Modified fusion probability by reflection boundary

  • We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.
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  • [1] Kramers H A. Physica (Utrecht), 1940, 7: 284[2] WU Xi-Zhen, ZHUO Yi-Zhong. Chin. Phys. C, 1980, 4(1): 113[3] WU Xi-Zhen, LI Zhu-Xia, ZHUO Yi-Zhong. Chin. Phys. C, 1990, 14(4): 345[4] Abe Y. Physique J de., 1986, 47(8): C4-329[5] Hanggi P, Talkner P, Borkovec M. Rev. Mod. Phys., 1990, 62: 251[6] Frobrich P, Gontchar I I. Phys. Rep., 1998, 292: 131[7] YE W, WANG N, TIAN J. Phys. Rev. C, 2014, 90: 041604(R)[8] Aritomo Y, Wada T, Ohta M, Abe Y. Phys. Rev. C, 1997, 55: R1011[9] Abe Y, Aritomo Y, Wada T, Ohta M. J. Phys. G: Nucl. Part. Phys., 1997, 23: 1275[10] Abe Y, Boilley D, Kosenko G, BAO J D, SHEN C W, Giraud B, Wada T. Prog. Theor. Phys. Suppl., 2002, 146: 104[11] SHEN C W, Kosenko G, Abe Y. Phys. Rev. C, 2002, 66: 061602(R)[12] Światecki W J, Siwek-Wilczyńska K, Wilczyński J. Acta Phys. Pol. B, 2003, 34: 2049[13] Światecki W J, Siwek-Wilczyńska K, Wilczyński J. Phys. Rev. C,2005, 71: 014602[14] LIU Z H, BAO J D. Phys. Rev. C, 2006, 74: 057602[15] LIU Z H, BAO J D. Phys. Rev. C, 2007, 76: 037604[16] LIU Z H, BAO J D. Phys. Rev. C, 2013, 87: 034616[17] Hofmann H, Samhammer R. Z. Phys. A, 1985, 322: 157[18] Abe Y, Boilley D, Giraud B G, Wada T. Phys. Rev. E, 2000, 61: 1125[19] BAO J D, Boilley D. Nucl. Phys. A, 2002, 707: 47[20] Boilley D, Abe Y, BAO J D. Eur. Phys. J. A, 2003, 18: 627[21] BAO J D, ZHUO Y Z. Phys. Rev. C, 2003, 67: 064606[22] MAO J W, Shen C W. Phys. Rev. E, 2011, 83: 041108[23] Abe Y, SHEN C W, Kosenko G, Boilley D, Giraud B G. Int. J. Mod. Phys. E, 2008, 17: 2214[24] Boilley D, Lallouet Y. J. Stat. Phys., 2006, 125: 2[25] Yilmaz B, Ayik S, Abe Y, Boilley D. Phys. Rev. E, 2008, 77: 011121[26] Gitterman M, Weiss G H, Stat J. Phys., 1993, 70: 107[27] Talkner P, Braun H, Chem J. Phys., 1988, 88: 7537[28] Grote R F, Hynes J T. J. Chem. Phys., 1980, 73: 2715[29] Mel'nikov V I, Meshkov S V. J. Chem. Phys., 2006, 85: 1018[30] Boilley D, Marchix A, Jurado B, Schmidt K H. Eur. Phys. J. A, 2007, 33: 47[31] Talkner P. Chem. Phys., 1994, 180: 199[32] Kim S K. J. Chem. Phys., 1985, 28: 1057[33] Hofmann H, Ivanyuk F A. Phys. Rev. Lett., 2003, 90: 132701[34] Hofmann H, Magner A G. Phys. Rev. C, 2003, 68: 014606[35] BAO J D, JIA Y. Phys. Rev. C, 2004, 69: 027602[36] Boilley D, Jurado B, Schmitt C. Phys. Rev. E, 2004, 70: 056129[37] Risken H. The Fokker-Planck Equation. Berlin: Springer, 1989; Gardiner C W. Handbook of Stochastic Methods. Berlin: Springer, 2002
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HAN Jie and BAO Jing-Dong. Modified fusion probability by reflection boundary[J]. Chinese Physics C, 2015, 39(5): 054104. doi: 10.1088/1674-1137/39/5/054104
HAN Jie and BAO Jing-Dong. Modified fusion probability by reflection boundary[J]. Chinese Physics C, 2015, 39(5): 054104.  doi: 10.1088/1674-1137/39/5/054104 shu
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Received: 2014-10-10
Revised: 1900-01-01
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Modified fusion probability by reflection boundary

    Corresponding author: HAN Jie,
    Corresponding author: BAO Jing-Dong,

Abstract: We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.

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