Critical dynamics of phase transition driven by dichotomous Markov noise

Emergence of stationary multimodality under two-timescaled dichotomic noise

We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic noise. It is shown that when the statistics of the time intervals between noise transitions is characterized by two well differentiated timescales, the stationary distribution may develop multimodality (bi- and trimodality). The underlying effects that lead to a probability concentration in different points include intermittence and also a dynamical locking of realizations. Our results are supported by numerical simulations as well as by an exact treatment obtained from a Markovian embedding of the full dynamics, which leads to a third-order differential equation for the stationary distribution.

Singular response of bistable systems driven by telegraph noise

We show that weak periodic driving can exponentially strongly change the rate of escape from a potential well of a system driven by telegraph noise. The analysis refers to an overdamped system, where escape requires that the noise amplitude θ exceed a critical value θ(c). For θ close to θ(c), the exponent of the escape rate displays a nonanalytic dependence on the amplitude of an additional low-frequency modulation. This leads to giant nonlinearity of the response of a bistable system to periodic modulation. Also studied is the linear response to periodic modulation far from θ(c). We analyze the scaling of the logarithm of the escape rate with the distance to the saddle-node and pitchfork bifurcation points. The analytical results are in excellent agreement with numerical simulations.

Dynamics in the anisotropic XY model driven by dichotomous Markov noise

The statistics of a subcritical spatially homogeneous XY spin system driven by dichotomous Markov noise as an external field is investigated, particularly focusing on the switching process of the sign of the order parameter parallel to the external field. The switching process is classified in two types, which are called the Bloch-type switching and the Ising-type switching, according to whether or not the order parameter perpendicular to the external field takes finite value at the switching. The phase diagram for the onset of the switching process with respect to the amplitude of the external field and the anisotropy parameter of the system is constructed. It is revealed that the power spectral density I(omega) for the time series of the order parameter in the case of the Bloch-type switching is proportional to omega(-32) in an intermediate region of omega. Furthermore, the scaling function of I(omega) near the onset point of the Bloch-type switching is derived.

Domain-size statistics in the time-dependent Ginzburg-Landau equation driven by a dichotomous Markov noise

The domain dynamics of magnetization obeying the time-dependent Ginzburg-Landau equation driven by a dichotomous Markov noise is discussed. The system with various domain sizes in the early stage temporally evolves following an annihilation of neighboring domain walls, where each domain wall moves diffusively. Three statistics on the domain size, i.e., average domain size, the ensemble average of the domain size distribution function, and the spatial power spectrum of the magnetization, are evaluated to characterize the domain wall annihilation process. A phenomenological evolution equation for the domain-size distribution function is constructed by simplifying the annihilation process of the domain wall appropriately, and the underlying mechanism of those statistics is investigated.