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We study analytically and numerically the probability density function in the stationary state of non-linear oscillators which are subjected to Lévy white noise and confined by a steep symmetric potential. The probability density function transforms from unimodality to bimodality or from bimodality to trimodality when the potential transforms from single well to double well; especially, the probability density function shows a peak at the saddle point of the potential. This result is far from the Gibbs-Boltzmann statistics.
[1] Bao J D 2009 Stochastic Simulation Methods for Classical and Quantum Dissipation Systems (Beijing: Science Press) p96-100 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法(北京: 科学出版社)第96—100页]
[2] Bouchaud J P, Georges A 1990 Phys. Rep. 195 127
[3] Metzler R, Klafter J 2000 Phys. Rep. 339 1
[4] Lin F, Bao J D 2008 Acta Phys. Sin 57 696 (in Chinese)[林 方、 包景东 2008 57 696] 〖5] Chang F X, Chen J, Huang W 2005 Acta Phys. Sin. 54 1113 (in Chinese)[常福宣、 陈 进、 黄 薇 2005 54 1113]
[5] Khintchine A Y, Lévy P 1936 C. R. Acad. Sci. Paris 202 374
[6] Bardou F, Bouchaud J P, Emile O, Aspect A, Cohen-Tannoudji C 1994 Phys. Rev. Lett. 72 203
[7] Schaufler S, Schleich W P, Yakovlev V P 1999 Phys. Rev. Lett. 83 3162
[8] Metzler R, Barkai E, Klafter J 1999 Europhys. Lett. 46 431
[9] Jespersen S, Metzler R, Fogedby H C 1999 Phys. Rev. E 59 2736
[10] Chechkin A, Gonchar V, Klafter J, Metzler R, Tanatarov L 2002 Chem. Phys. 284 233
[11] Chechkin A, Gonchar V, Klafter J, Metzler R, Tanatarov L 2004 J. Stat. Phys. 115 1505
[12] Bao J D, Wang H Y, Jia Y, Zhuo Y Z 2005 Phys. Rev. E 72 051105
[13] Bolotin Y L, Bulavin V V, Chechkin A V, Gonchar V Y 1999 Prog Nucl Energy 35 65
[14] Fulger D, Scalas E, Germano G 2008 Phys. Rev. E 77 021122
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[1] Bao J D 2009 Stochastic Simulation Methods for Classical and Quantum Dissipation Systems (Beijing: Science Press) p96-100 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法(北京: 科学出版社)第96—100页]
[2] Bouchaud J P, Georges A 1990 Phys. Rep. 195 127
[3] Metzler R, Klafter J 2000 Phys. Rep. 339 1
[4] Lin F, Bao J D 2008 Acta Phys. Sin 57 696 (in Chinese)[林 方、 包景东 2008 57 696] 〖5] Chang F X, Chen J, Huang W 2005 Acta Phys. Sin. 54 1113 (in Chinese)[常福宣、 陈 进、 黄 薇 2005 54 1113]
[5] Khintchine A Y, Lévy P 1936 C. R. Acad. Sci. Paris 202 374
[6] Bardou F, Bouchaud J P, Emile O, Aspect A, Cohen-Tannoudji C 1994 Phys. Rev. Lett. 72 203
[7] Schaufler S, Schleich W P, Yakovlev V P 1999 Phys. Rev. Lett. 83 3162
[8] Metzler R, Barkai E, Klafter J 1999 Europhys. Lett. 46 431
[9] Jespersen S, Metzler R, Fogedby H C 1999 Phys. Rev. E 59 2736
[10] Chechkin A, Gonchar V, Klafter J, Metzler R, Tanatarov L 2002 Chem. Phys. 284 233
[11] Chechkin A, Gonchar V, Klafter J, Metzler R, Tanatarov L 2004 J. Stat. Phys. 115 1505
[12] Bao J D, Wang H Y, Jia Y, Zhuo Y Z 2005 Phys. Rev. E 72 051105
[13] Bolotin Y L, Bulavin V V, Chechkin A V, Gonchar V Y 1999 Prog Nucl Energy 35 65
[14] Fulger D, Scalas E, Germano G 2008 Phys. Rev. E 77 021122
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