Coherent phenomena in stochastic dynamical systems

V.I. Klyatskin^a, D. Gurarie^b
^aA M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation
^bDepartment of Mathematics, Case Western Reserve University, Cleveland, Ohio, USA

Basic ideas of the statistical topography of random processes and fields are presented, which are used in the analysis of coherent phenomena in simple dynamical systems. Such phenomena take place with probability one, and provide links between individual realizations and statistical characteristics of systems at large. We confine ourselves to several examples: transfer phenomena in singular dynamic systems under the action of random forces; dynamic localization of plane waves in randomly stratified media; clustering of randomly advected passive tracers; and formation of caustic structures for wave fields in randomly inhomogeneous media. All these phenomena are studied based on the analysis of one-point (space-time) probability distribution functions.

PACS: 02.50.−r, 05.40.-j, 05.45.+b, 42.50.−p (all)
DOI: 10.1070/pu1999v042n02ABEH000522
URL: https://ufn.ru/en/articles/1999/2/c/
Web of Science

000079341200003
Citation: Klyatskin V I, Gurarie D "Coherent phenomena in stochastic dynamical systems" Phys. Usp. 42 165 (1999)

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Оригинал: Кляцкин В И, Гурарий Д «Когерентные явления в стохастических динамических системах» УФН 169 171–207 (1999); DOI: 10.3367/UFNr.0169.199902c.0171

References (69) Cited by (30) Similar articles (20) ↓

V.I. Klyatskin “Clustering and diffusion of particles and passive tracer density in random hydrodynamic flows” Phys. Usp. 46 667–688 (2003)
V.I. Klyatskin “Electromagnetic wave propagation in a randomly inhomogeneous medium as a problem in mathematical statistical physics” Phys. Usp. 47 169–186 (2004)
V.K. Vanag “Study of spatially extended dynamical systems using probabilistic cellular automata” Phys. Usp. 42 413–434 (1999)
V.I. Klyatskin “Integral characteristics: a key to understanding structure formation in stochastic dynamic systems” Phys. Usp. 54 441–464 (2011)
V.S. Anishchenko, A.B. Neiman et al “Stochastic resonance: noise-enhanced order” Phys. Usp. 42 7–36 (1999)
A. Loskutov “Fascination of chaos” Phys. Usp. 53 1257–1280 (2010)
Ya.B. Zel’dovich, S.A. Molchanov et al “Intermittency in random media” Sov. Phys. Usp. 30 353–369 (1987)
V.V. Lobzin, V.R. Chechetkin “Order and correlations in genomic DNA sequences. The spectral approach” Phys. Usp. 43 55–78 (2000)
M.L. Ter-Mikhaelyan “Simple atomic systems in resonant laser fields” Phys. Usp. 40 1195–1238 (1997)
A.S. Mikhailov, I.V. Uporov “Critical phenomena in media with breeding, decay, and diffusion” Sov. Phys. Usp. 27 695–714 (1984)
V.V. Uchaikin “Self-similar anomalous diffusion and Levy-stable laws” Phys. Usp. 46 821–849 (2003)
S.I. Vinitskii, V.L. Derbov et al “Topological phases in quantum mechanics and polarization optics” Sov. Phys. Usp. 33 (6) 403–428 (1990)
G.P. Berman, A.R. Kolovskii “Quantum chaos in interactions of multilevel quantum systems with a coherent radiation field” Sov. Phys. Usp. 35 (4) 303–326 (1992)
M.I. Tribel’skii “Short-wavelength instability and transition to chaos in distributed systems with additional symmetry” Phys. Usp. 40 159–180 (1997)
V.S. Anishchenko, T.E. Vadivasova et al “Statistical properties of dynamical chaos” Phys. Usp. 48 151–166 (2005)
D.N. Klyshko “Berry geometric phase in oscillatory processes” Phys. Usp. 36 (11) 1005–1019 (1993)
V.I. Klyatskin, V.I. Tatarskii “Diffusive random process approximation in certain nonstationary statistical problems of physics” Sov. Phys. Usp. 16 494–511 (1974)
K.V. Koshel, S.V. Prants “Chaotic advection in the ocean” Phys. Usp. 49 1151–1178 (2006)
S.A. Gredeskul, V.D. Freilikher “Localization and wave propagation in randomly layered media” Sov. Phys. Usp. 33 (2) 134–146 (1990)
Yu.I. Vorontsov “The phase of an oscillator in quantum theory. What is it ’in reality’?” Phys. Usp. 45 847–868 (2002)

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