s-Parameterized photocount formula

Employing the s-ordered operator expansion formula and the technique of integration within s-ordered product of operators, we derive a new photocount formula for general parameter s, which can unify the two quantum-mechanical photocount formulas in Opt. Lett. 33, 433 (2008). It brings convenience to photocount’s calculation when system’s density operator is known. The s-parameterized photocount formula for pure number state density operator is firstly derived.     

On the <Emphasis Type="Italic">s</Emphasis>-parameterized Quantization Scheme for Dirac’s Representation theory

Dirac is the founder of quantum mechanical representation theory. By virtue of the technique of integration within an ordered product (IWOP) of operators we introduce s-parameterized form of quantum mechanical coordinate and momentum representations, which are complete. We then point out that s-parameterized representation’s completeness relation is accompanied with operators’ s-ordering, the special cases s=1,0,−1 correspond to normal-ordering, Weyl ordering and antinormal-ordering, respectively. The s-parameterized form of the coherent state representation and the entangled state representation are also derived. In our view, the operators’ s-ordering should be traced back to s-parameterized form of the completeness relation of quantum mechanical coordinate and momentum representations, which is more fundamental. Many operator identities can be derived by virtue of the above mentioned s-parameterized representation’s completeness relations.     

Linear amplifier via the displaced Fock states superposition

The linear amplifier with the superposition of displaced Fock states (DFS’s) as an input field is discussed. The s-parameterized characteristic function (CF) of linear amplifier for the superposition of two DFS’s is considered. Several quantum statistical expectation values for the output of linear amplifier are evaluated once the time dependent CF has been computed. The Glauber secondorder coherence function is calculated. The squeezing properties of the output field are studied. The s-ordered quasiprobability distribution function (QDF) for the output of linear amplifier driven by DFS’s superposition is investigated. The phase properties of the superposition of DFS’s are studied. The s-parameterized phase distribution, obtained by integrating the s-parameterized QDF over radial variable is illustrated.     

A generalized Weyl—Wigner quantization scheme unifying P-Q and Q-P ordering and Weyl ordering of operators

By extending the usual Wigner operator to the s-parameterized one as 1/4π2 integral (dyduexp [iu(q-Q)+iy(p-P)+is/2yu]) from n=- ∞ to ∞ with s beng a,real parameter,we propose a generalized Weyl quantization scheme which accompanies a new generalized s-parameterized ordering rule.This rule recovers P-Q ordering,Q-P ordering,and Weyl ordering of operators in s = 1,1,0 respectively.Hence it differs from the Cahill-Glaubers’ ordering rule which unifies normal ordering,antinormal ordering,and Weyl ordering.We also show that in this scheme the s-parameter plays the role of correlation between two quadratures Q and P.The formula that can rearrange a given operator into its new s-parameterized ordering is presented.     

Two quantum-mechanical photocount formulas

We derive two quantum-mechanical photocount formulas when a light field's density operator rho is known; one involves rho's coherent state mean value and the other involves rho's Wigner function; when this information is known, then using these two formulas to calculate the photocount would be convenient. We employ the technique of integration within an antinormally ordered (or Weyl-ordered) product of operators in our derivation.     

Photon Modulated Coherent States of a Generalized Isotonic Oscillator by Weyl Ordering and their Non-Classical Properties

We construct photon modulated coherent states of a generalized isotonic oscillator by expanding the newly introduced superposed operator through Weyl ordering method. We evaluate the parameter A ₃ and the s-parameterized quasi probability distribution function to confirm the non - classical nature of the states. We also calculate the identities related with the quadrature squeezing to explore the squeezing property of the states. Finally, we investigate the fidelity between the photon modulated coherent states and coherent states to quantify the non-Gaussianity of the states. The constructed states and their associated non - classical properties will add further knowledge on the potential.     

Newton-Leibniz integration for ket-bra operators (II)—application in deriving density operator and generalized partition function formula

Via the route of applying Newton-Leibniz integration rule to Dirac’s symbolic operators, we show that the density operator e^−βH, where H is multi-mode quadratic interacting boson operators, is a mapping of symplectic transformation in the coherent state representation appearing in the form of non-symmetric ket-bra operator integration. By virtue of the technique of integration within an ordered product (IWOP) of operators, we deduce its normally ordered form which directly leads to the generalized partition function formula and the Wigner function. Some new representations, such as displacement-squeezing correlated squeezed coherent states, constructed by the IWOP technique, also bring convenience in deriving partition functions.     

Thermo Vacuum State for Describing the Density Operator of Photon-subtracted Squeezed Chaotic Light

For the density operator describing s?photon-subtracted squeezed chaotic light (PSSCL) we search for its thermo vacuum state (a pure state) in the real-fictitious space. We find that it reduces to a thermo vacuum state of squeezed chaotic light when s = 0, and to a thermo vacuum state of the optical negative binomial field when no squeezing. The new thermo vacuum state simplifies calculating photon number average, quantum fluctuation and Mandel’s Q parameter of PSSCL. Using the method of integration within ordered product (IWOP) of operators we also derive the normalization coefficient and explicitly analytical expressions of Wigner function for PSSCL.     

Quantum-state tomogram from <Emphasis Type="Italic">s</Emphasis>-parameterized quasidistributions

We find an integral transform realizing the connection between the s-parameterized quasidistributions of a quantum state and its corresponding tomogram, which looks like a Radon transform. We show that the kernel of the new Radon transform is a Gaussian function with s-parameterized dispersion. It can be considered as a broadened delta-function appeared in the standard Radon transform.     

Effect of annealing on the magnetic and superconducting properties of single-crystalline UCoGe

Single-crystals of the new ferromagnetic superconductor UCoGe have been grown. The quality of as-grown samples can be significantly improved by a heat-treatment procedure, which increases the residual resistance ratio (RRR) from ∼5 to ∼30. Magnetization M(T) and resistivity ρ(T) measurements show the annealed samples have a sharp ferromagnetic transition with a Curie temperature T_C is 2.8 K. The ordered moment of 0.06 μ_B is directed along the orthorhombic c-axis. Superconductivity is found below a resistive transition temperature T_s=0.65 K.     

Measuring the dimension of partially embedded networks

Scaling phenomena have been intensively studied during the past decade in the context of complex networks. As part of these works, recently novel methods have appeared to measure the dimension of abstract and spatially embedded networks. In this paper we propose a new dimension measurement method for networks, which does not require global knowledge on the embedding of the nodes, instead it exploits link-wise information (link lengths, link delays or other physical quantities). Our method can be regarded as a generalization of the spectral dimension, that grasps the network’s large-scale structure through local observations made by a random walker while traversing the links. We apply the presented method to synthetic and real-world networks, including road maps, the Internet infrastructure and the Gowalla geosocial network. We analyze the theoretically and empirically designated case when the length distribution of the links has the form P(ρ)∼1/ρ$P\left(\rho \right)\sim 1/\rho$. We show that while previous dimension concepts are not applicable in this case, the new dimension measure still exhibits scaling with two distinct scaling regimes. Our observations suggest that the link length distribution is not sufficient in itself to entirely control the dimensionality of complex networks, and we show that the proposed measure provides information that complements other known measures.     

Bivariate distributions in statistical spectroscopy studies: Fixed-J level densities,fixed-J averages and spin cut-off factors

Analytical studies with the TBRE ensemble, supplemented by numerical calculations with realistic interactions show that for large particle numbers, the bivariate cumulants (k _rs ) defined for the Hamiltonian operator (H) and theJ _z operator, are very small; ∥k _rs ∥?0.3 for 3≦r+s≦6. As a result the expansions around a bivariate normal density are meaningful for the fixed-M densities (ρ(E,M)). We adopt a bivariate Edgeworth expansion forρ(E,M) and give a compact form for the same. Finally using thisρ(E,M) (which also define fixed-J densities uniquely), new series expansions are given for fixed-M (and hence for fixed-J) averages of the powers ofH and also for the spin cut-off factors.     

Different representations of R-function and parameterized quantization scheme

Three different representations of R-function distribution are deduced for a given density operator of light field in terms of Q-function, Wigner function and positive P-representation, respectively. Furthermore, the τ-parameterized quantization scheme is proposed, where the P-representation, Weyl correspondence, and Q-function are as its special cases. As applications, the photon-count distribution from R-function and the nonclassical depth of photon-added coherent state are examined.     

Behaviour of hartree-fock and hartree-fock-slater (Xα) atomic form factors and electron momentum distributions for two-, three- and four-electron ions

The atomic form factor and the radial electron density in momentum space, from the solutions of the α-parameterized Hartree-Fock-Slater (Xα) equations, are studied within the framework ofZ ^?1 expansion theory for the two-, three- and four-electron ions in their ground state configurations (1s ²), (1s 1s′ 2s), and (1s ² 2s ²), and compared with the corresponding Hartree-Fock quantities.     

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

The evolution with β of the distributions of the spacing ‘s’ between nearest-neighbour levels of unfolded spectra of random matrices from the β-Hermite ensemble (β-HE) is investigated by Monte Carlo simulations. The random matrices from the β-HE are real symmetric and tridiagonal where β, which can take any positive value, is the reciprocal of the temperature in the classical electrostatic interpretation of eigenvalues. The distribution of eigenvalues coincide with those of the three classical Gaussian ensembles for β=1, 2, 4. The use of the β-HE ensemble results in an incomparable speed up and efficiency of numerical simulations of all spectral characteristics of large random matrices. Generalized gamma distributions are shown to be excellent approximations of the nearest-neighbor spacing (NNS) distributions for any β while being still simple. They account both for the level repulsion in ∼s^β when s→0 and for the whole shape of the NNS distributions in the range of ‘s’ which is accessible to experiment or to most numerical simulations. The exact NNS distribution of the GOE (β=1) is in particular significantly better described by a generalized gamma distribution than it is by the Wigner surmise while the best generalized gamma approximation coincides essentially with the Wigner surmise for β>∼2. They describe too the evolution of the level repulsion between that of a Poisson distribution and that of a GOE distribution when β increases from 0 to 1. The distribution of ln (s), related to the electrostatic interaction energy between neighbouring charges, is accordingly well approximated by a generalized Gumbel distribution for any β?0. The distributions of the minimum NN spacing between eigenvalues of matrices from the β-HE, obtained both from as-calculated eigenvalues and from unfolded eigenvalues are Brody distributions which are classically used to characterize the spectral fluctuations of various physical systems.     

Duality-mediated critical amplitude ratios for the (2 + 1)-dimensional S = 1XY model

The phase transition for the (2 + 1)-dimensional spin-S = 1XY model was investigated numerically. Because of the boson-vortex duality, the spin stiffness ρ _s in the ordered phase and the vortex-condensate stiffness ρ _v in the disordered phase should have a close relationship. We employed the exact diagonalization method, which yields the excitation gap directly. As a result, we estimate the amplitude ratios ρ _s,v /Δ (Δ: Mott insulator gap) by means of the scaling analyses for the finite-size cluster with N ≤ 22 spins. The ratio ρ _s /ρ _v admits a quantitative measure of deviation from selfduality.     

Influences of overtaking on two-lane traffic with signals

Based on the cellular automata method (CA method), two-lane traffic flow with the consideration of overtaking is investigated. Discrete equations are proposed to describe the traffic dynamics by using the rules of CA model. Influences of signal cycle time (t_s) and vehicular density (ρ) on the mean velocity 〈v〉 and mean overtaking times 〈c〉 of the traffic flow are discussed. The effects of slow vehicles and road barricades on the traffic flow are also studied. Simulation results shows that the vehicular density and the signal cycle time have significant influences on the traffic flow. The mean velocity of the traffic flow could keep a comparatively large value when ρ≤0.45. For a certain value of ρ, 〈v〉 displays a serrated fluctuation with t_s. Therefore, there may exist a certain combination of ρ and t_s which optimizes the traffic flow efficiency. As compared with the results in Nagatani (2009) [7], the model proposed here and the simulation results which took into account the effects of signal cycle time, slow vehicles, and road barricades on the traffic flow with overtaking allowed, can reflect the situation of traffic flow in a more realistic way.     

Statistical properties of the output of linear amplifier with superpositions of squeezed displaced Fock states as an input state

The s-parameterized characteristic function for the output field with the superposition of squeezed displaced Fock states (SDFS's) as input field is given. The s-ordered distribution functions for the output field with superposition of SDFS's as input state are investigated. Various moments are calculated by using the s-ordered characteristic function for that field. The Glauber second-order coherence function is calculated. The quadrature squeezing for the output field are discussed. Some Quasiprobability distribution functions of the output fields are plotted as functions of the interaction time. The quadrature squeezing for the output field are discussed. Received 30 September 1998     

ABCD rule for Gaussian beam propagation in the context of quantum optics derived by the IWOP technique

The development of technique of integration within an ordered product (IWOP) of operators extends the Newton-Leibniz integration rule, originally applying to permutable functions, to the non-commutative quantum mechanical operators composed of Dirac’s ket-bra, which enables us to obtain the images of directly mapping symplectic transformation in classical phase space parameterized by [A, B; C, D] into quantum mechanical operator through the coherent state representation, we call them the generalized Fresnel operators (GFO) since they correspond to Fresnel transforms in Fourier optics. Based on GFO we find the ABCD rule for Gaussian beam propagation in the context of quantum optics (both in one-mode and two-mode cases) whose classical correspondence is just the ABCD rule in matrix optics. The entangled state representation is used in discussing the two-mode case.