Crossovers in the thermal decay of metastable states in discrete systems

The thermal decay of linear chains from a metastable state is investigated. A crossover from rigid to elastic decay occurs when the number of particles, the single particle energy barrier or the coupling strength between the particles is varied. In the rigid regime, the single particle energy barrier is small compared to the coupling strength and the decay occurs via a uniform saddlepoint solution, with all degrees of freedom decaying instantly. Increasing the barrier one enters the elastic regime, where the decay is due to bent saddlepoint configurations using the elasticity of the chain to lower their activation energy. Close to the rigid-to-elastic crossover, nucleation occurs at the boundaries of the system. However, in large systems, a second crossover from boundary to bulk nucleation can be found within the elastic regime, when the single particle energy barrier is further increased. We compute the decay rate in the rigid and in the elastic regimes within the Gaussian approximation. Around the rigid-to-elastic crossover, the calculations are performed beyond the steepest descent approximation. In this region, the prefactor exhibits a scaling property. The theoretical results are discussed in the context of discrete Josephson transmission lines and pancake vortex stacks that are pinned by columnar defects.Comment: 13 pages, RevTeX, 7 PS-figure

Local Inhomogeneity Effects on Nucleation Process in a High External Bias

Quantum nucleation processes in the presence of local moderate inhomogeneities are studied theoretically at high biases. The quantum nucleation rate Gamma is calculated for one-dimensional systems in a form Gamma = A e^(-B/hbar) by using the `bounce' method. The bias-dependence of the exponent B is shown to be changed by inhomogeneities. This change is explained by the reduction of the effective spatial dimension of the system. By studying the system-size dependence of the prefactor A, the condition for the appearance of inhomogeneity effects is evaluated. Nucleation rates in thermal activation regimes are also calculated, and compared with quantum tunneling regimes. For higher-dimensional systems, it is shown that the local approximation of inhomogeneity does not hold, and that spatial profiles of inhomogeneity become important.Comment: 10 pages, 6 figure

Thermodynamics of the rupture in a Morse lattice

The rupture of a Morse lattice is considered in the present paper. The critical rupture force Fcr is found to decrease with the number of particles N as Fcr ~ 1/$\sqrt{N}$. The partition function is obtained for two states of the lattice – with all equal bond lengths and one broken bond. In the first case an accurate expressions for thermodynamic parameters are obtained, and thermodynamic expressions are derived in the harmonic approximation in the latter case. The analytical predictions are confirmed by extensive MD simulations. Cis-trans isomerization is considered as an example. Volume fractions of trans- and cis-isomers versus number of monomer units N are found depending on the torsion stiffnesses