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DY: Dynamik und Statistische Physik

DY 10: Statistical physics far from thermal equilibrium

DY 10.1: Hauptvortrag

Montag, 24. März 2003, 09:30–10:00, G\"OR/226

Dynamic phase transitions in diffusion-limited reactions — •Uwe C. Täuber — Physics Department, Virginia Tech, Blacksburg, VA 24061-0435, USA

Many systems can be described in terms of diffusion-limited ’chemical’ reactions. These may display non-equilibrium continuous transitions separating active from inactive, absorbing states, where stochastic fluctuations cease entirely. The universality classes of such active/absorbing phase transitions can be analyzed via a field-theory representation of the master equation, and the renormalization group. The generic case is represented by the processes A ⇌ A + A, and A → ∅, which map onto Reggeon field theory with the critical exponents of directed percolation (DP). For branching and annihilating random walks (BARW), A → (m+1) A and A + A → ∅, the mean-field rate equation predicts an active state only. Yet BARW with odd m display a DP transition for d ≤ 2. For even offspring number m, the particle number parity is conserved locally. Below d_c′ ≈ 4/3, this leads to the emergence of an inactive phase that is characterized by the power laws of the pair annihilation process. The critical exponents at the transition are those of the ’parity-conserving’ universality class. For local processes without memory, competing pair or triplet annihilation and fission reactions k A → ∅, k A → (k+m)A with k=2,3 yield the only other universality classes not described by mean-field theory. In these reactions, site occupation number restrictions play a crucial role.