Condensed Matter Theory

Abstract:

We investigate numerically the dynamical behavior of a polymer chain collapsing in a dilute solution. The rate of collapse is measured with and without the presence of hydrodynamic interactions. We find that hydrodynamic interactions accelerate polymer collapse. We present a scaling theory describing the physical process responsible for the collapse kinetics. Predicted collapse times in a hydrodynamic (tauH approximately N(4/3)) and a Brownian heat bath (tauB approximately N2) agree well with the numerical results (tauH approximately N(1.40+/-0.08) and tauB approximately N(1.89+/-0.09)) where N denotes chain length. The folding kinetics of Go models of proteins is also examined. We show that for these systems, where many free energy minima compete, hydrodynamics has little effect on the kinetics.

Abstract:

Low temperature dynamics of Ising ferromagnets under finite magnetic fields are studied in terms of quantum spin representations of stochastic evolution operators. These are constructed for the Glauber dynamic as well as for its modification, introduced by Park [Phys. Rev. Lett. 92, 015701 (2004)]. In both cases the relaxation time after a field quench is evaluated both numerically and analytically using the spectrum gap of the corresponding operators. The numerical work employs standard recursive techniques following a symmetrization of the evolution operator accomplished by a nonunitary spin rotation. The analytical approach uses low temperature limits to identify dominant terms in the eigenvalue problem. It is argued that the relaxation times already provide a measure of actual nucleation lifetimes under finite fields. The approach is applied to square, triangular and honeycomb lattices.