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本文研究了粒子在二维弱开口的Bunimovich Stadium型介观混沌器件中的逃逸规律. 利用经典统计的方法，通过改变器件端口宽度、圆弧半径及器件腔长等参数，首次发现随器件各项参数变化的分形维数与粒子逃逸率趋势符合，并揭示了混沌体系的逃逸指数受器件形状的影响. 统计并拟合了粒子逃逸率与粒子波数大小的关系，数值结果表明，粒子逃逸率与波数为二次函数关系，但逃逸率与能量大小不是严格的线性关系. 进一步分析了在器件入口处粒子的衍射效应对粒子逃逸的影响，结果表明，衍射效应使粒子逃逸率增加，且粒子数的演化在时间较短时不再满足指数关系，长时间的演化再次满足指数衰减规律.We have studied the chaotic escape of particles in a two-dimensional weakly opened mesoscopic components of the Bunimovich Stadium devices. Within the framework of classical statistics, we get the change of the fractal dimensions and the escape rates in several parameters of the device, such as the opening width, the arc radius and the cavity length. We first find the good agreement between the fractal dimensions and the escape rates, and reveal that the exponential law of escape is affected by the shape of device. We count and fit the relationship between the escape rates and the wave numbers of the particles. As is shown in the numerical results, the relation between the escape rates and the wave numbers is a quadratic function, but the escape rates are not strictly linearly varied with the change of the energy. Furthermore, we analyze the influence of diffraction at the lead opening on the escape of the particles. Numerical results show that the diffraction effect makes the escape rates increase, and the evolution of the number of particles no longer obeys the law of exponential decay in a short time, but observes it again in a long time.
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Keywords:
- mesoscopic devices /
- chaos /
- escape rates /
- diffraction effect
[1] Bauer W, Bertsch G F 1990 Phys. Rev. Lett. 65 2213
[2] [3] Legrand O, Sornette D 1991 Phys. Rev. Lett. 66 2172
[4] Zhao H J, Du M L 2007 Phys. Rev. E 76 027201
[5] [6] [7] Song X F, Du M L, Zhao H J 2012 Sci. Sin. Phys. Mech. Astron. 42 127 (in Chinese)[宋新芳, 杜孟利, 赵海军 2012 中国科学: 42 127]
[8] [9] Custdio M S, Beims M W 2011 Phys. Rev. E 83 056201
[10] Bastard G, Brum J A 1986 IEEE J. Quantum Electon. 22 1625
[11] [12] Alt H, Grf H D, Harney H L, Hofferbert R, Rehfeld H, Richter A, Schardt P 1996 Phys. Rev. E 53 2217
[13] [14] Gutzwiller M 1992 Chaos in Classical and Quantum Mechanics (New York: Springer Verlag) pp173-206
[15] [16] [17] Richter K 2000 Semiclassical Theory of Mesoscopic Quantum Systems (New York: Springer Verlag) pp49-73
[18] Bunimovich L A 1985 Sov. Phys. JETP 62 842
[19] [20] [21] Xu X Y, Zhang Y H, Huang F Z, Lin S L, Du M L 2005 Asta. Phys. Sin. 54 4538 (in Chinese)[徐学友, 张延惠, 黄发忠, 林圣路, 杜孟利 2005 54 4538]
[22] Fromhold T M, Tench C R, Taylor R P, Micolich A P, Newbury R 1998 Physica B 249 334
[23] [24] [25] Ree S 2002 Phys. Rev. E 65 055205
[26] Cai X J, Zhang Y H, Li Z L, Jiang G H, Yang Q N, Xu X Y 2013 Chin. Phys. B 22 020501
[27] [28] [29] Zhang Y H, Cai X J, Li Z L, Jiang G H, Yang Q N, Xu X Y 2013 Chin. Phys. Lett. 30 040501
[30] [31] Yang Q N, Zhang Y H, Cai X J, Jiang G H, Xu X Y 2013 Asta. Phys. Sin. 62 080505 (in Chinese)[杨秦男, 张延惠, 蔡祥吉, 蒋国辉, 徐学友 2013 62 080505]
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[1] Bauer W, Bertsch G F 1990 Phys. Rev. Lett. 65 2213
[2] [3] Legrand O, Sornette D 1991 Phys. Rev. Lett. 66 2172
[4] Zhao H J, Du M L 2007 Phys. Rev. E 76 027201
[5] [6] [7] Song X F, Du M L, Zhao H J 2012 Sci. Sin. Phys. Mech. Astron. 42 127 (in Chinese)[宋新芳, 杜孟利, 赵海军 2012 中国科学: 42 127]
[8] [9] Custdio M S, Beims M W 2011 Phys. Rev. E 83 056201
[10] Bastard G, Brum J A 1986 IEEE J. Quantum Electon. 22 1625
[11] [12] Alt H, Grf H D, Harney H L, Hofferbert R, Rehfeld H, Richter A, Schardt P 1996 Phys. Rev. E 53 2217
[13] [14] Gutzwiller M 1992 Chaos in Classical and Quantum Mechanics (New York: Springer Verlag) pp173-206
[15] [16] [17] Richter K 2000 Semiclassical Theory of Mesoscopic Quantum Systems (New York: Springer Verlag) pp49-73
[18] Bunimovich L A 1985 Sov. Phys. JETP 62 842
[19] [20] [21] Xu X Y, Zhang Y H, Huang F Z, Lin S L, Du M L 2005 Asta. Phys. Sin. 54 4538 (in Chinese)[徐学友, 张延惠, 黄发忠, 林圣路, 杜孟利 2005 54 4538]
[22] Fromhold T M, Tench C R, Taylor R P, Micolich A P, Newbury R 1998 Physica B 249 334
[23] [24] [25] Ree S 2002 Phys. Rev. E 65 055205
[26] Cai X J, Zhang Y H, Li Z L, Jiang G H, Yang Q N, Xu X Y 2013 Chin. Phys. B 22 020501
[27] [28] [29] Zhang Y H, Cai X J, Li Z L, Jiang G H, Yang Q N, Xu X Y 2013 Chin. Phys. Lett. 30 040501
[30] [31] Yang Q N, Zhang Y H, Cai X J, Jiang G H, Xu X Y 2013 Asta. Phys. Sin. 62 080505 (in Chinese)[杨秦男, 张延惠, 蔡祥吉, 蒋国辉, 徐学友 2013 62 080505]
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