The Field Perturbation Theory of Pseudogaps in HTSC

Here I establish the field perturbation theory of pseudogaps in HTSC. The proposed ground state suggests an internal particle-hole field, which is normal to nesting surfaces, and having twice the Fermi wave-number. It is proved that the system violates momentum conservation by the wave-vector of this internal field. This violation applies to the quasi-particle propagators, as well as to the interactions. Interaction vertices via the Pauli matrix- are established. This, in turn, establishes the validity of the pseudogap Hartree self-energy

Theory of Two-Photon Interactions with Broadband Down-Converted Light and Entangled Photons

When two-photon interactions are induced by down-converted light with a bandwidth that exceeds the pump bandwidth, they can obtain a behavior that is pulse-like temporally, yet spectrally narrow. At low photon fluxes this behavior reflects the time and energy entanglement between the down-converted photons. However, two-photon interactions such as two-photon absorption (TPA) and sum-frequency generation (SFG) can exhibit such a behavior even at high power levels, as long as the final state (i.e. the atomic level in TPA, or the generated light in SFG) is narrowband enough. This behavior does not depend on the squeezing properties of the light, is insensitive to linear losses, and has potential applications. In this paper we describe analytically this behavior for travelling-wave down-conversion with continuous or pulsed pumping, both for high- and low-power regimes. For this we derive a quantum-mechanical expression for the down-converted amplitude generated by an arbitrary pump, and formulate operators that represent various two-photon interactions induced by broadband light. This model is in excellent agreement with experimental results of TPA and SFG with high power down-converted light and with entangled photons [Dayan et al., Phys. Rev. Lett. 93, 023005 (2004), Dayan et al., Phys. Rev. Lett. 94, 043602, (2005), Pe'er et al., Phys. Rev. Lett. 94, 073601 (2005)].Comment: 23 pages, 4 figures, submitted to Phys. Rev.

The Inward Dispersion of the Neutron Scattering Experiments in HTSC Cuprates

The theory of the high temperature superconducting cuprates, which is based on the condensation of holes into strings in checker-board geometry, was successful to explain the elastically scattered Neutrons by spin waves. Here it is extended to analyze the inward dispersion curve of its inelastic counterpart, up to the resonance energy- . This extension is done by applying the perturbation theory of the linear response to the condensed strings. The approximated susceptibility is derived by means of the ring diagram. The dispersion relation is obtained from the dispersion of the poles of the susceptibility integral. It is found that the particle anti-particle pair that yields the susceptibility is the time reversal pair where the particle momentum is in phase A, and the anti-particle momentum is in phase B. The dispersion is found to be in agreement with experiment, subject to some suggested corrections. The weak intensity by the resonance energy, as well as the dispersion, is speculated to be modified due to interference with spin waves that are caused by direct spin flip, as in the mother undoped materials

Non-negative matrix factorization with sparseness constraints

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of `sparseness' improves the found decompositions. Additionally, we provide complete MATLAB code both for standard NMF and for our extension. Our hope is that this will further the application of these methods to solving novel data-analysis problems

Constraints on small-scale cosmological fluctuations from SNe lensing dispersion

We provide predictions on small-scale cosmological density power spectrum from supernova lensing dispersion. Parameterizing the primordial power spectrum with running $\alpha$ and running of running $\beta$ of the spectral index, we exclude large positive $\alpha$ and $\beta$ parameters which induce too large lensing dispersions over current observational upper bound. We ran cosmological N-body simulations of collisionless dark matter particles to investigate non-linear evolution of the primordial power spectrum with positive running parameters. The initial small-scale enhancement of the power spectrum is largely erased when entering into the non-linear regime. For example, even if the linear power spectrum at $k>10h {\rm Mpc}^{-1}$ is enhanced by $1-2$ orders of magnitude, the enhancement much decreases to a factor of $2-3$ at late time ($z \leq 1.5$). Therefore, the lensing dispersion induced by the dark matter fluctuations weakly constrains the running parameters. When including baryon-cooling effects (which strongly enhance the small-scale clustering), the constraint is comparable or tighter than the PLANCK constraint, depending on the UV cut-off. Further investigations of the non-linear matter spectrum with baryonic processes is needed to reach a firm constraint.Comment: 11 pages, 9 figures. Submitted to MNRA

Improved decision for a resource-efficient fusion scheme in cooperative spectrum sensing

Paper presented at at 2015 International Workshop on Telecommunications (IWT), 14th to 17th of June, Santa Rita do Sapucai, Brazil. Abstract Recently, a novel decision fusion scheme for cooperative spectrum sensing was proposed, aiming at saving resources in the reporting channel transmissions. Secondary users are allowed to report their local decisions through the symbols of binary modulations, at the same time and with the same carrier frequencies. As a consequence, the transmitted symbols add incoherently at the fusion center, forming a larger set of symbols in which a subset is associated to the presence of the primary signal, and another subset is associated to the absence of such a signal. A Bayesian decision criterion with uniform prior was applied for discriminating these subsets. In this paper we propose a modified decision rule in which the target probabilities of detection and false alarm are taken into account to produce a large performance improvement over the original decision criterion. This improvement comes with practically no cost in complexity and does not demand the knowledge of any additional information when compared to the original rule