A theory for critically divergent fluctuations of dynamical events at non-ergodic transitionsM. Iwata and S. Sasa
Department of Pure and Applied Sciences, University of Tokyo - Komaba, Tokyo 153-8902, Japan
received 14 September 2006; accepted in final form 22 January 2007; published March 2007
published online 27 February 2007
We theoretically study divergent fluctuations of dynamical events at non-ergodic transitions. We first focus on the finding that a non-ergodic transition can be described as a saddle connection bifurcation of an order parameter for a time correlation function. Then, following the basic idea of Ginzburg-Landau theory for critical phenomena, we construct a phenomenological framework with which we can determine the critical statistical properties at saddle connection bifurcation points. Employing this framework, we analyze a model by considering the fluctuations of an instanton in space-time configurations of the order parameter. We then obtain the exponents characterizing the divergences of the length scale, the time scale and the amplitude of the fluctuations of the order parameter at the saddle connection bifurcation. The results are to be compared with those of previous studies of the four-point dynamic susceptibility at non-ergodic transitions in glassy systems.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
02.50.-r - Probability theory, stochastic processes, and statistics.
64.70.Pf - Glass transitions.
© Europhysics Letters Association 2007