68,717 research outputs found

### 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

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