DMRG studies of the effect of constraint release on the viscosity of polymer melts

The scaling of the viscosity of polymer melts is investigated with regard to the molecular weight. We present a generalization of the Rubinstein-Duke model, which takes constraint releases into account and calculate the effects on the viscosity by the use of the Density Matrix Renormalization Group (DMRG) algorithm. Using input from Rouse theory the rates for the constraint release are determined in a self consistent way. We conclude that shape fluctuations of the tube caused by constraint release are not a likely candidate for improving Doi's crossover theory for the scaling of the polymer viscosity.Comment: 6 pages, 8 figure

Scaling of the magnetic linear response in phase-ordering kinetics

The scaling of the thermoremanent magnetization and of the dissipative part of the non-equilibrium magnetic susceptibility is analysed as a function of the waiting-time $s$ for a simple ferromagnet undergoing phase-ordering kinetics after a quench into the ferromagnetically ordered phase. Their scaling forms describe the cross-over between two power-law regimes governed by the non-equilibrium exponents $a$ and $\lambda_R/z$, respectively. A relation between $a$, the dynamical exponent $z$ and the equilibrium exponent $\eta$ is derived from scaling arguments. Explicit tests in the Glauber-Ising model and the kinetic spherical model are presented.Comment: 7 pages, 2 figures included, needs epl.cls, version to appear in Europhys. Let

Ageing in the critical contact process: a Monte Carlo study

The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations in one and two dimensions and through mean-field theory that time-translation invariance is broken and that dynamical scaling holds. We find that the autocorrelation and autoresponse exponents lambda_{Gamma} and lambda_R are equal but, in contrast to systems relaxing to equilibrium, the ageing exponents a and b are distinct. A recent proposal to define a non-equilibrium temperature through the short-time limit of the fluctuation-dissipation ratio is therefore not applicable.Comment: 18 pages, 7 figures, Latex2e with IOP macros; final for

The density-matrix renormalization group

The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This algorithm has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly acquired the status of method of choice for numerical studies of one-dimensional quantum systems. Its applications to the calculation of static, dynamic and thermodynamic quantities in such systems are reviewed. The potential of DMRG applications in the fields of two-dimensional quantum systems, quantum chemistry, three-dimensional small grains, nuclear physics, equilibrium and non-equilibrium statistical physics, and time-dependent phenomena is discussed. This review also considers the theoretical foundations of the method, examining its relationship to matrix-product states and the quantum information content of the density matrices generated by DMRG.Comment: accepted by Rev. Mod. Phys. in July 2004; scheduled to appear in the January 2005 issu