Prof John Cardy FRS

Abstract:

It is shown that the scaling operators in the conformal limit of a two-dimensional field theory have massive form factors which obey a simple factorisation property in rapidity space. This has been used to identify such operators within the form factor bootstrap approach. A sum rule which yields the scaling dimension of such operators is also derived.

Abstract:

We study theoretically and numerically the steady state diffusion controlled reaction [Formula Presented], where currents [Formula Presented] of [Formula Presented] and [Formula Presented] particles are applied at opposite boundaries. For a reaction rate [Formula Presented], and equal diffusion constants [Formula Presented], we find that when [Formula Presented] the reaction front is well described by mean-field theory. However, for [Formula Presented], the front acquires a Gaussian profile—a result of noise induced wandering of the reaction front center. We make a theoretical prediction for this profile which is in good agreement with simulation. Finally, we investigate the intrinsic (nonwandering) front width and find results consistent with scaling and field theoretic predictions. © 1996 The American Physical Society.

Abstract:

A systematic theory for the diffusion-limited reaction processes A + A → 0 and A → (m + 1) A is developed. Fluctuations are taken into account via the field-theoretic dynamical renormalization group. For even m, the mean field rate equation, which predicts only an active phase, remains qualitatively correct near dc = 2 dimensions; but below d'c≈4/3 a nontrivial transition to an inactive phase governed by power law behavior appears. For odd m, there is a dynamic phase transition for any d ≤ 2 which is described by the directed percolation universality class. © 1996 The American Physical Society.