Spin and energy correlations in the one dimensional spin 1/2 Heisenberg model

In this paper, we study the spin and energy dynamic correlations of the one dimensional spin 1/2 Heisenberg model, using mostly exact diagonalization numerical techniques. In particular, observing that the uniform spin and energy currents decay to finite values at long times, we argue for the absence of spin and energy diffusion in the easy plane anisotropic Heisenberg model.Comment: 10 pages, 3 figures, gzipped postscrip

Randomly incomplete spectra and intermediate statistics

By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review

Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1201.657

High-precision estimate of g4 in the 2D Ising model

We compute the renormalized four-point coupling in the 2d Ising model using transfer-matrix techniques. We greatly reduce the systematic uncertainties which usually affect this type of calculations by using the exact knowledge of several terms in the scaling function of the free energy. Our final result is g4=14.69735(3).Comment: 17 pages, revised version with minor changes, accepted for publication in Journal of Physics

Lunar particle shadows and boundary layer experiment: Plasma and energetic particles on the Apollo 15 and 16 subsatellites

The lunar particle shadows and boundary layer experiments aboard the Apollo 15 and 16 subsatellites and scientific reduction and analysis of the data to date are discussed with emphasis on four major topics: solar particles; interplanetry particle phenomena; lunar interactions; and topology and dynamics of the magnetosphere at lunar orbit. The studies of solar and interplanetary particles concentrated on the low energy region which was essentially unexplored, and the studies of lunar interaction pointed up the transition from single particle to plasma characteristics. The analysis concentrated on the electron angular distributions as highly sensitive indicators of localized magnetization of the lunar surface. Magnetosphere experiments provided the first electric field measurements in the distant magnetotail, as well as comprehensive low energy particle measurements at lunar distance

Nonequilibrium phase transition in a driven Potts model with friction

We consider magnetic friction between two systems of $q$-state Potts spins which are moving along their boundaries with a relative constant velocity $v$. Due to the interaction between the surface spins there is a permanent energy flow and the system is in a steady state which is far from equilibrium. The problem is treated analytically in the limit $v=\infty$ (in one dimension, as well as in two dimensions for large-$q$ values) and for $v$ and $q$ finite by Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase transitions take place, the properties of which depend on the type of phase transition in equilibrium. When this latter transition is of first order, a sequence of second- and first-order nonequilibrium transitions can be observed when the interaction is varied.Comment: 13 pages, 9 figures, one journal reference adde

Aperiodic Ising model on the Bethe lattice: Exact results

We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical behavior exactly for marginal aperiodic sequences. We present analytical formulae for the continuously varying critical exponents and discuss a relationship with the (surface) critical behavior of the aperiodic quantum Ising chain.Comment: 7 pages, 3 figures, minor correction

Correction induced by irrelevant operators in the correlators of the 2d Ising model in a magnetic field

We investigate the presence of irrelevant operators in the 2d Ising model perturbed by a magnetic field, by studying the corrections induced by these operators in the spin-spin correlator of the model. To this end we perform a set of high precision simulations for the correlator both along the axes and along the diagonal of the lattice. By comparing the numerical results with the predictions of a perturbative expansion around the critical point we find unambiguous evidences of the presence of such irrelevant operators. It turns out that among the irrelevant operators the one which gives the largest correction is the spin 4 operator T^2 + \bar T^2 which accounts for the breaking of the rotational invariance due to the lattice. This result agrees with what was already known for the correlator evaluated exactly at the critical point and also with recent results obtained in the case of the thermal perturbation of the model.Comment: 28 pages, no figure

The Importance of Meteorite Collections to Sample Return Missions: Past, Present, and Future Considerations

While much of the scientific community s current attention is drawn to sample return missions, it is the existing meteorite and cosmic dust collections that both provide the paradigms to be tested by these missions and the context for interpreting the results. Recent sample returns from the Stardust and Hayabusa missions provided us with new materials and insights about our Solar System history and processes. As an example, Stardust sampled CAIs among the population of cometary grains, requiring extensive and unexpected radial mixing in the early solar nebula. This finding would not have been possible, however, without extensive studies of meteoritic CAIs that established their high-temperature, inner Solar System formation. Samples returned by Stardust also revealed the first evidence of a cometary amino acid, a discovery that would not have been possible with current in situ flight instrument technology. The Hayabusa mission provided the final evidence linking ordinary chondrites and S asteroids, a hypothesis that developed from centuries of collection and laboratory and ground-based telescopic studies. In addition to these scientific findings, studies of existing meteorite collections have defined and refined the analytical techniques essential to studying returned samples. As an example, the fortuitous fall of the Allende CV3 and Murchison CM2 chondrites within months before the return of Apollo samples allowed testing of new state-of-the-art analytical facilities. The results of those studies not only prepared us to better study lunar materials, but unanticipated discoveries changed many of our concepts about the earliest history and processes of the solar nebula. This synergy between existing collections and future space exploration is certainly not limited to sample return missions. Laboratory studies confirmed the existence of meteorites from Mars and raised the provocative possibility of preservation of ancient microbial life. The laboratory studies in turn led to a new wave of Mars exploration that ultimately could lead to sample return focused on evidence for past or present life. This partnership between collections and missions will be increasingly important in the coming decades as we discover new questions to be addressed and identify targets for for both robotic and human exploration . Nowhere is this more true than in the ultimate search for the abiotic and biotic processes that produced life. Existing collections also provide the essential materials for developing and testing new analytical schemes to detect the rare markers of life and distinguish them from abiotic processes. Large collections of meteorites and the new types being identified within these collections, which come to us at a fraction of the cost of a sample return mission, will continue to shape the objectives of future missions and provide new ways of interpreting returned samples