Thermal Quantum Discord and Super Quantum Discord Teleportation Via a Two-Qubit Spin-Squeezing Model

We study thermal quantum correlations (quantum discord and super quantum discord) in a two-spin model in an external magnetic field and obtain relations between them and entanglement. We study their dependence on the magnetic field, the strength of the spin squeezing, and the temperature in detail. One interesting result is that when the entanglement suddenly disappears, quantum correlations still survive. We study thermal quantum teleportation in the framework of this model. The main goal is investigating the possibility of increasing the thermal quantum correlations of a teleported state in the presence of a magnetic field, strength of the spin squeezing, and temperature. We note that teleportation of quantum discord and super quantum discord can be realized over a larger temperature range than teleportation of entanglement. Our results show that quantum discord and super quantum discord can be a suitable measure for controlling quantum teleportation with fidelity. Moreover, the presence of entangled states is unnecessary for the exchange of quantum information.     

Pairwise correlations via quantum discord and its geometric measure in a four-qubit spin chain

The dynamic of pairwise correlations, including quantum entanglement (QE) and discord (QD) with geometric measure of quantum discord (GMQD), are shown in the four-qubit Heisenberg XX spin chain. The results show that the effect of the entanglement degree of the initial state on the pairwise correlations is stronger for alternate qubits than it is for nearest-neighbor qubits. This parameter results in sudden death for QE, but it cannot do so for QD and GMQD. With different values for this entanglement parameter of the initial state, QD and GMQD differ and are sensitive for any change in this parameter. It is found that GMQD is more robust than both QD and QE to describe correlations with nonzero values, which offers a valuable resource for quantum computation.     

Vanishing quantum discord and complete entropy exchange between subsystems in a bipartite system

Vanishing quantum discord and the entropy correlations between subsystems in a bipartite system are investigated. We numerically verify that there exists a condition of complete entropy exchange between the two subsystems, and it is found that the condition is in excellent agreement with that of the nullity of quantum discord in a certain range of parameters of the bipartite system.     

Persistent currents in open spin chains

Nonparallel boundary magnetic fields can induce a longitudinal (spin) current in a quantum spin chain. We use functional approaches to formulate the spectral problem for the spin-1/2 Heisenberg model subject to a class of integrable boundary conditions in terms of an infinite hierarchy of nonlinear integral equations. From these equations, we compute finite-size corrections to the ground-state energy of the antiferromagnetic chain and the induced spin current for a certain range of boundary parameters.     

Nonlinear transparency regimes for three-component acoustic pulses in a system of electron and nuclear spins

We study acoustic solitons consisting of one longitudinal and two transverse components and propagating in the direction perpendicular to an external magnetic field in a crystal containing paramagnetic impurities of electron and nuclear spins. The coupling of the electron spin subsystem to the longitudinal sound allows making the velocity of the latter close to that of the transverse acoustic waves, which provides an effective interaction between all components of the elastic field by means of the nuclear spin subsystem. We derive a three-component system of material and reduced wave equations describing this process and construct its soliton solutions in the form of stationary and breather pulses. Based on them, we study the peculiarities of the dynamics of the elastic field components and reveal the differences from the two-component model. The existence of two families of breathers is an important distinctive feature of the considered case.     

Boundary Energy of the Open XXZ Chain from New Exact Solutions

Bethe Ansatz solutions of the open spin- integrable XXZ quantum spin chain at roots of unity with nondiagonal boundary terms containing two free boundary parameters have recently been proposed.We use these solutions to compute the boundary energy (surface energy) in the thermodynamic limit. Communicated by Vincent Rivasseau Dedicated to Daniel Arnaudon Submitted: December 6, 2005; Accepted: February 16, 2006     

Indirect interaction between nuclear spins in easy-axis antiferromagnets

We consider two atoms with nuclear spins I = 1/2 belonging to a regular chain (spin register) of isotopes substituting basic nuclear-spin-free atoms in a plate of an antiferromagnet with the easy anisotropy axis. A constant external magnetic field is assumed to be directed along the easy axis perpendicular to the plate plane and to have a constant gradient along the register direction. For a simple model, we diagonalize the spin Hamiltonian in a spin-wave approximation using the Bogoliubov-Tyablikov transformation. We show that in the presence of a nonuniformity of the external magnetic field, the indirect interaction between nuclear spins caused by the hyperfine interaction of nuclear spins with virtual spin waves in the antiferromagnet can increase and even oscillate depending on the distance between the considered spins if the local field at the midpoint between them is close to the field of the orientational phase transition to the spin-flop phase in a homogeneous antiferromagnet.     

Spectrum and Bethe Ansatz Equations for the U_{q} {\left( {gl(\mathcal{N})} \right)} Closed and Open Spin Chains in any Representation

We consider the N-site integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to determine the spectrum and the corresponding Bethe ansatz equations for the general case, where each site of the spin chain is associated to any representation of In the case of open spin chain, we study finite dimensional representations of the quantum reflection algebra, and prove in full generality that the pseudo-vacuum is a highest weight of the monodromy matrix. For these two types of spin chain, we study the (generalized) “algebraic” fusion procedures, which amount to construct the quantum contraction and the Sklyanin determinant for the and quantum reflection algebras. We also determine the symmetry algebra of these two types of spin chains, including general K and K⁺ diagonal matrices for the open case. The case of open spin chains with soliton non-preserving boundary conditions is also presented in the framework of quantum twisted Yangians. The symmetry algebra of this spin chains is studied. We also give an exhaustive classification of the invertible matricial solutions to the corresponding reflection equation. Communicated by Petr Kulish Dedicated to our friend Daniel Arnaudon Submitted: December 12, 2005; Accepted: January 23, 2006     

The computational complexity of two‐state spin systems

The subject of this article is spin‐systems as studied in statistical physics. We focus on the case of two spins. This case encompasses models of physical interest, such as the classical Ising model (ferromagnetic or antiferromagnetic, with or without an applied magnetic field) and the hard‐core gas model. There are three degrees of freedom, corresponding to our parameters β, γ, and μ. Informally, β represents the weights of edges joining pairs of “spin blue” sites, γ represents the weight of edges joining pairs of “spin green” sites, and μ represents the weight of “spin green” sites. We study the complexity of (approximately) computing the partition function in terms of these parameters. We pay special attention to the symmetric case μ = 1. Exact computation of the partition function Z is NP‐hard except in the trivial case βγ = 1, so we concentrate on the issue of whether Z can be computed within small relative error in polynomial time. We show that there is a fully polynomial randomised approximation scheme (FPRAS) for the partition function in the “ferromagnetic” region βγ ≥ 1, but (unless RP = NP) there is no FPRAS in the “antiferromagnetic” region corresponding to the square defined by 0 < β < 1 and 0 < γ < 1. Neither of these “natural” regions—neither the hyperbola nor the square—marks the boundary between tractable and intractable. In one direction, we provide an FPRAS for the partition function within a region which extends well away from the hyperbola. In the other direction, we exhibit two tiny, symmetric, intractable regions extending beyond the antiferromagnetic region. We also extend our results to the asymmetric case μ ≠ 1. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 133–154, 2003     

Thermodynamic properties of two-layer quasi-two-dimensional antiferromagnets

For two-layer quasi-two-dimensional antiferromagnets of type YBaCuO in the Tyablikov approximation, we investigate the dependences of the energy spectrum and the temperature of transition into an ordered state on both the quasi-two-dimensionality parameter and the intensity of the exchange coupling of spin moments located in two close planes. We assume that the exchange parameters inside the CuO ₂ planes are much greater than the exchange parameters resulting in coupling between a spin located on a plane of an elementary cell and a spin on another plane of a different elementary cell. The obtained expressions for the Néel temperature and for the sublattice magnetic moment at zero temperature describe the dependences of these quantities on the parameters of interplane exchange interactions.     

Quantum and classical correlations in high-temperature dynamics of two coupled large spins

We study the dynamical correlations between two coupled spins depending on time and the value of the spin quantum numbers. In the high-temperature approximation, we obtain analytic expressions for the mutual information and the quantum and classical parts of correlations. We consider both orthogonal and nonorthogonal measurements in the basis of spin coherent states. We show that at small times, the quantum part of correlations becomes much less than the classical part as the spin quantum numbers increase, while the situation is quite different at times equal to half the quantum period.     

Classifying magnetic and superfluid equilibrium states in magnets with the spin <Emphasis Type="Italic">s</Emphasis> = 1

Based on the method of quasiaverages, we classify magnetic and superfluid equilibrium states in magnets with the spin s = 1. Under certain simplifications, assumptions about the residual symmetry of degenerate states and the transformation properties of order parameter operators under transformations generated by additive integrals of motions lead to linear algebraic equations for a classification of the equilibrium means of the order parameters. We consider different cases of the magnetic SO(3) or SU(3) symmetry breaking and obtain solutions for the vector and tensor order parameters for particular forms of the parameters of the residual symmetry generators. We study the equilibriums of magnets with simultaneously broken phase and magnetic symmetries. We find solutions of the classification equations for superfluid equilibrium states and establish relations between the parameters of the residual symmetry generator that allow the thermodynamic coexistence of nonzero equilibrium means of the order parameters.     

Quantum solitons and the Haldane phase in antiferromagnetic spin chains

A survey is given of the relevance of solitons for the present understanding of antiferromagnetic quantum spin chains. For the -chain the basic elementary excitations are solitons. Two solitons combine to form a magnon and its internal degree of freedom is observed as an excitation continuum. For S = 1 chains the existence of the massive Haldane phase is related to the dissociation of soliton pairs (pairs of domain walls with respect to antiferromagnetic order). Based on the hidden (or string) order, the appropriate mean field theory for antiferromagnetic S = 1 chains is introduced as based on uncorrelated solitons and applied to calculate correlation functions. It is described how to include correlations between solitons using an approximate mapping to an effective chain. The basic elementary excitations in the Haldane phase are identified as solitons with respect to the hidden order.     

XXZ Spin Chain with the Asymmetry Parameter Δ = −1/2: Evaluation of the Simplest Correlators

We consider a finite XXZ spin chain with periodic boundary conditions and an odd number of sites. It appears that for the special value of the asymmetry parameter = –1/2, the ground state of this system described by the Hamiltonian has the energy E ₀ = –3N/2. Although the ground state is antiferromagnetic, we can find the corresponding solution of the Bethe equations. Specifically, we can explicitly construct a trigonometric polynomial Q(u) of degree n = (N–1)/2, whose zeros are the parameters of the Bethe wave function for the ground state of the system. As is known, this polynomial satisfies the Baxter T–Q equation. This equation also has a second independent solution corresponding to the same eigenvalue of the transfer matrix T. We use this solution to find the derivative of the ground-state energy of the XXZ chain with respect to the crossing parameter . This derivative is directly related to one of the spin–spin correlators, which appears to be . In turn, this correlator gives the average number of spin strings for the ground state of the chain, . All these simple formulas fail if the number N of chain sites is even.     

Nonlinear electronic circuit, Part II: synchronization in a chaotic MODEM scheme

In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive-response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous 2nd order nonlinear oscillator system presented in [G. Mycolaitis, A. Tamasevicious, A. Cenys, A. Namajunas, K. Navionis, A. N. Anagnostopoulos, Globally synchronizable non-autonomous chaotic oscillator, in: Proc. of 7th International Workshop on Nonlinear Dynamics of Electronic Systems, Denmark, July 1999, pp. 277-280] which is particularly suitable for digital communications.Furthermore, we modified the previous chaotic communication system in order to exhibit enhanced security features. The enhancement in the security of the system is achieved by introducing a set of parameters used in the encoding and decoding of the message signal. We also introduce a time delay parameter in the dynamical system which on the one hand improves the chaotic behavior of the system and on the other hand, adds further security in the encoding-decoding scheme.     

Dynamic complexities of predator–prey system in a pulsed chemostat

In this paper, we study a food chain model with Holling III and Monod type functional response under periodic pulsed conditions, which contains with predator, prey and periodically pulsed substrate. We investigate the subsystem with substrate and prey and study the stability of the boundary periodic solution. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in prey and predator. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the system shows two kinds of bifurcations, whose are period-doubling and period-halving.     

Nonlinear electronic circuit,Part II: synchronization in a chaotic MODEM scheme

In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a drive–response configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous 2nd order nonlinear oscillator system presented in [G. Mycolaitis, A. Tamasevicious, A. Cenys, A. Namajunas, K. Navionis, A. N. Anagnostopoulos, Globally synchronizable non-autonomous chaotic oscillator, in: Proc. of 7th International Workshop on Nonlinear Dynamics of Electronic Systems, Denmark, July 1999, pp. 277–280] which is particularly suitable for digital communications.Furthermore, we modified the previous chaotic communication system in order to exhibit enhanced security features. The enhancement in the security of the system is achieved by introducing a set of parameters used in the encoding and decoding of the message signal. We also introduce a time delay parameter in the dynamical system which on the one hand improves the chaotic behavior of the system and on the other hand, adds further security in the encoding–decoding scheme.     

Polynomials with palindromic and unimodal coefficients

Let f(q) = ar qr+ ··· + as qs, with ar = 0 and as = 0, be a real polynomial. It is a palindromic polynomial of darga n if r + s = n and ar+i = as-i for all i. Polynomials of darga n form a linear subspace Pn(q) of R(q)n+1 of dimension n2 + 1. We give transition matrices between two bases qj(1 + q + ··· + qn-2j), qj(1 + q)n-2j and the standard basis qj(1 + qn-2j)of Pn(q).We present some characterizations and sufficient conditions for palindromic polynomials that can be expressed in terms of these two bases with nonnegative coefficients. We also point out the link between such polynomials and rank-generating functions of posets.     

Inhomogeneous Current States in a Gauged Two-Component Ginzburg-Landau Model

We consider the energy bounds of inhomogeneous current states in doped antiferromagnetic insulators in the framework of the two-component Ginzburg-Landau model. Using the formulation of this model in terms of the gauge-invariant order parameters (the unit vector n, spin stiffness field ρ², and particle momentum c), we show that this strongly correlated electron system involves a geometric small parameter that determines the degree of packing in the knots of filament manifolds of the order parameter distributions for the spin and charge degrees of freedom. We find that as the doping degree decreases, the filament density increases, resulting in a transition to an inhomogeneous current state with a free energy gain.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 182–189, July, 2005.     

BiLevel programming Data Envelopment Analysis with constrained resource

A new BiLevel programming Data Envelopment Analysis (DEA) approach is created to provide valuable managerial insights when assessing the performance of a system with Stackelberg-game relationships. This new approach allows us to evaluate the firm performance in decentralized decisions, which consist of the objective(s) of the leader at its first level and that is of the follower at the second level. This approach can help decentralized companies to optimize their performance using multiple inputs to produce multiples outputs in a cost-effective way, where both the system “black-box” and subsystem performance are exposed in details. We show the algorithms and solutions to our new models. We illustrate and validate the proposed new approach using two case studies: a banking chain and a manufacturing supply chain. The computation shows that subsystem being efficient at all levels results in an overall efficiency achievement in a decentralized BiLevel structure.