Dresden 2006 – wissenschaftliches Programm

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SYSS: Structure Formation and Self-Organization in non-equilibrium Systems

SYSS 3: Structure Formation and Self-Organization in non-equilibrium Systems - Poster

SYSS 3.10: Poster

Donnerstag, 30. März 2006, 16:00–18:00, P1

H-theorem for interacting systems driven by multiplicative noise — •Fabian Senf and Ulrich Behn — Institut für Theoretische Physik, Universität Leipzig, POB 100 920, 04009 Leipzig

The H-theorem for a system of N globally coupled Stratonovich models is found and the convergence to the stationary solution independent of the initial distribution is proved. Due to the multiplicative noise and the interaction between the particles there is no detailled balance and therefore an analytical expression for the stationary distribution is not easily found.

Nevertheless, the information contained in the system of coupled Langevin equations provides important hints to the qualitative structure of the stationary state. The state space of the stochastic motion is divided in sectors whose topology depends on the system parameters. The Langevin flow between these sectors can be determined.

For large times the system is found with probability one in one of those sectors which have their boundary flows pointing inward, only. These are the ergodic components. This result is independent of the system size so that phase transistions associated with the breaking of ergodicity exist already for finite N. The critical exponent characterizing the order parameter near the critical point depends on all parameters of the Stratonovich model including the system size N if the latter is finite, for N → ∞ see [1].

[1] T. Birner, K. Lippert, R. Müller, A. Kühnel, U. Behn, Critical behavior of nonequilibrium phase transitions to magnetically ordered states, Phys. Rev. E 65, 046110 (2002)