Current Carrying States in a Random Magnetic Field

We report results of a numerical study of noninteracting electrons moving in two dimensions, in the presence of a random potential and a random magnetic field for a sequence of finite sizes, using topological properties of the wave functions to identify extended states. Our results are consistent with the existence of a second order localization-delocalization transition driven by the random potential. The critical randomness strength and localization length exponent are estimated via a finite size scaling analysis.Comment: 4 pages, 7 eps figure

Universality class of fiber bundles with strong heterogeneities

We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0<\alpha<1 of fibers is unbreakable, while the remaining 1-\alpha fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components \alpha_c which separates two qualitatively different regimes of the system: below \alpha_c the burst size distribution is a power law with the usual exponent \tau=5/2, while above \alpha_c the exponent switches to a lower value \tau=9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena

Generation of Large Moments in a Spin-1 Chain with Random Antiferromagnetic Couplings

We study the spin-1 chain with nearest neighbor couplings that are rotationally invariant, but include both Heisenberg and biquadratic exchange, with random strengths. We demonstrate, using perturbative renormalization group methods as well as exact diagonalization of clusters, that the system generates ferromagnetic couplings under certain circumstances even when all the bare couplings are antiferromagnetic. This disorder induced instability leads to formation of large magnetic moments at low temperatures, and is a purely quantum mechanical effect that does not have a classical counterpart. The physical origin of this instability, as well as its consequences, are discussed.Comment: 4 pages, 4 eps figure

Slip avalanches in a fiber bundle model

We study slip avalanches in disordered materials under an increasing external load in the framework of a fiber bundle model. Over-stressed fibers of the model do not break, instead they relax in a stick-slip event which may trigger an entire slip avalanche. Slip avalanches are characterized by the number slipping fibers, by the slip length, and by the load increment, which triggers the avalanche. Our calculations revealed that all three quantities are characterized by power law distributions with universal exponents. We show by analytical calculations and computer simulations that varying the amount of disorder of slip thresholds and the number of allowed slips of fibers, the system exhibits a disorder induced phase transition from a phase where only small avalanches are formed to another one where a macroscopic slip appears.Comment: 6 pages, 6 figure

Slow cross-symmetry phase relaxation in complex collisions

We discuss the effect of slow phase relaxation and the spin off-diagonal $S$-matrix correlations on the cross section energy oscillations and the time evolution of the highly excited intermediate systems formed in complex collisions. Such deformed intermediate complexes with strongly overlapping resonances can be formed in heavy ion collisions, bimolecular chemical reactions and atomic cluster collisions. The effects of quasiperiodic energy dependence of the cross sections, coherent rotation of the hyperdeformed $\simeq (3:1)$ intermediate complex, Schr\"odinger cat states and quantum-classical transition are studied for $^{24}$Mg+$^{28}$Si heavy ion scattering.Comment: 10 pages including 2 color ps figures. To be published in Physics of Atomic Nuclei (Yadernaya fizika

Network Density of States

Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of associated differential operators. But the translation from spectral geometry to spectral graph theory has largely focused on results involving only a few extreme eigenvalues and their associated eigenvalues. Unlike in geometry, the study of graphs through the overall distribution of eigenvalues - the spectral density - is largely limited to simple random graph models. The interior of the spectrum of real-world graphs remains largely unexplored, difficult to compute and to interpret. In this paper, we delve into the heart of spectral densities of real-world graphs. We borrow tools developed in condensed matter physics, and add novel adaptations to handle the spectral signatures of common graph motifs. The resulting methods are highly efficient, as we illustrate by computing spectral densities for graphs with over a billion edges on a single compute node. Beyond providing visually compelling fingerprints of graphs, we show how the estimation of spectral densities facilitates the computation of many common centrality measures, and use spectral densities to estimate meaningful information about graph structure that cannot be inferred from the extremal eigenpairs alone.Comment: 10 pages, 7 figure

Rigorous Proof of Pseudospin Ferromagnetism in Two-Component Bosonic Systems with Component-Independent Interactions

For a two-component bosonic system, the components can be mapped onto a pseudo-spin degree of freedom with spin quantum number S=1/2. We provide a rigorous proof that for a wide-range of real Hamiltonians with component independent mass and interaction, the ground state is a ferromagnetic state with pseudospin fully polarized. The spin-wave excitations are studied and found to have quadratic dispersion relations at long wave length.Comment: 4 pages, no figur

Disorder induced brittle to quasi-brittle transition in fiber bundles

We investigate the fracture process of a bundle of fibers with random Young modulus and a constant breaking strength. For two component systems we show that the strength of the mixture is always lower than the strength of the individual components. For continuously distributed Young modulus the tail of the distribution proved to play a decisive role since fibers break in the decreasing order of their stiffness. Using power law distributed stiffness values we demonstrate that the system exhibits a disorder induced brittle to quasi-brittle transition which occurs analogously to continuous phase transitions. Based on computer simulations we determine the critical exponents of the transition and construct the phase diagram of the system.Comment: 6 pages, 6 figure