Low-Energy Nondipole Effects in Molecular Nitrogen Valence-Shell Photoionization

Observations are reported for the first time of significant nondipole effects in the photoionization of the outer-valence orbitals of diatomic molecules. Measured nondipole angular-distribution parameters for the 3sigmag, 1piu, and 2sigmau shells of N2 exhibit spectral variations with incident photon energies from thresholds to ~200 eV which are attributed via concomitant calculations to particular final-state symmetry waves arising from (E1)[direct-product](M1,E2) radiation-matter interactions first-order in photon momentum. Comparisons with previously reported K-edge studies in N2 verify linear scaling with photon momentum, accounting in part for the significantly enhanced nondipole behavior observed in inner-shell ionization at correspondingly higher momentum values in this molecule

Finite size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is being examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite size effects are estimated for comparing the results to the bounds set by Shannon. The critical noise level achieved for certain code-rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low

Mean Field Behavior of Cluster Dynamics

The dynamic behavior of cluster algorithms is analyzed in the classical mean field limit. Rigorous analytical results below $T_c$ establish that the dynamic exponent has the value $z_{sw}=1$ for the Swendsen-Wang algorithm and $z_{uw}=0$ for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below $T_c$ demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.Comment: Revtex, 9 pages with 7 figure

Multilayer neural networks with extensively many hidden units

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter the storage capacity if found to scale with the logarithm of the number of implementable Boolean functions. The generalization behaviour is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.Comment: 4 pages, 2 figure

Microscopic Study of the Superconducting State of the Iron Pnictide RbFe_2As_2

A study of the temperature and field dependence of the penetration depth \lambda of the superconductor RbFe_2As_2 (T_c=2.52 K) was carried out by means of muon-spin rotation measurements. In addition to the zero temperature value of the penetration depth \lambda(0)=267(5) nm, a determination of the upper critical field B_c2(0)=2.6(2) T was obtained. The temperature dependence of the superconducting carrier concentration is discussed within the framework of a multi-gap scenario. Compared to the other "122" systems which exhibit much higher Fermi level, a strong reduction of the large gap BCS ratio 2\Delta/k_B T_c is observed. This is interpreted as a consequence of the absence of interband processes. Indications of possible pair-breaking effect are also discussed.Comment: 5 pages, 4 figure

Interplay of composition, structure, magnetism, and superconductivity in SmFeAs1-xPxO1-y

Polycrystalline samples and single crystals of SmFeAs1-xPxO1-y were synthesized and grown employing different synthesis methods and annealing conditions. Depending on the phosphorus and oxygen content, the samples are either magnetic or superconducting. In the fully oxygenated compounds the main impact of phosphorus substitution is to suppress the N\'eel temperature TN of the spin density wave (SDW) state, and to strongly reduce the local magnetic field in the SDW state, as deduced from muon spin rotation measurements. On the other hand the superconducting state is observed in the oxygen deficient samples only after heat treatment under high pressure. Oxygen deficiency as a result of synthesis at high pressure brings the Sm-O layer closer to the superconducting As/P-Fe-As/P block and provides additional electron transfer. Interestingly, the structural modifications in response to this variation of the electron count are significantly different when phosphorus is partly substituting arsenic. Point contact spectra are well described with two superconducting gaps. Magnetic and resistance measurements on single crystals indicate an in-plane magnetic penetration depth of 200 nm and an anisotropy of the upper critical field slope of 4-5. PACS number(s): 74.70.Xa, 74.62.Bf, 74.25.-q, 81.20.-nComment: 36 pages, 13 figures, 2 table

Error-correcting code on a cactus: a solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction

Partitioning and modularity of graphs with arbitrary degree distribution

We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with . In contrast, earlier results studying the problem in graphs with a Poissonian degree distribution had found a scaling with ^1/2 [Fu and Anderson, J. Phys. A: Math. Gen. 19, 1986]. The new results also generalize to the problem of q-partitioning. They can be used to find the expected modularity Q [Newman and Grivan, Phys. Rev. E, 69, 2004] of random graphs and allow for the assessment of statistical significance of the output of community detection algorithms.Comment: Revised version including new plots and improved discussion of some mathematical detail

Error-correcting codes that nearly saturate Shannon's bound

Gallager-type error-correcting codes that nearly saturate Shannon's bound are constructed using insight gained from mapping the problem onto that of an Ising spin system. The performance of the suggested codes is evaluated for different code rates in both finite and infinite message length