Quantum Entanglement in Heisenberg Antiferromagnets

Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate S=0 ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. A few finite clusters are studied numerically, to see the trend in higher dimensions. It is argued that nearest-neighbour concurrence is zero for triangular and Kagome lattices. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the S=0 states.Comment: 7 pages, 3 figure

Finite Volume Analysis of Nonlinear Thermo-mechanical Dynamics of Shape Memory Alloys

In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modelling of shape memory alloys. Computational experiments are carried out to study the thermo-mechanical wave interactions in a shape memory alloy rod, and a patch. Both mechanically and thermally induced phase transformations, as well as hysteresis effects, in a one-dimensional structure are successfully simulated with the developed methodology. In the two-dimensional case, the main focus is given to square-to-rectangular transformations and examples of martensitic combinations under different mechanical loadings are provided.Comment: Keywords: shape memory alloys, phase transformations, nonlinear thermo-elasticity, finite volume metho

Numerical Model For Vibration Damping Resulting From the First Order Phase Transformations

A numerical model is constructed for modelling macroscale damping effects induced by the first order martensite phase transformations in a shape memory alloy rod. The model is constructed on the basis of the modified Landau-Ginzburg theory that couples nonlinear mechanical and thermal fields. The free energy function for the model is constructed as a double well function at low temperature, such that the external energy can be absorbed during the phase transformation and converted into thermal form. The Chebyshev spectral methods are employed together with backward differentiation for the numerical analysis of the problem. Computational experiments performed for different vibration energies demonstrate the importance of taking into account damping effects induced by phase transformations.Comment: Keywords: martensite transformation, thermo-mechanical coupling, vibration damping, Ginzburg-Landau theor

Thermo-Mechanical Wave Propagation In Shape Memory Alloy Rod With Phase Transformations

Many new applications of ferroelastic materials require a better understanding of their dynamics that often involve phase transformations. In such cases, an important prerequisite is the understanding of wave propagation caused by pulse-like loadings. In the present study, a mathematical model is developed to analyze the wave propagation process in shape memory alloy rods. The first order martensite transformations and associated thermo-mechanical coupling effects are accounted for by employing the modified Ginzburg-Landau-Devonshire theory. The Landau-type free energy function is employed to characterize different phases, while a Ginzburg term is introduced to account for energy contributions from phase boundaries. The effect of internal friction is represented by a Rayleigh dissipation term. The resulted nonlinear system of PDEs is reduced to a differential-algebraic system, and Chebyshev's collocation method is employed together with the backward differentiation method. A series of numerical experiments are performed. Wave propagations caused by impact loadings are analyzed for different initial temperatures. It is demonstrated that coupled waves will be induced in the material. Such waves will be dissipated and dispersed during the propagation process, and phase transformations in the material will complicate their propagation patterns. Finally, the influence of internal friction and capillary effects on the process of wave propagation is analyzed numerically.Comment: Keywords: nonlinear waves, thermo-mechanical coupling, martensite transformations, Ginzburg-Landau theory, Chebyshev collocation metho

Microscopic mechanisms of magnetization reversal

Two principal scenarios of magnetization reversal are considered. In the first scenario all spins perform coherent motion and an excess of magnetic energy directly goes to a nonmagnetic thermal bath. A general dynamic equation is derived which includes a tensor damping term similar to the Bloch-Bloembergen form but the magnetization magnitude remains constant for any deviation from equilibrium. In the second reversal scenario, the absolute value of the averaged sample magnetization is decreased by a rapid excitation of nonlinear spin-wave resonances by uniform magnetization precession. We have developed an analytic k-space micromagnetic approach that describes this entire reversal process in an ultra-thin soft ferromagnetic film for up to 90^{o} deviation from equilibrium. Conditions for the occurrence of the two scenarios are discussed

Charge transfer via a two-strand superexchange bridge in DNA

Charge transfer in a DNA duplex chain is studied by constructing a system with virtual electrodes connected at the ends of each DNA strand. The systeym is described by the tight-binding model and its transport is analyzed by the transfer matrix method. The very weak distance dependence in long (G:C)(T:A)_M(G:C)_3 DNA chain observed in experiment [B. Giese, et al., Nature 412, 318 (2001)] is explained by a unistep two-strand superexchange bridge without the need for the multi-step thermally-induced hopping mechanism or the dephasing effect. The crossover number M_c of (T:A) base pairs, where crossover between strong and weak distance dependence occurs, reflects the ratio of intra- and inter-strand neighboring base-base couplings.Comment: accepted for publication in Phys. Rev. Let

Thermal and ground-state entanglement in Heisenberg XX qubit rings

We study the entanglement of thermal and ground states in Heisernberg $XX$ qubit rings with a magnetic field. A general result is found that for even-number rings pairwise entanglement between nearest-neighbor qubits is independent on both the sign of exchange interaction constants and the sign of magnetic fields. As an example we study the entanglement in the four-qubit model and find that the ground state of this model without magnetic fields is shown to be a four-body maximally entangled state measured by the $N$-tangle.Comment: Four pages and one figure, small change

Localized Entanglement in one-dimensional Anderson model

The entanglement in one-dimensional Anderson model is studied. We show that the pairwise entanglement measured by the average concurrence has a direct relation to the localization length. The numerical study indicates that the disorder significantly reduces the average entanglement, and entanglement distribution clearly displays the entanglement localization. The maximal pairwise entanglement exhibits a maximum as the disorder strength increases,experiencing a transition from increase to decrease. The entanglement between the center of localization and other site decreases exponentially along the spatial direction. Finally,we study effects of disorder on dynamical properties of entanglement.Comment: 5 pages, 6 figure