Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t) of spins not flipped by time t decays to zero like t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples --- one disordered and one homogeneous --- where p(t) decays exponentially to p(infinity).Comment: 8 pages (LaTeX); to appear in Physical Review Letter

Non-equilibrium Dynamics of Finite Interfaces

We present an exact solution to an interface model representing the dynamics of a domain wall in a two-phase Ising system. The model is microscopically motivated, yet we find that in the scaling regime our results are consistent with those obtained previously from a phenomenological, coarse-grained Langevin approach.Comment: 12 pages LATEX (figures available on request), Oxford preprint OUTP-94-07

Measurement of the interaction strength in a Bose-Fermi mixture with 87Rb and 40K

A quantum degenerate, dilute gas mixture of bosonic and fermionic atoms was produced using 87Rb and 40K. The onset of degeneracy was confirmed by observing the spatial distribution of the gases after time-of-flight expansion. Further, the magnitude of the interspecies scattering length between the doubly spin polarized states of 87Rb and 40K, |a_RbK|, was determined from cross-dimensional thermal relaxation. The uncertainty in this collision measurement was greatly reduced by taking the ratio of interspecies and intraspecies relaxation rates, yielding |a_RbK| = 250 +/- 30 a_0, which is a lower value than what was reported in [M. Modugno et al., Phys. Rev. A 68, 043626 (2003)]. Using the value for |a_RbK| reported here, current T=0 theory would predict a threshold for mechanical instability that is inconsistent with the experimentally observed onset for sudden loss of fermions in [G. Modugno et al., Science 297, 2240 (2002)].Comment: RevTeX4 + 4 eps figures; Replaced with published versio

Spectral densities of scale-free networks

The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and $\beta$.Comment: 14 pages, two figure

Probabilistic Approach to Time-Dependent Load-Transfer Models of Fracture

A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during the breaking process (annealed randomness) while in the usual method, the random lifetimes are fixed at the beginning (quenched disorder). Both approaches are equivalent.Comment: 13 pages, 4 figures. To appear in Phys.Rev.

The Relativistically Spinning Charged Sphere

When the equatorial spin velocity, $v$, of a charged conducting sphere approaches $c$, the Lorentz force causes a remarkable rearrangement of the total charge $q$. Charge of that sign is confined to a narrow equatorial belt at latitudes $b \leqslant \sqrt{3} (1 - v^2/c^2)^{{1/2}}$ while charge of the opposite sign occupies most of the sphere's surface. The change in field structure is shown to be a growing contribution of the `magic' electromagnetic field of the charged Kerr-Newman black hole with Newton's G set to zero. The total charge within the narrow equatorial belt grows as $(1-v^2/c^2)^{-{1/4}}$ and tends to infinity as $v$ approaches $c$. The electromagnetic field, Poynting vector, field angular momentum and field energy are calculated for these configurations. Gyromagnetic ratio, g-factor and electromagnetic mass are illustrated in terms of a 19th Century electron model. Classical models with no spin had the small classical electron radius $e^2/mc^2\sim$ a hundredth of the Compton wavelength, but models with spin take that larger size but are so relativistically concentrated to the equator that most of their mass is electromagnetic. The method of images at inverse points of the sphere is shown to extend to charges at points with imaginary co-ordinates.Comment: 15 pages, 1figur

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199

Short-range spin glasses and Random Overlap Structures

Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs measure. Since the ROSt construction is the same for mean-field models (like the Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the setup is a good common ground to study the effect of dimensionality on the properties of the Gibbs measure. In this spirit, it is shown, using translation invariance, that the ROSt of the EA model possesses a local stability that is stronger than stochastic stability, a property known to hold at almost all temperatures in many spin glass models with Gaussian couplings. This fact is used to prove stochastic stability for the EA spin glass at all temperatures and for a wide range of coupling distributions. On the way, a theorem of Newman and Stein about the pure state decomposition of the EA model is recovered and extended.Comment: 27 page

Temperature-stable Gunn-diode oscillator

Oscillator consisting of Gunn diode embedded in coaxial circuit has excellent temperature stability and low fabrication costs as compared with automatic-frequency-control crystal oscillators