Exact and scaling approaches to nonequilibrium models

Stephen William Lovesey

T. Hanney, Robin B. Stinchcombe

Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality symmetries, yielding exact fixed points for a variety of exclusion models. In addition, it is shown how the asymmetric simple exclusion process in one dimension can be written in terms of a classical Hamiltonian in two dimensions using a Suzuki-Trotter decomposition.

Grégory Schehr, Pierre Le Doussal

We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal parts yields a closed exact RG equation for the local part, to a given order in the local part. The method is illustrated on the O(N) model by straightforwardly recovering the eta exponent and scaling functions. Then it is applied to study the glass phase of the Cardy-Ostlund, random phase sine Gordon model near the glass transition temperature. The static correlations and equilibrium dynamical exponent z are recovered and several results are obtained, such as the equilibrium two-point scaling functions. The nonequilibrium, finite momentum, two-time t,t' response and correlations are computed. They are shown to exhibit scaling forms, characterized by exponents lambda(R) not equal lambda(C), as well as universal scaling functions that we compute. The fluctuation dissipation ratio is found to be nontrivial and of the form X[q(z)(t-t'),t/t']. Analogies and differences with pure critical models are discussed.

U. C. Täuber

Holger Baur, Andrea Fubini, Ulrich Weiß

Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium transfer rates of the boundary sine-Gordon and the anisotropic Kondo model at zero temperature. Combining these results with findings from the thermodynamic Bethe ansatz, we derive exact closed form expressions for the transfer rate in the biased spin-boson model in the scaling limit. They illustrate how the crossover from weak to strong tunneling takes place. Using a conjectured correspondence between the transfer and the decoherence rate, we also determine the exact lower bound for damping of the coherent oscillation as a function of bias and dissipation strength in this paradigmic model for nuclear magnetic resonance and superposition of macroscopically distinct states (qubits).