Pointwise estimates for the Bergman kernel of the weighted Fock space

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2\phi})$ where $\phi$ is a subharmonic function with $\Delta \phi$ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous Cauchy-Riemann equation and we characterize the compactness of this operator in terms of $\Delta \phi$

Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity

On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. This condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range -- roughly speaking -- from being ``mildly infinite-type'' to very flat at the infinite-type points.Comment: Significant revisions made; simpler estimates; very mild strengthening of the hypotheses on Theorem 1.2 to get much stronger conclusions than in ver.1. To appear in Math. An

Appraising Kirchhoff approximation theory for the scattering of elastic shear waves by randomly rough defects

Rapid and accurate methods, based on the Kirchhoff approximation (KA), are developed to evaluate the scattering of shear waves by rough defects and quantify the accuracy of this approximation. Defect roughness has a strong effect on the reflection of ultrasound, and every rough defect has a different surface, so standard methods of assessing the sensitivity of inspection based on smooth defects are necessarily limited. Accurately resolving rough cracks in non-destructive evaluation (NDE) inspections often requires shear waves since they have higher sensitivity to surface roughness than longitudinal waves. KA models are attractive, since they are rapid to deploy, however they are an approximation and it is important to determine the range of validity for the scattering of ultrasonic shear waves; this range is found here. Good agreement between KA and high fidelity finite element simulations is obtained for a range of incident/scattering angles, and the limits of validity for KA are found to be much stricter than for longitudinal wave incidence; as the correlation length of rough surfaces is reduced to the order of the incident shear wavelength, a combination of multiple scattering and surface wave mode conversion leads to KA predictions diverging from those of the true diffuse scattered fields

Two-Particle Interference with Double Twin-Atom Beams

We demonstrate a source for correlated pairs of atoms characterized by two opposite momenta and two spatial modes forming a Bell state only involving external degrees of freedom. We characterize the state of the emitted atom beams by observing strong number squeezing up to -10 dB in the correlated two-particle modes of emission. We furthermore demonstrate genuine two-particle interference in the normalized second-order correlation function $g^{(2)}$ relative to the emitted atoms.Comment: 6 pages, 3 figure

First order superconducting transition near a ferromagnetic quantum critical point

We address the issue of how triplet superconductivity emerges in an electronic system near a ferromagnetic quantum critical point (FQCP). Previous studies found that the superconducting transition is of second order, and Tc is strongly reduced near the FQCP due to pair-breaking effects from thermal spin fluctuations. In contrast, we demonstrate that near the FQCP, the system avoids pair-breaking effects by undergoing a first order transition at a much larger Tc. A second order superconducting transition emerges only at some distance from the FQCP.Comment: 4 pages, 2 figure

Singularities in the optical response of cuprates

We argue that the detailed analysis of the optical response in cuprate superconductors allows one to verify the magnetic scenario of superconductivity in cuprates, as for strong coupling charge carriers to antiferromagnetic spin fluctuations, the second derivative of optical conductivity should contain detectable singularities at $2\Delta +\Delta_{\rm spin}$, $4\Delta$, and $2\Delta+2\Delta_{\rm spin}$, where $\Delta$ is the amplitude of the superconducting gap, and $\Delta_{s}$ is the resonance energy of spin fluctuations measured in neutron scattering. We argue that there is a good chance that these singularities have already been detected in the experiments on optimally doped $YBCO$.Comment: 6 pages, 4 figure

Kinetic Energy, Condensation Energy, Optical Sum Rule and Pairing Mechanism in High-Tc Cuprates

The mechanism of high-Tc superconductivity is investigated with interests on the microscopic aspects of the condensation energy. The theoretical analysis is performed on the basis of the FLEX approximation which is a microscopic description of the spin-fluctuation-induced-superconductivity. Most of phase transitions in strongly correlated electron system arise from the correlation energy which is copmetitive to the kinetic energy. However, we show that the kinetic energy cooperatively induces the superconductivity in the underdoped region. This unusual decrease of kinetic energy below T_c is induced by the feedback effect. The feedback effect induces the magnetic resonance mode as well as the kink in the electronic dispersion, and alters the properties of quasi-particles, such as mass renormalization and lifetime. The crossover from BCS behavior to this unusual behavior occurs for hole dopings. On the other hand, the decrease of kinetic energy below T_c does not occur in the electron-doped region. We discuss the relation to the recent obserbation of the violation of optical sum rule