6,623 research outputs found
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
-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
intermediate complex, Schr\"odinger cat states and
quantum-classical transition are studied for Mg+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
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