Nonlinear Young integrals via fractional calculus

For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.Comment: arXiv admin note: substantial text overlap with arXiv:1404.758

Quantum mechanical photon-count formula derived by entangled state representation

By introducing the thermo entangled state representation, we derived four new photocount distribution formulas for a given density operator of light field. It is shown that these new formulas, which is convenient to calculate the photocount, can be expressed as such integrations over Laguree-Gaussian function with characteristic function, Wigner function, Q-function, and P-function, respectively.Comment: 5 pages, no figur

Comment on "Single-mode excited entangled coherent states"

In Xu and Kuang (\textit{J. Phys. A: Math. Gen.} 39 (2006) L191), the authors claim that, for single-mode excited entangled coherent states $| \Psi_{\pm}(\alpha,m)>$, \textquotedblleft the photon excitations lead to the decrease of the concurrence in the strong field regime of $| \alpha | ^{2}$ and the concurrence tends to zero when $| \alpha | ^{2}\to \infty$". This is wrong.Comment: 4 apges, 2 figures, submitted to JPA 15 April 200

The asymmetric structure of the Galactic halo

Using the stellar photometry catalogue based on the latest data release (DR4) of the Sloan Digital Sky Survey (SDSS), a study of the Galactic structure using star counts is carried out for selected areas of the sky. The sample areas are selected along a circle at a Galactic latitude of +60$^\circ$, and 10 strips of high Galactic latitude along different longitudes. Direct statistics of the data show that the surface densities of $\ell$ from $180^{\circ}$ to $360^{\circ}$ are systematically higher than those of $\ell$ from $0^{\circ}$ to $180^{\circ}$, defining a region of overdensity (in the direction of Virgo) and another one of underdensity (in the direction of Ursa Major) with respect to an axisymmetric model. It is shown by comparing the results from star counts in the $(g-r)$ colour that the density deviations are due to an asymmetry of the stellar density in the halo. Theoretical models for the surface density profile are built and star counts are performed using a triaxial halo of which the parameters are constrained by observational data. Two possible reasons for the asymmetric structure are discussed.Comment: 17 pages, 7 figures, 5 tables, MNRAS accepte

Wigner functions of thermo number state, photon subtracted and added thermo vacuum state at finite temperature

Based on Takahashi-Umezawa thermo field dynamics and the order-invariance of Weyl ordered operators under similar transformations, we present a new approach to deriving the exact Wigner functions of thermo number state, photon subtracted and added thermo vacuum state. We find that these Wigner functions are related to the Gaussian-Laguerre type functions of temperature, whose statistical properties are then analysed.Comment: 10 pages and 2 figure