Non-equilibrium Phase Transitions in a Single-Mode Laser Model Driven by Non-Gaussian Noise

  • Yanfei Jin
Conference paper


The non-equilibrium phase transition of a single-mode laser model driven by non-Gaussian noise is studied in this paper. The stationary probability distribution (SPD) and its extremal equation are derived by using the path integral approach and the unified colored noise approximation. It is found that there is a critical relation between the noise intensity and the correlation time so that there is a transition line separating the mono-stable region and the bi-stable region. Given the noise intensity and the correlation time, the single-mode laser system undergoes a successive phase transition by varying the departure of the non-Gaussian noise from the Gaussian noise. Meanwhile, as indicated in the phase diagram, when the noise intensity and the correlation time are varied, the system undergoes a reentrance phenomenon.



This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 10702025, 10972032, and 70771005, in part by the Excellent Young Scholars Research Fund of Beijing Institute of Technology under Grant No. 2008Y0175, Beijing Municipal Commission of Education Project under Grant No. 20080739027, and the Ministry of Education Foundation of China under Grant No. 20070004045.


  1. 1.
    Nicolis G, Prigogine I (1976) Selforganization in nonequilibrium system. Wiley, New YorkGoogle Scholar
  2. 2.
    Haken H (1977) Synergetics. Springer, BerlinCrossRefGoogle Scholar
  3. 3.
    Horsthemke W (1984) Noise-induced transitions. Springer, New YorkMATHGoogle Scholar
  4. 4.
    Hu G (1994) Stochastic force and nonlinear systems. Shanghai Science and Technological Education Publishing House, ShanghaiGoogle Scholar
  5. 5.
    Fulinski A (1995) Relaxation, noise-induced transitions, and stochastic resonance driven by non-Markovian dichotomic noise. Phys Rev E 52:4523CrossRefGoogle Scholar
  6. 6.
    Zhu SQ (1989) Multiplicative colored noise in a dye laser at steady state. Phys Rev A 40:3441CrossRefGoogle Scholar
  7. 7.
    Gudyma YV (2004) Nonequilibrium first-order phase transition in semiconductor system driven by colored noise. Physica A 331:61CrossRefGoogle Scholar
  8. 8.
    Van den Broeck C, Parrondo JMR, Toral R (1994) Noise-induced nonequilibrium phase transition. Phys Rev Lett 73:3395CrossRefGoogle Scholar
  9. 9.
    Zaikin AA, Garcia-Ojalvo J, Schimansky-Geier L (1999) Nonequilibrium first-order phase transition induced by additive noise. Phys Rev E 60:R6275CrossRefGoogle Scholar
  10. 10.
    Castro F, Sanchez AD, Wio HS (1995) Reentrance phenomena in noise induced transitions. Phys Rev Lett 75:1691CrossRefGoogle Scholar
  11. 11.
    Jia Y, Li JL (1997) Reentrance phenomena in a bistable kinetic model driven by correlated noise. Phys Rev Lett 78:994CrossRefGoogle Scholar
  12. 12.
    Zhu SQ (1990) White noise in dye-laser transients. Phys Rev A 42:5758CrossRefGoogle Scholar
  13. 13.
    Cao L, Wu DJ, Lin L (1994) First-order-like transition for colored saturation models of dye lasers: effects of quantum noise. Phys Rev A 49:506CrossRefGoogle Scholar
  14. 14.
    Cao L, Wu DJ (1999) Cross-correlation of multiplicative and additive noises in a single-mode laser white-gain-noise model and correlated noises induced transitions. Phys Lett A 260:126CrossRefGoogle Scholar
  15. 15.
    Liang GY, Cao L, Wu DJ (2002) Moments of intensity of single-mode laser driven by additive and multiplicative colored noises with colored cross-correlation. Phys Lett A 294:190CrossRefGoogle Scholar
  16. 16.
    Luo XQ, Zhu SQ, Chen XF (2001) Effects of colored noise on the intensity and phase in a laser system. Phys Lett A 287:111CrossRefMATHGoogle Scholar
  17. 17.
    Xie CW, Mei DC (2004) Effects of correlated noises on the intensity fluctuation of a single-mode laser system. Phys Lett A 323:421CrossRefMATHGoogle Scholar
  18. 18.
    Jin YF, Xu W, Xie WX, Xu M (2005) The relaxation time of a single-mode dye laser system driven by cross-correlated additive and multiplicative noises. Physica A 354:143CrossRefGoogle Scholar
  19. 19.
    Bezrukov SM, Vodyanoy I (1997) Stochastic resonance in non-dynamical systems without response thresholds. Nature 385:319CrossRefGoogle Scholar
  20. 20.
    Goychuk I, Hänggi P (2000) Stochastic resonance in ion channels characterized by information theory. Phys Rev E 61:4272CrossRefGoogle Scholar
  21. 21.
    Fuentes MA, Toral R, Wio HS (2001) Enhancement of stochastic resonance: the role of non-Gaussian noises. Physica A 295:114CrossRefMATHGoogle Scholar
  22. 22.
    Fuentes MA, Wio HS, Toral R (2002) Effective Markovian approximation for non-Gaussian noises: a path integral approach. Physica A 303:91MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Revelli JA, Sanchez AD, Wio HS (2002) Effect of non-Gaussian noises on the stochastic resonance-like phenomenon in gated traps. Physica D 168:165CrossRefGoogle Scholar
  24. 24.
    Wio HS, Toral R (2004) Effect of non-Gaussian noise sources in a noise-induced transition. Physica D 193:161CrossRefMATHGoogle Scholar
  25. 25.
    Goswami G, Majee P, Ghosh PK, Bag BC (2007) Colored multiplicative and additive non-Gaussian noise-driven dynamical system: mean first passage time. Physica A 374:549CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MechanicsBeijing Institute of TechnologyBeijingPeople’s Republic of China

Personalised recommendations