Spin- and entanglement-dynamics in the central spin model with homogeneous couplings

We calculate exactly the time-dependent reduced density matrix for the central spin in the central-spin model with homogeneous Heisenberg couplings. Therefrom, the dynamics and the entanglement entropy of the central spin are obtained. A rich variety of behaviors is found, depending on the initial state of the bath spins. For an initially unpolarized unentangled bath, the polarization of the central spin decays to zero in the thermodynamic limit, while its entanglement entropy becomes maximal. On the other hand, if the unpolarized environment is initially in an eigenstate of the total bath spin, the central spin and the entanglement entropy exhibit persistent monochromatic large-amplitude oscillations. This raises the question to what extent entanglement of the bath spins prevents decoherence of the central spin.Comment: 8 pages, 2 figures, typos corrected, published versio

Project for the analysis of technology transfer Annual report, 1969

Technology utilization of NASA programs and other research and development programs in Federal Government - project analysis results of technology transfe

SIRS dynamics on random networks: simulations and analytical models

The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree $k$ predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter $k$ and of its relevance to understand the behaviour of simulations on networks. For $k=4$, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.Comment: 6 pages, 3 figures, WIPP to be published in Conference proceedings Complex'2009 February 23-25, Shanghai, Chin

The open XXZ-chain: Bosonisation, Bethe ansatz and logarithmic corrections

We calculate the bulk and boundary parts of the free energy for an open spin-1/2 XXZ-chain in the critical regime by bosonisation. We identify the cutoff independent contributions and determine their amplitudes by comparing with Bethe ansatz calculations at zero temperature T. For the bulk part of the free energy we find agreement with Lukyanov's result [Nucl.Phys.B 522, 533 (1998)]. In the boundary part we obtain a cutoff independent term which is linear in T and determines the temperature dependence of the boundary susceptibility in the attractive regime for $T\ll 1$. We further show that at particular anisotropies where contributions from irrelevant operators with different scaling dimensions cross, logarithmic corrections appear. We give explicit formulas for these terms at those anisotropies where they are most important. We verify our results by comparing with extensive numerical calculations based on a numerical solution of the T=0 Bethe ansatz equations, the finite temperature Bethe ansatz equations in the quantum-transfer matrix formalism, and the density-matrix renormalisation group applied to transfer matrices.Comment: 35 pages, 8 figure

The one-dimensional Hubbard model with open ends: Universal divergent contributions to the magnetic susceptibility

The magnetic susceptibility of the one-dimensional Hubbard model with open boundary conditions at arbitrary filling is obtained from field theory at low temperatures and small magnetic fields, including leading and next-leading orders. Logarithmic contributions to the bulk part are identified as well as algebraic-logarithmic divergences in the boundary contribution. As a manifestation of spin-charge separation, the result for the boundary part at low energies turns out to be independent of filling and interaction strength and identical to the result for the Heisenberg model. For the bulk part at zero temperature, the scale in the logarithms is determined exactly from the Bethe ansatz. At finite temperature, the susceptibility profile as well as the Friedel oscillations in the magnetisation are obtained numerically from the density-matrix renormalisation group applied to transfer matrices. Agreement is found with an exact asymptotic expansion of the relevant correlation function.Comment: 30 pages, 8 figures, reference adde

Lattice Gas Dynamics; Application to Driven Vortices in Two Dimensional Superconductors

A continuous time Monte Carlo lattice gas dynamics is developed to model driven steady states of vortices in two dimensional superconducting networks. Dramatic differences are found when compared to a simpler Metropolis dynamics. Subtle finite size effects are found at low temperature, with a moving smectic that becomes unstable to an anisotropic liquid on sufficiently large length scales.Comment: 5 pages, 4 figure

A Rapid Dynamical Monte Carlo Algorithm for Glassy Systems

In this paper we present a dynamical Monte Carlo algorithm which is applicable to systems satisfying a clustering condition: during the dynamical evolution the system is mostly trapped in deep local minima (as happens in glasses, pinning problems etc.). We compare the algorithm to the usual Monte Carlo algorithm, using as an example the Bernasconi model. In this model, a straightforward implementation of the algorithm gives an improvement of several orders of magnitude in computational speed with respect to a recent, already very efficient, implementation of the algorithm of Bortz, Kalos and Lebowitz.Comment: RevTex 7 pages + 4 figures (uuencoded) appended; LPS preprin