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We show that a high-frequency field may resonantly decrease the activation energy of escape from a potential well. For systems in spatially periodic potentials, the effect is different for the transitions in opposite directions, which gives rise to resonantly directed diffusion (DD). DD arises in both asymmetric and symmetric periodic potentials. It depends exponentially strongly on the field magnitude, and its direction can be controlled by varying the field spectrum.[S0031-9007 (97)03880-5] PACS numbers: 05.40. + j, 02.50. -r, 05.20. -y, 05.60. + wMuch attention has been given recently to the occurrence of unidirectional motion of systems which fluctuate in a periodic potential. This motion is superimposed on diffusion and arises if the system is away from thermal equilibrium. It is substantially due to fluctuations and can be viewed as a directed diffusion (DD). The effect was initially considered for potentials asymmetric within the period (ratchets) [1,2]. It then became clear that DD may arise also in symmetric potentials [3]. The interest in DD is stimulated by its relevance to a broad class of processes, from atomic diffusion in crystals, solid surfaces, and optical lattices to phase diffusion in Josephson junctions and the motion of proteins along biopolymers. For the most part, the analysis of DD has been limited to systems driven by nonequilibrium noise or by thermal noise and an adiabatically slow driving field where the diffusion rate is determined by the instantaneous value of the field [1-3]. The adiabatic picture does not apply if the field period t F is less than the characteristic relaxation time of the system t rel . One might expect that DD will be "averaged out" with the decreasing t F . We show that, on the contrary, the rate of DD may display resonant peaks as a function of the field frequency.For small fluctuation intensity, the rate of directed diffusion j in a periodic potential U͑q͒ with period l is determined by the difference between the probabilities W 1 , W 2 of the transitions from a potential minimum to the right and to the left,The analysis of resonant DD requires general nonadiabatic theory of escape rates W 6 . It should differ qualitatively from the theories where the effect of a high-frequency field is described in terms of fieldenhanced diffusion over energy [4]. Such diffusion gives rise to the correction to the distribution over energy which is quadratic in the field amplitude, whereas the rates W 1 and W 2 would still coincide with each other.In the present paper we provide a nonadiabatic theory of directed diffusion for the nontrivial and important case of moderately strong driving fields. We show that, even for the amplitude of forced vibrations about the minima of the potential U͑q͒ being small compared to the period l, the probabilities of transitions between potential wells depend on the field magnitude exponentially strongly. We also show that both the direction and speed of DD depend on spectral characteristics of the driving field.Interwell transitions require lar...

We analyze the probabilities of large infrequent fluctuations in nonadiabatically driven systems. In a broad range of the driving field magnitudes, the logarithm of the fluctuation probability is linear in the field, and the response can be characterized by a logarithmic susceptibility (LS). We evaluate the activation energies for nucleation, with account taken of the field-induced lifting of time and spatial degeneracy of instantonlike nucleation trajectories. LS for nucleation in systems with nonconserved order parameter is shown to be a nonmonotonic function of v and k. [S0031-9007(97)04328-7]

The dielectric response in relaxor ferroelectrics is analyzed in the framework a model for the polarization dynamics in the presence of polar clusters. We associate the origin of polar clusters with the atoms displaced from their centrosymmerical positions even above T c . Their collective hopping in multi-well potentials induced by disorder is analogous with the situation in glasses. The theory explicitly takes into account the distribution of cluster reorientation frequencies and the effect of cluster-cluster interactions in highly polarizable crystals, which we describe in terms of the local field distribution function.The dielectric constant is obtained from an integral master equation for the polarization dynamics in the presence of a time dependent electric field. The theory is applied for the analysis of the shape of the frequency dependent permittivity in the typical relaxor ferrolectrics P ST as a function of temperature. The comparison of the theory with experiment shows that in contrast to earlier assumptions, the observed Vogel-Fulcher dependence of the permittivity maximum is a consequence of the Vogel-Fulcher temperature dependence of the cluster reorientation frequency.

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