Abstract
The motion of a heavy Brownian particle in a low-dimensional bounded solid structure under the effect of a phonon’s excitation fluctuations is considered. Because of the finiteness of the system, the fluctuation spectrum has zero spectral density at zero frequency. The effect of this kind of noise, which is conditionally called “green” noise, is studied both analytically by using the averaging method and numerically on the basis of predictor-corrector algorithms. The effective potential is introduced, and its form is shown to govern the particle dynamics. Considering a Gaussian potential well (a trap) as an example, it is demonstrated that green noise leads to abrupt phase transitions in the system as a result of very small parameter variations (a catastrophe-type effect). The results are compared with the case of white noise in an unbounded structure. From numerical calculations, it follows that the boundedness of the structure, which changes the noise spectrum, favors a considerable increase in the lifetime of the particle in the trap.
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References
H. A. Kramers, Physica 7, 284 (1940).
P. Hänggi and P. Talkner, Rev. Mod. Phys. 62, 251 (1990).
V. I. Mel’nikov, Phys. Rep. 209, 1 (1991).
H. Risken, The Fker-Planck Equation (Springer, Berlin, Heidelberg, 1996).
P. Hänggi and P. Jung, Adv. Chem. Phys. 89, 239 (1995).
S. M. Rytov, Introduction to Statistical Radiophysics (Nauka, Moscow, 1976), Vol. 1, part 1 [in Russian].
W. Horsthemke and P. Lefever, Noise-Induced Transitions (Springer, Heidelberg, 1984; Mir, Moscow, 1987).
V. I. Cherednik and M. Yu. Dvoesherstov, Akust. Zh. 51, 550 (2005) [Acoust. Phys. 51, 469 (2005)].
M. V. Kurbatov and S. A. Rybak, Akust. Zh. 45, 370 (1999) [Acoust. Phys. 45, 326 (1999)].
H. A. T. Bethe, Phys. Rev. 66, 163 (1944).
E. Simiu, M. Frey, and R. Melnikov, J. Eng. Mech. 122, 263 (1996).
C. A. Guz and M. V. Sviridov, Phys. Lett. A 240, 43 (1998).
S. A. Guz, Yu. G. Krasnikov, and M. V. Sviridov, in Acoustics of Inhomogeneous Media, Ed. by S. A. Rybak (MFTI, Moscow, 2001), pp. 157–166 [in Russian].
P. V. Pavlov and A. V. Khhlov, Solid State Physics (Vyssh. Shkola, Moscow, 1985) [in Russian].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics, 2nd ed. (Nauka, Moscow, 1964; Pergamon, Oxford, 1980), Vol. 2.
S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Introduction to Statistical Radio Physics. Random Fields (Nauka, Moscow, 1978), Part 2, Vol. 2 [in Russian].
S. A. Guz and M. V. Sviridov, Chaos 11, 605 (2001).
S. A. Guz, Zh. Eksp. Teor. Fiz. 122, 188 (2002) [JETP 95, 166 (2002)].
A. D. Ventzel and M. I. Freidlin, Random Perturbations of Dynamical Systems (Nauka, Moscow, 1979; Springer, New York, 1984).
S. A. Guz, I. G. Ruzavin, and M. V. Sviridov, Phys. Lett. A 274, 104 (2000).
R. Mannella and V. Palleschi, Phys. Rev. A 40, 3381 (1989).
S. A. Guz, R. Mannella, and M. V. Sviridov, Phys. Lett. A 317, 233 (2003).
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Original Russian Text © S.A. Guz, M.G. Nikulin, M.V. Sviridov, 2010, published in Akusticheskiĭ Zhurnal, 2010, Vol. 56, No. 1, pp. 16–25.
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Guz, S.A., Nikulin, M.G. & Sviridov, M.V. Brownian motion in a solitary potential well in a bounded solid structure. Acoust. Phys. 56, 14–23 (2010). https://doi.org/10.1134/S1063771010010033
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DOI: https://doi.org/10.1134/S1063771010010033