Comparisons of spectra determined using detector atoms and spatial correlation functions

We show how two level atoms can be used to determine the local time dependent spectrum. The method is applied to a one dimensional cavity. The spectrum obtained is compared with the mode spectrum determined using spatially filtered second order correlation functions. The spectra obtained using two level atoms give identical results with the mode spectrum. One benefit of the method is that only one time averages are needed. It is also more closely related to a realistic measurement scheme than any other definition of a time dependent spectrum.Comment: 8 pages, 8 figure

Bivariate spline interpolation with optimal approximation order

Let be a triangulation of some polygonal domain f c R2 and let S9 (A) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to A. We develop the first Hermite-type interpolation scheme for S9 (A), q >_ 3r + 2, whose approximation error is bounded above by Kh4+i, where h is the maximal diameter of the triangles in A, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and nearsingular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of Sr, (A). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [71 and [181

Similarity Analysis of Nonlinear Equations and Bases of Finite Wavelength Solitons

We introduce a generalized similarity analysis which grants a qualitative description of the localised solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the solutions, and it is shown to be useful in analysing nonlinear structures like solitons, dublets, triplets, compact supported solitons and other patterns. We also introduce kink-antikink compact solutions for a nonlinear-nonlinear dispersion equation, and we construct a basis of finite wavelength functions having self-similar properties.Comment: 18 pages Latex, 6 figures ep

Magnetic Field Induced Insulating Phases at Large rsr_s

Exploring a backgated low density two-dimensional hole sample in the large $r_s$ regime we found a surprisingly rich phase diagram. At the highest densities, beside the $\nu=1/3$, 2/3, and 2/5 fractional quantum Hall states, we observe both of the previously reported high field insulating and reentrant insulating phases. As the density is lowered, the reentrant insulating phase initially strengthens, then it unexpectedly starts weakening until it completely dissapears. At the lowest densities the terminal quantum Hall state moves from $\nu=1/3$ to $\nu=1$. The intricate behavior of the insulating phases can be explained by a non-monotonic melting line in the $\nu$-$r_s$ phase space

Phase separation and vortex states in binary mixture of Bose-Einstein condensates in the trapping potentials with displaced centers

The system of two simultaneously trapped codensates consisting of $^{87}Rb$ atoms in two different hyperfine states is investigated theoretically in the case when the minima of the trapping potentials are displaced with respect to each other. It is shown that the small shift of the minima of the trapping potentials leads to the considerable displacement of the centers of mass of the condensates, in agreement with the experiment. It is also shown that the critical angular velocities of the vortex states of the system drastically depend on the shift and the relative number of particles in the condensates, and there is a possibility to exchange the vortex states between condensates by shifting the centers of the trapping potentials.Comment: 4 pages, 2 figure

Negative Magnetoresistance of Granular Metals in a Strong Magnetic Field

The magnetoresistance of a granular superconductor in a strong magnetic field destroying the gap in each grain is considered. It is assumed that the tunneling between grains is sufficiently large such that all conventional effects of localization can be neglected. A non-trivial sensitivity to the magnetic field comes from superconducting fluctuations leading to the formation of virtual Cooper pairs and reducing the density of states. At low temperature, the pairs do not contribute to the macroscopic transport but their existence can drastically reduce the conductivity. Growing the magnetic field one destroys the fluctuations, which improves the metallic properties and leads to the negative magnetoresistance.Comment: 4 pages, 1 figure, RevTe

Thermodynamic Density Matrix renormalization Group Study of the Magnetic Susceptibility of Half-integer Quantum Spin Chains

It is shown that White's density matrix renormalization group technique can be adapted to obtain thermodynamic quantities. As an illustration, the magnetic susceptibility of Heisenberg S=1/2 and S=3/2 spin chains are computed. A careful finite size analysis is made to determine the range of temperatures where the results are reliable. For the S=1/2 chain, the comparison with the exact Bethe ansatz curve shows an agreement within 1% down to T=0.05J.Comment: 9 pages, 4 figures. To be published in PR

Delay and distortion of slow light pulses by excitons in ZnO

Light pulses propagating through ZnO undergo distortions caused by both bound and free excitons. Numerous lines of bound excitons dissect the pulse and induce slowing of light around them, to the extend dependent on their nature. Exciton-polariton resonances determine the overall pulse delay and attenuation. The delay time of the higher-energy edge of a strongly curved light stripe approaches 1.6 ns at 3.374 eV with a 0.3 mm propagation length. Modelling the data of cw and time-of-flight spectroscopies has enabled us to determine the excitonic parameters, inherent for bulk ZnO. We reveal the restrictions on these parameters induced by the light attenuation, as well as a discrepancy between the parameters characterizing the surface and internal regions of the crystal.Comment: 4 pages, 4 figure

The Addition Spectrum and Koopmans' Theorem for Disordered Quantum Dots

We investigate the addition spectrum of disordered quantum dots containing spinless interacting fermions using the self-consistent Hartree-Fock approximation. We concentrate on the regime r_s >~1, with finite dimensionless conductance g. We find that in this approximation the peak spacing fluctuations do not scale with the mean single particle level spacing for either Coulomb or nearest neighbour interactions when r_s >~1. We also show that Koopmans' approximation to the addition spectrum can lead to errors that are of order the mean level spacing or larger, both in the mean addition spectrum peak spacings, and in the peak spacing fluctuations.Comment: 35 pages including 22 figures (eps

Magnetoresistance of Granular Superconducting Metals in a Strong Magnetic Field

The magnetoresistance of a granular superconductor in a strong magnetic field is considered. It is assumed that this field destroys the superconducting gap in each grain, such that all interesting effects considered in the paper are due to superconducting fluctuations. The conductance of the system is assumed to be large, which allows us to neglect all localization effects as well as the Coulomb interaction. It is shown that at low temperatures the superconducting fluctuations reduce the one-particle density of states but do not contribute to transport. As a result, the resistivity of the normal state exceeds the classical resistivity approaching the latter only in the limit of extremely strong magnetic fields, and this leads to a negative magnetoresistance. We present detailed calculations of physical quatities relevant for describing the effect and make a comparison with existing experiments.Comment: 24 pages, 10 figure