Jensen M H, Kadanoff L P, Procaccia I, Shraimant B I 1986 Phys. Rev. A 33 1141
[9] Nakamura K, Bishop A R, Shudo A 1989 Phys. Rev. B 39 12422
[10] Chhabra A, Jensen R V 1989 Phys. Rev. Lett. 62 1328
[11] Martin J, Giraud O, Georgeot B 2008 Phys. Rev. E 77 035201
[12] Goldberger A L, Amaral L A N, Hausdorff J M, Ivanov P C, Peng C K, Stanley H E 2009 Proc. Natl. Acad. Sci. USA 99 2466
[13] Sorensen C M 2001 Aerosol Sci. Tech. 35 648
[14] Evers F, Mirlin A D 2008 Rev. Mod. Phys. 80 1355
[15] Albrecht C, Smet J H, von Klitzing K, Weiss D, Umansky V, Schweizer H 2001 Phys. Rev. Lett. 86 147
[16] Gu G F, Zhou W X 2010 Phys. Rev. E 82 011136
[17] Qiao W, Sun J, Liu S T 2015 Chin. Phys. B 24 050504
[18] Cai J C 2014 Chin. Phys. B 23 044701
[19] Gu G F, Zhou W X 2006 Phys. Rev. E 74 061104
[20] Gutzwiller M C1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
[21] Hönig A, Wintgen D 1989 Phys. Rev. A 39 5642
[22] Huang L, Lai Y C, Grebogi C 2011 Chaos 21 013102
[23] Qin C C, Yang S B 2014 Acta Phys. Sin. 63 140507 (in Chinese) [秦陈陈, 杨双波 2014 63 140507]
[24] Liu D K, Yang S B 2014 J. Nanjing Normal University (Natural Science Edition) 37 2 (in Chinese) [刘达可, 杨双波 2014 南京师大学报(自然科学版) 37 2]
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