Material dependence of Casimir forces: gradient expansion beyond proximity

A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) and insulators (SiO$_2$) at room temperature. We derive an explicit expression for the amplitude $\hat\theta_1$ of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, $\hat\theta_1$ has an unusually large temperature dependence.Comment: 4 pages, 2 figure

Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery

The coefficient of normal restitution of colliding viscoelastic spheres is computed as a function of the material properties and the impact velocity. From simple arguments it becomes clear that in a collision of purely repulsively interacting particles, the particles loose contact slightly before the distance of the centers of the spheres reaches the sum of the radii, that is, the particles recover their shape only after they lose contact with their collision partner. This effect was neglected in earlier calculations which leads erroneously to attractive forces and, thus, to an underestimation of the coefficient of restitution. As a result we find a novel dependence of the coefficient of restitution on the impact rate.Comment: 11 pages, 2 figure

Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models

We calculate the Casimir interaction between a sphere and a plate, both described by the plasma model, the Drude model, or generalizations of the two models. We compare the results at both zero and finite temperatures. At asymptotically large separations we obtain analytical results for the interaction that reveal a non-universal, i.e., material dependent interaction for the plasma model. The latter result contains the asymptotic interaction for Drude metals and perfect reflectors as different but universal limiting cases. This observation is related to the screening of a static magnetic field by a London superconductor. For small separations we find corrections to the proximity force approximation (PFA) that support correlations between geometry and material properties that are not captured by the Lifshitz theory. Our results at finite temperatures reveal for Drude metals a non-monotonic temperature dependence of the Casimir free energy and a negative entropy over a sizeable range of separations.Comment: 11 pages, 5 figure

Finite-sample frequency distributions originating from an equiprobability distribution

Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the expected corresponding rank ordered frequency distribution f(i), i=1..N, if an ensemble of M events is drawn?Comment: 4 pages, 4 figure

Density Matrix Renormalization for Model Reduction in Nonlinear Dynamics

We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in computational effort for the calculation of the reduced system, compared to a POD. The efficiency of the algorithm is tested on the one dimensional Burgers equations and a one dimensional equation of the Fisher type as nonlinear model systems.Comment: 12 pages, 12 figure

Diversidad de especies de Xanthoparmelia (Parmeliaceae) en la vegetación de matorrales xerofíticos mexicanos, evidenciada por datos moleculares, morfológicos y químicos

The genus Xanthoparmelia is the largest genus of lichen- forming fungi with about 800 species worldwide. Xanthoparmelia is also common in the deserts of central Mexico, but only a few molecular studies exist on its species’ diversity in this region. In this study, we sampled 38 Xanthoparmelia species from around the world including species from the xerophytic scrubs of central Mexico to assess the diversity using an integrative approach. Molecular phylogenetic analyses were performed using a combination of the ITS, mtSSU and nuLSU genetic markers. We evaluated our phylogenetic results in a context of traditional morphological and chemical characters. The combined evidence of molecular, morphological, and chemical data identified a total of 18 Xanthoparmelia species-level lineages occurring in central Mexico. However, numerous traditionally circumscribed species did not form monophyletic groups in the molecular phylogenetic reconstructions. This conflict indicates that taxonomy and species delimitation in the genus Xanthoparmelia requires revision and emphasizes the importance of molecular evidence for more robust species delimitations in this genus.Xanthoparmelia es el género más grande de hongos liquenizados, con alrededor de 800 especies en todo el mundo. Xanthoparmelia es común en los desiertos del centro de México, pero existen pocos estudios moleculares sobre la diversidad de especies en esta región. En este estudio, muestreamos 38 especies de Xanthoparmelia de diferentes partes del mundo, incluidas especies de los matorrales xerófilos del centro de México, para evaluar la diversidad usando una aproximación integrativa. Los análisis filogenéticos moleculares se realizaron combinando los marcadores genéticos ITS, mtSSU y nuLSU. Además, evaluamos nuestros resultados filogenéticos en un contexto de caracteres morfológicos y químicos usados en la taxonomía tradicional. Teniendo en cuenta las evidencias obtenidas a partir de caracteres moleculares, morfológicos y químicos se identificaron un total de 18 linajes de Xanthoparmelia con categoría de especie que aparecen en el centro de México. Sin embargo, muchas especies tradicionalmente circunscritas no formaron grupos monofiléticos. Este conflicto indica que la taxonomía y delimitación de especies en el género Xanthoparmelia requiere revisión y enfatiza la importancia de los datos moleculares para una delimitación más robusta de especies en este género

Femtochemistry of mass-selected negative-ion clusters of dioxygen: Charge-transfer and solvation dynamics

Femtosecond, time-resolved photoelectron spectroscopy is used to investigate the dissociation dynamics of mass-selected anionic molecular-oxygen clusters. The observed transient photoelectron signal for the clusters (O_2)^−_n  (n = 3–5) shows the O^−_2 production; for n = 1 and 2, we observe no time-dependence at this wavelength of 800 nm. The observed transients are bi-exponential in form with two distinct time constants, but with clear trends, for all investigated cluster sizes. These striking observations describe the reaction pathways of the solvated core and we elucidate two primary processes: Charge transfer with concomitant nuclear motion, and direct dissociation of the O^−_4 core-ion via electron recombination; the former takes 700–2700 fs, while the latter is on a shorter time scale, 110–420 fs. Both rates decrease differently upon increasing cluster size, indicating the critical role of step-wise solvation

Thermodynamic Fingerprints of Disorder in Flux Line Lattices and other Glassy Mesoscopic Systems

We examine probability distributions for thermodynamic quantities in finite-sized random systems close to criticality. Guided by available exact results, a general ansatz is proposed for replicated free energies, which leads to scaling forms for cumulants of various macroscopic observables. For the specific example of a planar flux line lattice in a two dimensional superconducting film near H_c1, we provide detailed results for the statistics of the magnetic flux density, susceptibility, heat capacity, and their cross-correlations.Comment: 4 page

Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects

We present a detailed derivation of heat radiation, heat transfer and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal non-equilibrium. The results can be expressed as basis-independent trace formulae in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave-expansions, we transform the results for radiation, transfer and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nano-spheres is typically invalid. We derive asymptotic formulae for heat transfer and non-equilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nano-sphere can levitate above a plate with the repulsive non-equilibrium force overcoming gravity -- an effect that is not due to radiation pressure.Comment: 29 pages, 6 figures (v2: Sentence added in Sec. 1