New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation about the Wigner operator (in its entangled form) in phase space quantum mechanics and its inverse transformation. In this way, some operator ordering problems can be solved and the contents of phase space quantum mechanics can be enriched.Comment: 8 pages, 0 figure

The basic parameters of gamma-ray-loud blazars

We determined the basic parameters, such as the central black hole mass ($M$), the boosting factor (or Doppler factor) ($\delta$), the propagation angle ($\Phi$) and the distance along the axis to the site of $\gamma$-ray production ($d$) for 23 $\gamma$-ray-loud blazars using their available variability timescales. In this method, the absorption effect depends on the $\gamma$-ray energy, emission size and property of the accretion disk. Using the intrinsic $\gamma$-ray luminosity as a fraction $\lambda$ of the Eddington luminosity, $L^{in}_{\gamma}=\lambda L_{Ledd.}$ and the optical depth equal to unity, we can determine the upper limit of the central black hole masses. We found that the black hole masses range between $10^{7}M_{\odot}$ and $10^{9}M_{\odot}$ when $\lambda$ = 0.1 and 1.0 are adopted. Since this method is based on gamma-ray emissions and the short time-scale of the sources, it can also be used for central black hole mass determination of high redshift gamma-ray sources. In the case of the upper limit of black hole mass there is no clear difference between BLs and FSRQs, which suggests that the central black hole masses do not play an important role in the evolutionary sequence of blazars.Comment: 8 pages, 3 figures, 1 table, Accepted by A&

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

Entangled Husimi distribution and Complex Wavelet transformation

Based on the proceding Letter [Int. J. Theor. Phys. 48, 1539 (2009)], we expand the relation between wavelet transformation and Husimi distribution function to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that the entangled Husimi distribution function of a two-mode quantum state |phi> is just the modulus square of the complex wavelet transform of exp{-(|eta|^2)/2} with phi(eta)being the mother wavelet up to a Gaussian function.Comment: 7 page

Effects of solute content on grain refinement in an isothermal melt

This is the port-print version of the article. The official published version can be obtained from the link below - Copyright @ 2011 Acta Materialia Inc. Published by Elsevier LtdIt is well accepted in the literature that for effective grain refinement some solute is required in the melt to restrict the growth of the solid even if potent nucleating particles with a favourable physical nature are present. In this paper we investigate the effect of the solute on grain initiation in an isothermal melt, and an analytical model is developed to account for the effect of solute elements on grain size. This study revealed that the solute elements in the liquid ahead of the growing crystals reduce the growth velocity of the nucleated crystals and increase the maximum undercooling achievable before recalescence. This allows more particles to be active in nucleation and, consequently, increases the number density of active particles, giving rise to a finer grain size. The analytical model shows that the final grain size can be related to the maximum undercooling, average growth velocity and solid fraction at the moment of recalescence. Further analysis using the free growth model and experimental data in the literature revealed that for a given alloy system solidified under similar conditions the grain size can be empirically related to 1/Q (Q is the growth restriction factor) to a power of 1/3, which is considerably different from the empirical linear relationship in the literature. It is demonstrated that the 1/3 power law can describe the experimental data more accurately than a linear relationship.The EPSRC is gratefully acknowledged for providing financial support under Grant EP/H026177/1

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.Comment: 6 pages, 2 figure

Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment

We study the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissonian statistics increasing as m increases. Then we derive the explicit analytical expression of time evolution of WF of m-PASV in the thermal channel and discuss the loss of nonclassicality using the negativity of WF. The threshold value of decay time is presented for the single PASV.Comment: 14 pages and 7 figure

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur