Level statistics of XXZ spin chains with a random magnetic field

The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude of the random magnetic field h. In the energy spectrum, quantum integrability competes with nonintegrability derived from the randomness, where the XXZ interaction is modified by the parameter $\Delta$. When $\Delta \ne 0$, the level-spacing distribution mostly shows Wigner-like behavior, while when $\Delta$=0, Poisson-like behavior appears although the system is nonintegrable due to randomness. Poisson-like behavior also appears for $\Delta \ne 0$ in the large h limit. Furthermore, the level-spacing distribution depends on the lattice size L, particularly when the random field is weak.Comment: 4 pages, 3 figures, to be published in Phys. Rev.

Crossover from Poisson to Wigner-Dyson Level Statistics in Spin Chains with Integrability Breaking

We study numerically the evolution of energy-level statistics as an integrability-breaking term is added to the XXZ Hamiltonian. For finite-length chains, physical properties exhibit a cross-over from behavior resulting from the Poisson level statistics characteristic of integrable models to behavior corresponding to the Wigner-Dyson statistics characteristic of the random-matrix theory used to describe chaotic systems. Different measures of the level statistics are observed to follow different crossover patterns. The range of numerically accessible system sizes is too small to establish with certainty the scaling with system size, but the evidence suggests that in a thermodynamically large system an infinitesimal integrability breaking would lead to Wigner-Dyson behavior.Comment: 8 pages, 8 figures, Revtex

Simulation of Autonomic Logistics System (ALS) Sortie Generation

The Air Force needs tools for analysis and evaluation of new logistic operational concepts. The purpose of this research was to conflict a discrete event simulation model of the aircraft sortie generation process to permit what-if analyses of these concepts. The current Air Force logistics operations system is reactive in nature meaning that after the aircraft detects a part failure, the maintenance person must perform fault isolation procedures and then steps are taken to repair or replace the faulty item. The Autonomic Logistics System (ALS) concept changes the reactive process into a proactive one with the employment of technologies such as prognostics and distributed information network. Certain logistics tasks can be handled automatically or autonomously i.e. ordering parts, requesting maintenance specialists, and notifying maintenance control center. The conclusion of this research was that an aircraft equipped with the ALS increased the measures of effectiveness (MOE) like mission capable rate and flying scheduling effectiveness tip to a point. The research indicated that as ALS false alarms grew these MOEs decreased and eventually were worse than the baseline system. However, it is worth noting that this research simulated a worst case false alarm scenario, a part removal and replacement with each false alarm

Unexpected non-Wigner behavior in level-spacing distributions of next-nearest-neighbor coupled XXZ spin chains

The level-spacing distributions of XXZ spin chains with next-nearest-neighbor couplings are studied under periodic boundary conditions. We confirm that integrable XXZ spin chains mostly have the Poisson distribution as expected. On the contrary, the level-spacing distributions of next-nearest-neighbor coupled XXZ chains are given by non-Wigner distributions. It is against the expectations, since the models are nonintegrable.Comment: 4 pages, 4 figures, to be published in Physical Review

Energy level statistics for models of coupled single-mode Bose--Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.Comment: 5 pages, 4 figures, revte

Energy level statistics of the two-dimensional Hubbard model at low filling

The energy level statistics of the Hubbard model for $L \times L$ square lattices (L=3,4,5,6) at low filling (four electrons) is studied numerically for a wide range of the coupling strength. All known symmetries of the model (space, spin and pseudospin symmetry) have been taken into account explicitly from the beginning of the calculation by projecting into symmetry invariant subspaces. The details of this group theoretical treatment are presented with special attention to the nongeneric case of L=4, where a particular complicated space group appears. For all the lattices studied, a significant amount of levels within each symmetry invariant subspaces remains degenerated, but except for L=4 the ground state is nondegenerate. We explain the remaining degeneracies, which occur only for very specific interaction independent states, and we disregard these states in the statistical spectral analysis. The intricate structure of the Hubbard spectra necessitates a careful unfolding procedure, which is thoroughly discussed. Finally, we present our results for the level spacing distribution, the number variance $\Sigma^2$, and the spectral rigidity $\Delta_3$, which essentially all are close to the corresponding statistics for random matrices of the Gaussian ensemble independent of the lattice size and the coupling strength. Even very small coupling strengths approaching the integrable zero coupling limit lead to the Gaussian ensemble statistics stressing the nonperturbative nature of the Hubbard model.Comment: 31 pages (1 Revtex file and 10 postscript figures

Finite temperature mobility of a particle coupled to a fermion environment

We study numerically the finite temperature and frequency mobility of a particle coupled by a local interaction to a system of spinless fermions in one dimension. We find that when the model is integrable (particle mass equal to the mass of fermions) the static mobility diverges. Further, an enhanced mobility is observed over a finite parameter range away from the integrable point. We present a novel analysis of the finite temperature static mobility based on a random matrix theory description of the many-body Hamiltonian.Comment: 11 pages (RevTeX), 5 Postscript files, compressed using uufile

A Brownian Motion Model of Parametric Correlations in Ballistic Cavities

A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We derive a formula for the power spectrum of the fluctuations of transport observables as a response to an external adiabatic perturbation. Our formula correctly recovers the Lorentzian-squared behaviour obtained by semiclassical approaches for the correlation function of conductance fluctuations.Comment: 19 pages, written in RevTe