Spin-lattice interactions of ions with unfilled F-shells measured by ESR in uniaxially stressed crystals

Spin-lattice interactions of ions with unfilled F-shells measured by electron spin resonance in uniaxially stressed crystal

Direct one-phonon spin-lattice relaxation times for Nd sup 3 plus and U sup 3 plus ions in CaF sub 2 in sites of tetragonal symmetry

Phonon spin-lattice relaxation times for uranium and neodymium ions in calcium fluorid

On the irreversibility of entanglement distillation

We investigate the irreversibility of entanglement distillation for a symmetric d-1 parameter family of mixed bipartite quantum states acting on Hilbert spaces of arbitrary dimension d x d. We prove that in this family the entanglement cost is generically strictly larger than the distillable entanglement, such that the set of states for which the distillation process is asymptotically reversible is of measure zero. This remains true even if the distillation process is catalytically assisted by pure state entanglement and every operation is allowed, which preserves the positivity of the partial transpose. It is shown, that reversibility occurs only in cases where the state is quasi-pure in the sense that all its pure state entanglement can be revealed by a simple operation on a single copy. The reversible cases are shown to be completely characterized by minimal uncertainty vectors for entropic uncertainty relations.Comment: 5 pages, revtex

Spin-lattice Interaction in Ruby Measured by ESR in Uniaxially Stressed Crystals

Spin-lattice Hamiltonian determined for chromium ions in ruby single crystal

Very high quality image restoration by combining wavelets and curvelets

We outline digital implementations of two newly developed multiscale representation systems, namely, the ridgelet and curvelet transforms. We apply these digital transforms to the problem of restoring an image from noisy data and compare our results with those obtained via well established methods based on the thresholding of wavelet coefficients. We develop a methodology to combine wavelets together these new systems to perform noise removal by exploiting all these systems simultaneously. The results of the combined reconstruction exhibits clear advantages over any individual system alone. For example, the residual error contains essentially no visually intelligible structure: no structure is lost in the reconstruction

Position and momentum observables on R and on R^3

We characterize all position and momentum observables on R and on R^3. We study some of their operational properties and discuss their covariant joint observables.Comment: 18 page

Analysis of the Spatial Distribution of Galaxies by Multiscale Methods

Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy distribution and discriminate the different cosmological models. We present in this paper results relative to the use of new statistical tools using the 3D isotropic undecimated wavelet transform, the 3D ridgelet transform and the 3D beamlet transform. We show that such multiscale methods produce a new way to measure in a coherent and statistically reliable way the degree of clustering, filamentarity, sheetedness, and voidedness of a datasetComment: 26 pages, 20 figures. Submitted to EURASIP Journal on Applied Signal Processing (special issue on "Applications of Signal Processing in Astrophysics and Cosmology"

Statistical physics-based reconstruction in compressed sensing

Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is measured. Currently used reconstruction techniques are, however, limited to acquisition rates larger than the true density of the signal. We design a new procedure which is able to reconstruct exactly the signal with a number of measurements that approaches the theoretical limit in the limit of large systems. It is based on the joint use of three essential ingredients: a probabilistic approach to signal reconstruction, a message-passing algorithm adapted from belief propagation, and a careful design of the measurement matrix inspired from the theory of crystal nucleation. The performance of this new algorithm is analyzed by statistical physics methods. The obtained improvement is confirmed by numerical studies of several cases.Comment: 20 pages, 8 figures, 3 tables. Related codes and data are available at http://aspics.krzakala.or