Spectrometer for Hard X-Ray Free Electron Laser Based on Diffraction Focusing

X-ray free electron lasers (XFELs) generate sequences of ultra-short, spatially coherent pulses of x-ray radiation. We propose the diffraction focusing spectrometer (DFS), which is able to measure the whole energy spectrum of the radiation of a single XFEL pulse with an energy resolution of $\Delta E/E\approx 2\times 10^{-6}$. This is much better than for most modern x-ray spectrometers. Such resolution allows one to resolve the fine spectral structure of the XFEL pulse. The effect of diffraction focusing occurs in a single crystal plate due to dynamical scattering, and is similar to focusing in a Pendry lens made from the metamaterial with a negative refraction index. Such a spectrometer is easier to operate than those based on bent crystals. We show that the DFS can be used in a wide energy range from 5 keV to 20 keV.Comment: 9 pages, 8 figures, 2 table

The sharp-interface limit of the action functional for Allen-Cahn in one space dimension

We analyze the sharp-interface limit of the action minimization problem for the stochastically perturbed Allen-Cahn equation in one space dimension. The action is a deterministic functional which is linked to the behavior of the stochastic process in the small noise limit. Previously, heuristic srguments and numerical result heve suggested that the limiting action should“count” two competing costs: the cost to nucleate interfaces and the cost to propagate them. In addition, constructions have been used to derive an upper bound for the minimal action which was proved optimal on the level of \it{scaling}. In this paper, we prove that for $(d=1)$, the upper bound achieved by the constructions is in fact sharp. Furthermore, we derive a lower bound for the functional itself, which is in agreement with the heuristic picture. To do so, we characterize the sharp-interface limit of the space-time energy measures. The proof relies on an extension of earlier results for the related elliptic problem

Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors

We show that any pair of real symmetric tensors \BGve and \BGm can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitt{\'e} and Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor, and the other having a positive permittivity tensor, and a permeability tensor having exactly one negative eigenvalue. To achieve the desired effective properties these materials are laminated together in a hierarchical multiple rank laminate structure, with widely separated length scales, and varying directions of lamination, but with the largest length scale still much shorter than the wavelengths and attenuation lengths in the macroscopic effective medium.Comment: 12 pages, no figure

Thermodynamic Properties of Generalized Exclusion Statistics

We analytically calculate some thermodynamic quantities of an ideal $g$-on gas obeying generalized exclusion statistics. We show that the specific heat of a $g$-on gas ($g \neq 0$) vanishes linearly in any dimension as $T \to 0$ when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at $g$ to the hole-statistics at $1/g$ at low temperatures. We derive the complete solution for the cluster coefficients $b_l(g)$ as a function of Haldane's statistical interaction $g$ in $D$ dimensions. We also find that the cluster coefficients $b_l(g)$ and the virial coefficients $a_l(g)$ are exactly mirror symmetric ($l$=odd) or antisymmetric ($l$=even) about $g=1/2$. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the $g$-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.Comment: 24 pages, Revtex, Corrected typo

Terahertz and infrared spectroscopic evidence of phonon-paramagnon coupling in hexagonal piezomagnetic YMnO3

Terahertz and far-infrared electric and magnetic responses of hexagonal piezomagnetic YMnO3 single crystals are investigated. Antiferromagnetic resonance is observed in the spectra of magnetic permeability mu_a [H(omega) oriented within the hexagonal plane] below the Neel temperature T_N. This excitation softens from 41 to 32 cm-1 on heating and finally disappears above T_N. An additional weak and heavily-damped excitation is seen in the spectra of complex dielectric permittivity epsilon_c within the same frequency range. This excitation contributes to the dielectric spectra in both antiferromagnetic and paramagnetic phases. Its oscillator strength significantly increases on heating towards room temperature thus providing evidence of piezomagnetic or higher-order couplings to polar phonons. Other heavily-damped dielectric excitations are detected near 100 cm-1 in the paramagnetic phase in both epsilon_c and epsilon_a spectra and they exhibit similar temperature behavior. These excitations appearing in the frequency range of magnon branches well below polar phonons could remind electromagnons; however, their temperature dependence is quite different. We have used density functional theory for calculating phonon dispersion branches in the whole Brillouin zone. A detailed analysis of these results and of previously published magnon dispersion branches brought us to the conclusion that the observed absorption bands stem from phonon-phonon and phonon- paramagnon differential absorption processes. The latter is enabled by a strong short-range in-plane spin correlations in the paramagnetic phase.Comment: subm. to PR

Ground state instability in systems of strongly interacting fermions

We analyze stability of a fermion system with model repulsive pair interaction potential. The possibility for different types of restructuring of the Fermi ground state (at sufficiently great coupling constant) is related to the analytic properties of such potential. In particular, for the screened Coulomb law it is shown that the restructuring cannot be of the Fermi condensation type, known earlier for some exactly solvable models, and instead it belongs to the class of topological transitions (TT). For this model, a phase diagram has been built in the variables "screening parameter - coupling constant" which displays two kinds of TT: a 5/2-kind similar to the known Lifshitz transitions in metals, and a 2-kind characteristic for a uniform strongly interacting system.Comment: The article has 11 pages, in Latex 2e (from Lyx), 3 eps figures or a ps fil

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space

Single Electron Spin Decoherence by Nuclear Spin Bath: Linked Cluster Expansion Approach

We develop a theoretical model for transverse dynamics of a single electron spin interacting with a nuclear spin bath. The approach allows a simple diagrammatic representation and analytical expressions of different nuclear spin excitation processes contributing to electron spin decoherence and dynamical phase fluctuations. It accounts for nuclear spin dynamics beyond conventional pair correlation models. As an illustration of the theory, we evaluated the coherence dynamics of a P donor electron spin in a Si crystal.Comment: 37 pages, 13 figure

Itinerant in-plane magnetic fluctuations and many-body correlations in Nax_xCoO2_2

Based on the {\it ab-initio} band structure for Na$_x$CoO$_2$ we derive the single-electron energies and the effective tight-binding description for the $t_{2g}$ bands using projection procedure. Due to the presence of the next-nearest-neighbor hoppings a local minimum in the electronic dispersion close to the $\Gamma$ point of the first Brillouin zone forms. Correspondingly, in addition to a large Fermi surface an electron pocket close to the $\Gamma$ point emerges at high doping concentrations. The latter yields the new scattering channel resulting in a peak structure of the itinerant magnetic susceptibility at small momenta. This indicates dominant itinerant in-plane ferromagnetic fluctuations above certain critical concentration $x_m$, in agreement with neutron scattering data. Below $x_m$ the magnetic susceptibility shows a tendency towards the antiferromagnetic fluctuations. We further analyze the many-body effects on the electronic and magnetic excitations using various approximations applicable for different $U/t$ ratio.Comment: 10 page