Metastable and scaling regimes of a one-dimensional Kawasaki dynamics

We investigate the large-time scaling regimes arising from a variety of metastable structures in a chain of Ising spins with both first- and second-neighbor couplings while subject to a Kawasaki dynamics. Depending on the ratio and sign of these former, different dynamic exponents are suggested by finite-size scaling analyses of relaxation times. At low but nonzero-temperatures these are calculated via exact diagonalizations of the evolution operator in finite chains under several activation barriers. In the absence of metastability the dynamics is always diffusive.Comment: 18 pages, 8 figures. Brief additions. To appear in Phys. Rev.

Directed diffusion of reconstituting dimers

We discuss dynamical aspects of an asymmetric version of assisted diffusion of hard core particles on a ring studied by G. I. Menon {\it et al.} in J. Stat Phys. {\bf 86}, 1237 (1997). The asymmetry brings in phenomena like kinematic waves and effects of the Kardar-Parisi-Zhang nonlinearity, which combine with the feature of strongly broken ergodicity, a characteristic of the model. A central role is played by a single nonlocal invariant, the irreducible string, whose interplay with the driven motion of reconstituting dimers, arising from the assisted hopping, determines the asymptotic dynamics and scaling regimes. These are investigated both analytically and numerically through sector-dependent mappings to the asymmetric simple exclusion process.Comment: 10 pages, 6 figures. Slight corrections, one added reference. To appear in J. Phys. Cond. Matt. (2007). Special issue on chemical kinetic

The Neurobiology and Psychology of Empathy

This work was supported by a grant from The Character Project (Psychology of Character), from Wake Forest University, via the John Templeton Foundation

Solution of a class of one-dimensional reaction-diffusion models in disordered media

We study a one-dimensional class of reaction-diffusion models on a $10-$parameters manifold. The equations of motion of the correlation functions close on this manifold. We compute exactly the long-time behaviour of the density and correlation functions for {\it quenched} disordered systems. The {\it quenched} disorder consists of disconnected domains of reaction. We first consider the case where the disorder comprizes a superposition, with different probabilistic weights, of finite segments, with {\it periodic boundary conditions}. We then pass to the case of finite segments with {\it open boundary conditions}: we solve the ordered dynamics on a open lattice with help of the Dynamical Matrix Ansatz (DMA) and investigate further its disordered version.Comment: 11 pages, no figures. To appear in Phys.Rev.

Generating Entangled Microwave Radiation Over Two Transmission Lines

Using a superconducting circuit, the Josephson mixer, we demonstrate the first experimental realization of spatially separated two-mode squeezed states of microwave light. Driven by a pump tone, a first Josephson mixer generates, out of quantum vacuum, a pair of entangled fields at different frequencies on separate transmission lines. A second mixer, driven by a $\pi$-phase shifted copy of the first pump tone, recombines and disentangles the two fields. The resulting output noise level is measured to be lower than for vacuum state at the input of the second mixer, an unambiguous proof of entanglement. Moreover, the output noise level provides a direct, quantitative measure of entanglement, leading here to the demonstration of 6 Mebit.s$^{-1}$ (Mega entangled bits per second) generated by the first mixer.Comment: 5 pages, 4 figures. Supplementary Information can be found here as an ancillary fil

Solution of a one-dimensional stochastic model with branching and coagulation reactions

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as an epidemic model and/or as a generalization of the {\it voter} model, is treated analytically beyond the {\it conventional} solvable situations. With help of a suitably chosen {\it string function}, which is simply related to the density and the non-instantaneous two-point correlation functions of the particles, exact expressions of the density and of the non-instantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.Comment: 5 pages, no figure. To appear as a Rapid Communication in Physical Review E (September 2001

Non-universal dynamics of dimer growing interfaces

A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum gap of the underlying evolution operator. The finite size scaling of the latter is found to be affected by a standard surface tension term on which the growth rates depend. This non-universal aspect is also corroborated by the growth behavior observed in large scale simulations. By contrast, the roughening exponent remains robust over wide temperature ranges.Comment: 11 pages, 7 figures. v2 with some slight correction

Comparison between disordered quantum spin 1/2 chains

We study the magnetic properties of two types of one dimensional XX spin 1/2 chains. The first type has only nearest neighbor interactions which can be either antiferromagnetic or ferromagnetic and the second type which has both nearest neighbor and next nearest neighbor interactions, but only antiferromagnetic in character. We study these systems in the presence of low transverse magnetic fields both analytically and numerically. Comparison of results show a close relation between the two systems, which is in agreement with results previously found in Heisenberg chains by means of a numerical real space renormalization group procedure.Comment: 7 page

Interfaces with a single growth inhomogeneity and anchored boundaries

The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an equilibrium stationary regime which allows for an exact calculation of roughening exponents. The stochastic evolution is related to a spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of late stages. For vanishing gaps the interface can exhibit a slow morphological transition followed by a change of scaling regimes which are studied numerically. Instead, a faceting dynamics arises for gapful situations.Comment: REVTeX, 11 pages, 9 Postscript figure