Using groups in the splitting preconditioner computation for interior point methods

Interior point methods usually rely on iterative methods to solve the linear systems of large scale problems. The paper proposes a hybrid strategy using groups for the preconditioning of these iterative methods. The objective is to solve large scale linear programming problems more efficiently by a faster and robust computation of the preconditioner. In these problems, the coefficient matrix of the linear system becomes ill conditioned during the interior point iterations, causing numerical difficulties to find a solution, mainly with iterative methods. Therefore, the use of preconditioners is a mandatory requirement to achieve successful results. The paper proposes the use of a new columns ordering for the splitting preconditioner computation, exploring the sparsity of the original matrix and the concepts of groups. This new preconditioner is designed specially for the final interior point iterations; a hybrid approach with the controlled Cholesky factorization preconditioner is adopted. Case studies show that the proposed methodology reduces the computational times with the same quality of solutions when compared to previous reference approaches. Furthermore, the benefits are obtained while preserving the sparse structure of the systems. These results highlight the suitability of the proposed approach for large scale problems.     

Quantum-state transfer through long-range correlated disordered channels

We study quantum-state transfer in XX spin-1/2 chains where both communicating spins are weakly coupled to a channel featuring disordered on-site magnetic fields. Fluctuations are modeled by long-range correlated sequences with self-similar profile obeying a power-law spectrum. We show that the channel is able to perform almost perfect quantum-state transmissions even in the presence of significant amounts of disorder provided the degree of those correlations is strong enough, with the cost of having long transfer times and unavoidable timing errors. Still, we show that the lack of mirror symmetry in the channel does not affect much the likelihood of having high-quality outcomes. Our results suggest that coexistence between localized and delocalized states can diminish effects of static perturbations in solid-state devices for quantum communication.     

Roughness scaling and sensitivity to initial conditions in a symmetric restricted ballistic deposition model

In this work, we introduce a restricted ballistic deposition model with symmetric growth rules that favors the formation of local finite slopes. It is the simplest model which, even without including a diffusive relaxation mode of the interface, leads to a macroscopic groove instability. By employing a finite-size scaling of numerical simulation data, we determine the scaling behavior of the surface structure grown over a one-dimensional substrate of linear size L. We found that the surface profile develops a macroscopic groove with the asymptotic surface width scaling as , with . The early-time dynamics is governed by the scaling law , with . We further investigate the sensitivity to initial conditions of the present model by applying damage spreading techniques. We find that the early-time distance between two initially close surface configurations grows in a ballistic fashion as , but a slower Brownian-like scaling () sets up for evolution times much larger than a characteristic time scale . Received 26 May 2000     

Effective scaling behavior of magnetization and Hamming distance in Ising thin films under a surface field

The recent improvements on the technology for developing high-quality thin magnetic films has renewed the interest in the study of surface effects in both static and dynamic magnetic responses. In this work, we use a Monte-Carlo algorithm with Metropolis dynamics together with a spreading of damage technique to study the interplay between the effects of finite thickness and surface ordering field in thin ferromagnetic Ising (S=1/2) films. We calculate, near the bulk critical temperature and several values of the surface field, the dependence on the film thickness of the average magnetization M and Hamming distance D. We employ a finite size scaling analysis to show that both obey an effective one-parameter scaling but exhibit distinct characteristic surface fields. At their corresponding characteristic surface fields both M and D become roughly thickness independent and we estimate the critical exponent characterizing the behavior of the typical scaling lengths. Received 29 March 1999 and Received in final form 21 April 1999     

Crossover from strong to weak exciton confinement and third-harmonic generation on one-dimensional quantum dots

We study the effects of exciton confinement on the nonlinear optical susceptibility of one-dimensional quantum dots. We use a direct numerical diagonalization to obtain the eigenenergies and eigenstates of the discretized Hamiltonian representing an electron–hole pair confined by a semiparabolic potential and interacting with each other via a Coulomb potential. Density matrix perturbation theory is used to compute the nonlinear optical susceptibilities due to third-harmonic generation and the corresponding nonlinear corrections to the refractive index and absorption coefficient. These quantities are analyzed as a function of ratio between the confinement length L and the exciton Bohr radius a₀. The Coulomb potential degrades the uniformity of the level separation. We show that this effect promotes the emergence of multiple resonance peaks in the third-harmonic generation spectrum. In the weak confinement regime β = L/a₀ ? 1, the third-order susceptibility is shown to decay as 1/β⁸ due to the prevalence of the hydrogenoid character of the exciton eigenstates.     

Self-trapping of interacting electrons in crystalline nonlinear chains

Considering the nonlinearity arising from the interaction between electrons and latticevibrations, an effective electronic model with a self-interaction cubic term is employedto study the interplay between electron-electron and electron-phonon interactions. Basedon numerical solutions of the time-dependent nonlinear Schroedinger equation for aninitially localized two-electron singlet state, we show that the magnitude of theelectron-phonon coupling χ necessary to promote the self-trapping of theelectronic wave packet decreases as a function of the electron-electron interactionU. We show that such dependence is directly linked to the narrowing ofthe band of bounded two-electron states as U increases. We obtain thetransition line in the χ × U parameter space separatingthe phases of self-trapped and delocalized electronic wave packets. The present resultsindicates that nonlinear contributions plays a relevant role in the electronic wave packetdynamics, particularly in the regime of strongly correlated electrons.     

Interplay between spin frustration and thermal entanglement in the exactly solved Ising–Heisenberg tetrahedral chain

The spin-1/2 Ising–Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry (the total spin of the Heisenberg bonds is locally conserved) and the transfer-matrix approach. Exact results derived for spin–spin correlation functions are employed to obtain the frustration temperature. In addition, we have exactly calculated a concurrence quantifying thermal entanglement. It is shown that the frustration and threshold temperature coincide at sufficiently low temperatures, while they exhibit a very different behavior in the high-temperature region when tending towards completely different asymptotic limits. The threshold temperature additionally shows a notable reentrant behavior when it extends over a narrow temperature region above the classical ground state without any quantum correlations.