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We study the linear response in a soft potential, the Landau-type temperature dependence of which is responsible for the monostable-to-bistable transformation. The system can be considered as a model of a sample with internal noise, where a second-order phase transition takes place in the bulk limit. The intensity of noise influencing the order parameter is supposed to be a function of the volume. We demonstrate that the anomaly of susceptibility at the phase transition point described by the Landau phase transition theory transforms into the maximal response caused by stochastic resonance if the volume of the system decreases. The phenomenon can be treated also as an increase in the diffuseness of a phase transition with lowering of the critical temperature. We suggest that it is this crossover that contributes to the mechanism of dielectric peculiarities in ceramic and relaxor ferroelectrics.

In the present paper we study the overdamped motion of Brownian particles in tilted periodic piecewise linear potentials of two maxima per period. This system allows one to observe additional phenomena with respect to the case of single-periodic potentials. We show that for certain types of potentials the effective diffusion coefficient D (F) can be enhanced or suppressed compared to the simple sawtooth case. As the most unexpected result it is found that the curve of diffusion coefficient vs tilt can have two maxima. In the region of Poissonian hopping processes we demonstrate the possibility to have a resonantlike peak in the Péclet number Pe(F) . At the tilting force corresponding to the maximum of Pe(F) , the curve of Péclet number vs temperature possesses two maxima.

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the nonmonotonic behavior of the diffusion coefficient as a function of temperature are determined. The diffusion coefficient and coherence level are found to be extremely sensitive to the asymmetry of the potential. It is established that at the values of the external force, for which the enhancement of diffusion is most rapid, the level of coherence has a wide plateau at low temperatures with the value of the Péclet factor 2. An interpretation of the amplification of diffusion in comparison with free thermal diffusion in terms of probability distribution is proposed.