We study spectral Galerkin approximations of an Allen–Cahn equation over the two-dimensional torus perturbed by weak space-time white noise of strength √ ε. We introduce a Wick renormalisation of the equation in order to have a system that is welldefined as the regularisation is removed. We show sharp upper and lower bounds on the transition times from a neighbourhood of the stable configuratio...

Titanium carbide (TiC) nanocrystals were recently proposed as the carrier of the mysterious 21 mm emission feature observed in post–asymptotic giant branch stars, based on their close spectral match and the presolar nature of meteoritic TiC nanograins (which reveals their stellar ejecta origin). But we show in this Letter that the KramersKronig dispersion relations, which relate the wavelength-...

Noise-induced escape from a metastable potential is considered on timescales preceding the formation of quasi-equilibrium within the metastable part of the potential. It is shown that the escape flux may then depend exponentially strongly, and in a complicated manner, on time and friction.

We review dispersion relations, which relate the real part of the optical susceptibility (refraction) to the imaginary part (absorption). We derive and discuss these relations as applied to nonlinear optical systems. It is shown that in the nonlinear case, for self-action effects the correct form for such dispersion relations is nondegenerate, i.e. it is necessary to use multiple frequency argu...

We demonstrate that the fusion algebra of conformal defects of a two-dimensional conformal field theory contains information about the internal symmetries of the theory and allows one to read off generalizations of Kramers-Wannier duality. We illustrate the general mechanism in the examples of the Ising model and the three-state Potts model.

Fluctuational escape from a multiwell potential is shown to display new features, as compared to the conventional single-well case. The flux J may depend on friction gamma exponentially strongly, over an exponentially long period; for small enough temperatures, J(gamma) undergoes marked oscillations in the range of small gamma, and the time evolution of J changes drastically as gamma exceeds a ...

We introduce a new scheme to analyze the kinetics of homogeneous nucleation in terms of a global order parameter. Our approach is based on the application of the internal degrees of freedom formalism 1 to derive a kinetic equation of the Kramers type formulated for a global reaction coordinate. We provide explicit expressions for the quantities and coefficients involved in the process, suitable...

We present the first analysis of harmonic generation data where the full potential of the generalized nonlinear Kramers-Krönig (KK) relations and sum rules is exploited. We consider two published sets of wide spectral range experimental data of third harmonic generation susceptibility on different polymers, the polysilane (frequency

In this paper we show that the standard causality condition for attenuated waves, i.e. the Kramers-Kronig relation that relates the attenuation law and the phase speed of the wave, is necessary but not sufficient for causality of a wave. By causality of a wave we understand the property that its wave front speed is bounded. Although this condition is not new, the consequences for wave attenuati...

Systems where multiple trapping or other manifestations of disorder lead to a non-local temporal evolution which results in the macroscopic observation of anomalous kinetics, are shown to exhibit a non-exponential, Mittag–Leffler decay in Kramers-type escape problems. The detailed behaviour of the survival probability is studied, and it is demonstrated that the associated escape rate is time de...