Valence bond analysis of the Kondo chain Hamiltonian

Accurate extrapolations for the ground state energy per site of the one - dimensional Kondo chain system is obtained from exact finite system calculations carried out employing a valence bond scheme. An analysis of the ground state wave function indicates that the localized spin is quenched for all nonzero values of the Kondo exchange constant in one dimension.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

Adiabatic quantum computation with a one-dimensional projector Hamiltonian

Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyze a particular class of quantum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum-energy gap, which governs the time required for a successful evolution, is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.

ESR study of dibarium copper formate tetrahydrate Part II. Optical absorption and temperature dependence of spin-hamiltonian parameters

The variations in certain spin-Hamiltonian parameters of the Cu++ ion in dibarium copper formate tetrahydrate with temperature have been studied. Optical absorption investigations on single crystals of the salt at room temperature and 90° K. are reported. The results are discussed in terms of a model in which vibronic mixing of certain electron levels of the Cu++ ion play an important role.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.

Symplectic integration of nonlinear Hamiltonian systems

There exist several standard numerical methods for integrating ordinary differential equations. However, if one is interested in integration of Hamiltonian systems, these methods can lead to wrong results. This is due to the fact that these methods do not explicitly preserve the so-called 'symplectic condition' (that needs to be satisfied for Hamiltonian systems) at every integration step. In this paper, we look at various methods for integration that preserve the symplectic condition.

Magnetization properties of some quantum spin ladders

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Hen we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/2 ladder, and a two-legged spin-1/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the XXZ model, We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat. [S0163-1829(99)303001-5].

Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

First-passage failure of quasi-integrable Hamiltonian systems

The first-passage failure of quasi-integrable Hamiltonian si-stems (multidegree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is investigated. The motion equations of such a system are first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving these equations with suitable initial and boundary conditions. Two examples are given to illustrate the proposed procedure and the results from digital simulation are obtained to verify the effectiveness of the procedure.

Quantum teleportation via a two-qubit Heisenberg XXZ chain - effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ, chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.

Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field

The thermal entanglement in a two-qubit Heisenberg XXZ spin chain is investigated under an inhomogeneous magnetic field b. We show that the ground-state entanglement is independent of the interaction of z-component J(z). The thermal entanglement at the fixed temperature can be enhanced when J(z) increases. We strictly show that for any temperature T and J(z), the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field b(c) is independent of J(z). The critical magnetic field B-c increases with the increasing parallel to b parallel to but the maximum entanglement value that the system can arrive at becomes smaller.

SWAP operation in the two-qubit Heisenberg XXZ model: Effects of anisotropy and magnetic field

In this paper we study the SWAP operation in a two-qubit anisotropic XXZ model in the presence of an inhomogeneous magnetic field. We establish the range of anisotropic parameter lambda within which the SWAP operation is feasible. The SWAP errors caused by the inhomogeneous field are evaluated.

MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS VIA CONLEY INDEX THEORY

In this paper we study the existence of periodic solutions of asymptotically linear Hamiltonian systems which may not satisfy the Palais-Smale condition. By using the Conley index theory and the Galerkin approximation methods, we establish the existence of at least two nontrivial periodic solutions for the corresponding systems.