The mean first passage time of a three-level atomic optical bistable system subjected to noise

doi:10.1088/1674-1056/22/6/060503

Abstract The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time (MFPT) of the transition from the high intracavity intensity state to low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise D_M and the additive noise D_A, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show: (i) For the case of no correlation between two noises (λ=0.0), the increase in D_M and D_A can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and (ii) for the case of correlation between two noises (λ≠0.0), the increase in λ can cause an increase in the probability of the transition, and the increase in D_A can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.

Keywords: additive noise multiplicative noise correlations between two noises mean first passage time

Received: 17 September 2012
Revised: 07 January 2013
Accepted manuscript online:

PACS:	05.40.-a	(Fluctuation phenomena, random processes, noise, and Brownian motion)
	05.70.-a	(Thermodynamics)
	87.10.+e

Fund: Project supported by the Natural Science Foundation of Yunnan Province of China (Grant No. 2010CD031) and the Key Project of Research Fund of Education Department of Yunnan Province of China (Grant No. 2001Z011), and the Candidate Talents Training Fund of Yunnan Province, China (Grant No. 2012HB009).

Corresponding Authors: Zeng Chun-Hua, Wang Hua
E-mail: zchh2009@126.com; wanghuaheat@hotmail.com

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Wei Yong-Gang (魏永刚), Zeng Chun-Hua (曾春华), Wang Hua (王华), Li Kong-Zhai (李孔斋), Hu Jian-Hang (胡建杭) The mean first passage time of a three-level atomic optical bistable system subjected to noise 2013 Chin. Phys. B 22 060503

[1]	Moss F and McClintock P V E 1989 Noise in Nonliner Dynamical Systems Vols. I-III (Cambridge: Cambridge University Press)
[2]	Horsthemke W and Lefever R 1984 Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology (Berlin: Springer-Verlag)
[3]	Gammaitoni L, Hanggi P, Jung P and Marchesoni F 1998 Rev. Mod. Phys. 70 224
[4]	Anishchenko V S, et al. 2003 Nonlinear Dynamics of Chaotic and Stochastic Systems (Berlin: Springer-Verlag)
[5]	Zeng C H, Wang H and Wang H T 2011 Chin. Phys. B 20 050502
[6]	Zeng C H and Wang H 2012 Chin. Phys. B 21 050502
[7]	Bonifacio R and Lugiato L A 1978 Phys. Rev. Lett. 40 1023
[8]	Bonifacio R, et al. 1978 Phys. Rev. A 18 2266
[9]	Bartussek R, et al. 1994 Phys. Rev. E 49 3930
[10]	Ning L J and Xu W 2006 Chin. Phys. Lett. 23 3180
[11]	Ning L J and Xu W 2007 Acta Phys. Sin. 56 1944 (in Chinese)
[12]	Jiang L L, Luo X Q, Wan D and Zhu S Q 2012 Chin. Phys. B 21 090503
[13]	Guo F, Cheng X F, Li S F, Cao W and Li H 2012 Chin. Phys. B 21 080502
[14]	Zhang L, Cao L and Wu D J 2008 Phys. Rev. A 77 015801
[15]	Du L C and Mei D C 2008 Phys. Lett. A 372 5529
[16]	Li Y Q and Xiao M 1995 Opt. Lett. 20 1489
[17]	Wang H, Goorskey D and Xiao M 2002 Opt. Lett. 27 258
[18]	Wang H, Goorskey D and Xiao M 2002 Opt. Lett. 27 1354
[19]	Joshi A, Brown A, Wang H and Xiao M 2003 Phys. Rev. A 67 041801
[20]	Joshi A, Yang W and Xiao M 2005 Opt. Lett. 30 905
[21]	Joshi A and Xiao M 2008 J. Opt. Soc. Am. B 25 2015
[22]	Li X L, Zhang L S, Sun J and Feng X M 2012 Acta Phys. Sin. 61 044202 (in Chinese)
[23]	Zeng C H and Wang H 2012 Ecological Modelling 233 52
[24]	Joshi A and Xiao M 2006 Phys. Rev. A 74 013817
[25]	Wu H, Joshi A and Xiao M 2007 J. Mod. Opt. 54 2441
[26]	Zeng C H and Wang H 2011 Commun. Theor. Phys. 56 877
[27]	Zeng C H, Wang H and Gong A L 2012 J. Stat. Mech. 2012 P07012
[28]	Zeng C H and Wang H 2012 Eur. Phys. J. B 85 127
[29]	Wang L Z, Zhao W L and Chen X 2012 Acta Phys. Sin. 61 160501 (in Chinese)
[30]	Wu H, Singh S and Xiao M 2009 Phys. Rev. A 79 023835
[31]	Madureira A J R, Hänggi P and Wio H S 1996 Phys. Lett. A 217 248
[32]	Fulinski A and Telejko T 1991 Phys. Lett. A 152 11
[33]	Cao L and Wu D J 1994 Phys. Lett. A 185 59
[34]	Jia Y and Li J R 1996 Phys. Rev. E 53 5764
[35]	Cao L and Wu D J 2000 Phys. Rev. E 62 7478
[36]	Cao L and Wu D J 2001 Phys. Lett. A 291 371
[37]	Zhu S 1993 Phys. Rev. A 47 2405
[38]	Jia Y, Cao L and Wu D J 1995 Phys. Rev. A 51 3196
[39]	Xie C W and Mei D C 2004 Phys. Lett. A 323 421
[40]	Wu D J, Cao L and Ke S Z 1994 Phys. Rev. E 50 2496
[41]	Jia Y and Li J 1997 Phys. Rev. Lett. 78 994
[42]	Ai B Q, Wang X J, Liu G T and Liu L G 2003 Phys. Rev. E 67 022903
[43]	Ai B Q, Wang X J, Liu G T and Liu L G 2008 Phys. Rev. E 77 013902
[44]	Chaudhuri J R, Chattopadhya S and Banik S K 2007 Phys. Rev. E 76 021125
[45]	Chaudhuri J R, Chattopadhya S and Banik S K 2008 J. Chem. Phys. 0128 154513
[46]	Berdichevsky V and Gitterman M 1999 Phys. Rev. E 60 1494
[47]	Bag B C, Banik S K and Ray D S 2001 Phys. Rev. E 64 026110
[48]	Novikov E A 1964 Zh. Eksp. Teor. Fiz. 47 1919
[49]	Novikov E A 1964 Sov. Phys. JETP 20 1290
[50]	Fox R F 1986 Phys. Rev. A 34 4525
[51]	Hänggi P, Marchesoni F and Grigolini P 1984 Z. Phys. B 56 333
[52]	Fox R F 1986 Phys. Rev. A 33 467
[53]	Jia Y, Yu S N and Li J R 2000 Phys. Rev. E 62 1869
[54]	Liu Q and Jia Y 2004 Phys. Rev. E 70 041907
[55]	Li J H and Huang Z Q 1996 Phys. Rev. E 53 3315
[56]	Li J H and Huang Z Q 1998 Phys. Rev. E 57 3917
[57]	Li J H, Luczka J and Hänggi P 2001 Phys. Rev. E 64 011113
[58]	Dayan I, Gitterman M and Weiss G H 1992 Phys. Rev. A 46 757
[59]	Mantegna R N and Spagnolo B 1996 Phys. Rev. Lett. 76 563

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The mean first passage time of a three-level atomic optical bistable system subjected to noise

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