Abstract
Considering the time-delayed feedback and environmental perturbations in spin-crossover system, we construct a stochastic delayed differential equation to study the state transitions from the low spin (LS) state to the high spin (HS) state in spin-crossover solids. It is shown that the delayed feedback and noise can induce optical bistability and state transitions. The mean first-passage time (MFPT) of the transition from the LS state to the HS state as the function of the noise intensity exhibits a maximum, and the noise-enhanced stability is observed. However the MFPT decreases with increase of the delayed feedback intensity, thus the delayed feedback accelerates the conversion from the LS state to the HS state.
Similar content being viewed by others
References
P. Gütlich, A. Hauser, H. Spiering, Angew. Chem. 106, 2109 (1994)
A. Desaix, O. Roubeau, J. Jeftic, J.G. Haasnoot, K. Boukheddaden, E. Codjovi, J. Linarès, M. No-guès, F. Varret, Eur. Phys. J. B 6, 183 (1998)
A. Hauser, C. Enachescu, M.L. Daku, A. Vargas, N. Amstutz, Coord. Chem. Rev. 250, 1642 (2006)
M.A. Halcrow, Chem. Soc. Rev. 37, 278 (2008)
Spin Crossover in Transition Metal Compounds I, II, III, edited by P. Gütlich, H.A. Goodwin (Springer-Verlag, Berlin, 2004)
S. Decurtins, P. Gütlich, C.P. Köhler, H. Spiering, A. Hauser, Chem. Phys. Lett. 105, 1 (1984)
G. Gallé, D. Deldicque, J. Degert, Th. Forestier, J.-F. Létard, E. Freysz, Appl. Phys. Lett. 96, 041907 (2010)
I. Krivokapic, P. Chakraborty, C. Enachescu, R. Bronisz, A. Hauser, Inorg. Chem. 50, 1856 (2011)
C. Parreira, C. Enachescu, J. Linarès, K. Boukheddaden, F. Varret, J. Phys.: Condens. Matter 12, 9395 (2000)
Yu. Gudyma, O. Semenko, Phys. Status Solidi B 241, 370 (2004)
Iu.V. Gudyma, A.Iu. Maksymov, Physica B 405, 2534 (2010)
Iu.V. Gudyma, A.Iu. Maksymov, Semiconductor Physics, Quantum Electronics and Optoelectronics 13, 357 (2010)
Iu. Gudyma, A. Maksymov, Appl. Opt. 51, C55 (2012)
Iu.V. Gudyma, A.Iu. Maksymov, J. Phys. Chem. Solids 72, 73 (2011)
Iu. Gudyma, A. Maksymov, S. Miyashita, Phys. Rev. E 84, 031126 (2011)
Iu. Gudyma, A. Maksymov, C. Enachescu, Eur. Phys. J. B 78, 167 (2010)
L.S. Tsimring, A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001)
C. Masoller, Phys. Rev. Lett. 90, 020601 (2003)
D. Huber, L.S. Tsimring, Phys. Rev. Lett. 91, 260601 (2003)
D. Curtin, S.P. Hegarty, D. Goulding, J. Houlihan, Th. Busch, C. Masoller, G. Huyet, Phys. Rev. E 70, 031103 (2004)
J. Houlihan, D. Goulding, Th. Busch, C. Masoller, G. Huyet, Phys. Rev. Lett. 92, 050601 (2004)
C. Masoller, Phys. Rev. Lett. 88, 034102 (2002)
N.B. Janson, A.G. Balanov, E. Schöll, Phys. Rev. Lett. 93, 010601 (2004)
R. Yang, A. Song, Int. J. Mod. Phys. B 26, 1250019 (2012)
T.L. To, N. Maheshri, Science 327, 1142 (2010)
X.-P. Zhang, Z. Cheng, F. Liu, W. Wang, Phys. Rev. E 76, 031924 (2007)
J. Tang, X. Yang, J. Ma, Y. Jia, Phys. Rev. E 80, 011907 (2009)
X.-J. Tian, X.-P. Zhang, F. Liu, W. Wang, Phys. Rev. E 80, 011926 (2009)
C.H. Zeng, H. Wang, Chem. Phys. 402, 1 (2012)
C.H. Zeng, H. Wang, Ecol. Modell. 233, 52 (2012)
C.H. Zeng et al., Eur. Phys. J. B 85, 347 (2012)
A. Hauser, P. Gutlich, H. Spiering, Inorg. Chem. 25, 4245 (1986)
A. Hauser, J. Chem. Phys. 94, 2741 (1991)
F. Varret, K. Boukheddaden, J. Jeftic, O. Roubeau, Mol. Cryst. Liquid Cryst. 335, 561 (1999)
T.L. Saaty, Modern Nonlinear Equations (Dover Publ., New York, 1981)
J. Wiener, J.K. Hale, Ordinary and Delay Differential Equations (Wiley, New York, 1992)
S. Guillouzic, I. L’Heureux, A. Longtin, Phys. Rev. E 59, 3970 (1999)
S. Guillouzic, I. L’Heureux, A. Longtin, Phys. Rev. E 61, 4906 (2000)
T.D. Frank, Phys. Rev. E 71, 031106 (2005)
T.D. Frank, Phys. Rev. E 72, 011112 (2005)
S. Decurtins, P. Gütlich, C.P. Köhler, H. Spiering, A. Hauser, Chem. Phys. Lett. 139, 1 (1984)
P. Gütlich, A. Hauser, H. Spiering, Angew. Chem. Int. Ed. Engl. 33, 2024 (1994)
F. Varret, K. Boukheddaden, E. Codjovi, C. Enachescu, J. Linarès, Top. Curr. Chem. 234, 199 (2004)
L. Ramírez-Piscina, J.M. Sancho, A. Hernadez-Machado, Phys. Rev. B 48, 125 (1993)
E.A. Novikov, Zh. Eksp. Teor. Fiz. 47, 1919 (1964)
E.A. Novikov, Sov. Phys. JETP 20, 1290 (1964)
R.F. Fox, Phys. Rev. A 34, 4525 (1986)
D.J. Wu, L. Cao, S.Z. Ke, Phys. Rev. E 50, 2496 (1994)
F. Castro, A.D. Sanchez, H.S. Wio, Phys. Rev. Lett. 75, 1691 (1995)
Y. Jia, J.R. Li, Phys. Rev. Lett. 78, 994 (1997)
R. Messina, H. Löwen, Phys. Rev. Lett. 91, 146101 (2003)
H. Kleinert, S. Schmidt, A. Pelster, Phys. Rev. Lett. 93, 160402 (2004)
R.F. Fox, Phys. Rev. A 33, 467 (1986)
M.M. Kłosek-Dygas, B.J. Matkowsky, Z. Schuss, SIAM J. Appl. Math. 48, 425 (1988)
M.M. Kłosek-Dygas, P.S. Hagan, J. Math. Phys. 39, 931 (1998)
P. Hänggi, F. Marchesoni, P. Grigolini, Z. Phys. B 56, 333 (1984)
I. Dayan, M. Gitterman, G.H. Weiss, Phys. Rev. A 46, 757 (1992)
R.N. Mantegna, B. Spagnolo, Phys. Rev. Lett. 76, 563 (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sang, X., Zeng, CH. & Wang, H. Noise-induced optical bistability and state transitions in spin-crossover solids with delayed feedback. Eur. Phys. J. B 86, 229 (2013). https://doi.org/10.1140/epjb/e2013-40179-y
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2013-40179-y