Hidden Measurements,Hidden Variables and the Volume Representation of Transition Probabilities

We construct, for any finite dimension n, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For n=2 our model is equivalent to the Aerts sphere model and serves as a generalization of it for dimensions n . 3 We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and their relationship with the results of Fine [J. Math. Phys. 23 1306 (1982)].     

On the physical impossibility of ideal quantum measurements

Albert and Loewer have argued in this journal [4] that modal interpretations of quantum mechanics are ruled out if the abstract structure of Hilbert space is taken realistically. Their argument contains a dubious inference from a measure-zero set of non-ideal interactions. I look at possible ways to make this inference valid and I conclude that the evidence against the modal interpretation cannot be found in the Hilbert space alone. Instead an analysis of specific cases is required.I want to thank the audience at the 1995 Florence IUHPS Conference, and Harvey Brown, Nancy Cartwright, Jim Cushing, Marco Del Seta, Arthur Fine, Margaret Morrison, Fred Müller and Pieter Vermaas for comments and suggestions.     

Symmetry of the pentacene molecule and classification of electron states studied in the frame of group action on a set

Pentacene have recently become the subject of intense studies due to their physical properties which follow from the states of their outer-shell electrons that are able to take part in molecule bonding. The symmetry of these molecules provides the classification of quantum states according to the group theory method. In this paper, we apply a molecular state-space factorization scheme for the classification of pentacene molecules based on the structure of their electron states.     

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

Background and objective

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0° to 40°, revealed the existence of an anomalous “pseudo-Rayleigh” mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n = 1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40° for various elastic and viscoelastic cylinder materials.

Method

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0° ? α < 90°. The “pure” resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

Results and conclusion

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka? 0.1 at a critical angle α_c bounded by the longitudinal and shear waves coupling angles θ_L=sin^-1(c/c_L) and θ_S=sin^-1(c/c_S) such that θ_L<α_c<θ_S (where c_L and c_S are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle θ_L<α_c<θ_S result from the excitation of the monopole (n = 0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 ?ka? 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle θ_R=sin^-1(c/c_R) (where c_R is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n = 1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder’s surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.     

施加电场的半抛物量子阱中束缚态的能级结构

采用位移谐振子与数值求解相结合的方法,研究和讨论了施加电场的半抛物量子阱中束缚态的能级结构,得到了体系的本征能量与本征函数的表达式．数值结果显示,随着电场强度的增大,束缚态的能量几乎线性地下降,电场对半抛物束缚势频率较低的系统以及系统的高能级的影响较大,相邻能级间隔也随着电场强度的增大而减小,这与施加电场的抛物量子阱中的情况明显不同．     

Application of the differential method to uniaxial gratings with an infinite number of refraction channels: Scalar case

The differential method (also called the C method) is applied to the diffraction of linearly polarized plane waves at a periodically corrugated boundary between vacuum and a linear, homogeneous, uniaxial, dielectric-magnetic medium characterized by hyperbolic dispersion equations. Numerical results for sinusoidal gratings are presented and compared with those obtained by means of the Rayleigh method, showing that both the differential method and the Rayleigh method can fail to give adequate results for gratings supporting an infinite number of refracted Floquet harmonics.     

Laser induced fluorescence of formaldehyde and Raman measurements of major species during partial catalytic oxidation of methane with large H2O and CO2 dilution at pressures up to 10 bar

The catalytic partial oxidation (CPO) of CH₄/O₂ mixtures diluted with large amounts of H₂O and CO₂ (up to 43% and 21% vol., respectively) was investigated experimentally and numerically in the pressure range 4 bar  p  10 bar. Experiments were carried out in an optically accessible channel-flow catalytic reactor coated with Rh/ZrO₂, and included planar laser induced fluorescence (LIF) of formaldehyde for the assessment of homogeneous (gas-phase) ignition and one-dimensional spontaneous Raman measurements of all major gas-phase species for the evaluation of the heterogeneous (catalytic) processes. Simulations were performed with a full elliptic model that included detailed heterogeneous and homogeneous chemical reaction schemes. Over the reactor length with negligible gas-phase chemistry contribution, the employed heterogeneous reaction scheme provided good agreement to the measured methane consumption and synthesis gas yields, overpredicting mildly the partial over the total oxidation route. It was shown that the added water provided a source of O(s) and OH(s) surface radicals that enhanced the methane conversion and H₂ yields and reduced the CO yields. Moreover, the addition of CO₂ had a negligible chemical effect on the aforementioned parameters. An increase in pressure from 4 to 10 bar had a minor impact on the methane conversion and hydrogen selectivity. The employed gaseous scheme reproduced the LIF-measured onset of homogeneous ignition, although it underpredicted the extent of the formaldehyde zone ahead of the flame and the flame propagation characteristics at the highest investigated pressure (10 bar).     

Quantum corrections to the thermodynamic properties of a two-dimensional fluid with hard-core potential

A simple theory, based on the physical interpretation of the reciprocal of activity, is developed to evaluate the thermodynamic properties of a two-dimensional fluid in the semi-classical limit. The theory is applied to calculate the quantum corrections to the equation of state and excess free energy of two-dimensional fluids, whose molecules interactvia hard-disc and square-well potential. It is found that the quantum effect increases with the increase of density and decrease of temperature.     

附加克尔介质Jaynes—Cummings模型场的位相特性

运用Pegg-Barnett厄米位相公式,研究了附加克尔(Kerr)介质Jaynes-Cummings(J-C)模型场的位相特性.具体讨论了场的位相概率分布、厄米位相算符的期待值以及位相的涨落,通过与标准J-C模型作比较,讨论了克尔介质与模场的非线性相互作用对场位相特性的影响.     

Optical mode characterization of single photons prepared by means of conditional measurements on a biphoton state

A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into a transform-limited classical optical mode is calculated and ways for its optimization are determined. An experimentally feasible technique of generating the optimally matching classical mode is proposed. The theory is applied to a recent experiment on pulsed homodyne tomography of the single-photon Fock state [A.I. Lvovsky et al., Phys. Rev. Lett. 87, 050402 (2001)]. Received 16 July 2001     

What Can the Quantum Liquid Say on the Brane Black Hole, the Entropy of an Extremal Black Hole, and the Vacuum Energy?

Using quantum liquids one can simulate the behavior of the quantum vacuum in the presence of the event horizon. The condensed matter analogs demonstrate that in most cases the quantum vacuum resists formation of the horizon, and even if the horizon is formed different types of the vacuum instability develop, which are faster than the process of Hawking radiation. Nevertheless, it is possible to create the horizon on the quantum-liquid analog of the brane, where the vacuum life-time is long enough to consider the horizon as the quasistationary object. Using this analogy we calculate the Bekenstein entropy of the near-extremal and extremal black holes, which comes from the fermionic microstates in the region of the horizon—the fermion zero modes. We also discuss how the cancellation of the large cosmological constant follows from the thermodynamics of the vacuum.     

也谈转动和振动的概率分布与能均分定理的证明

严格推导出分子转动角速度、振动位移概率分布,指明三种概率分布并不局限于近独立子系,它们适用于有相互作用的很多系统。     

再论端面受到空气阻力的弹性杆的振动

重新研究了端面受到空气阻力的弹性杆振动的分离变量法.建立了复本征函数的广义正交性.用复数形式的本征振动展开一般解.利用正交性求出了一般解中的系数以满足任意给定的初始条件.求解了多种边界条件下的振动,包括两端均受到空气阻力、一端有集中质量物体和弹性连接并受到空气阻力等情况.     

Algebra of Effects in the Formalism of Quantum Mechanics on Phase Space as an M. V. and a Heyting Effect Algebra

We prove that the algebra of effects in the phase space formalism of quantum mechanics forms an M. V. effect algebra and moreover a Heyting effect algebra. It contains no nontrivial projections. We equip this algebra with certain nontrivial projections by passing to the limit of the quantum expectation with respect to any density operator. PACS: Primary 02.10.Gd, 03.65.Bz, Secondary 002.20.Qs This paper was a submission to the Sixth International Quantum Structure Association Conference (QS6), which took place in Vienna, Austria, July 1–7, 2002.     

Influence of radiation fluctuations on the magnitude of optoelectronic signal in semiconductor lasers with external optical feedback

Numerical modeling of dynamical processes in semiconductor lasers with external delayed optical feedback has been performed on the basis of the rate equations taking into account the quantum fluctuations of radiative transition rates. It has been shown that the nature of the optoelectronic signal as a function of pump current is determined by the magnitude of the optoelectronic coupling and corresponds to the behavior of the autocorrelation function of the radiation. It has been found that the radiation coherence decreases substantially with strong optical feedback. Experimental measurements confirming the theoretical results have been performed. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 809–813, November–December, 2008.     

A method to evaluate the relative weights of structural and functional constraints on a genome

Summary A method that numerically evaluates the relative influence of structural or functional constraints on the codon composition of a gene is presented. The method applies to any constraint provided that it can be translated intoa priori probability table of codon usage. The method is very easy to apply to different constraints and to different pools of sequences. Theoretical codon usage obtained from a linear combination of the various constraints was compared with experimental codon frequencies of several classes of genes taxonomically homogeneous and, applying a minimization tecnique, the relative weights of the examined constraints have been evaluated. The results show that a common strategy exists for all coding sequences even though most of the constraints are represented by different probability tables for different pools of genes. We also demonstrate that the method is reliable when it is applied to a single gene, so that it can also be used as a tool to predict the characteristics of a gene from its sequence.     

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     

Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field

We investigate the phase decoherence effects on the entanglement of a two-qubit anisotropic Heisenberg model with a nonuniform magnetic field in the x–z-plane. As a measure of the entanglement, the concurrence of the system is calculated. It is shown that when the magnetic field is along the z-axis, the nonuniform and uniform components of the field have no influence on the entanglement for the cases of and , respectively. But when the magnetic field is not along the z-axis, both the uniform and the nonuniform components of the field will introduce the decoherence effects. It is found that the effects of the Heisenberg chain's anisotropy in the Z-direction on the entanglement are dependent on the direction of the field. Moreover, the larger the initial concurrence is, the higher value it will exhibit during the time evolution of the system for a proper set of the parameters ν, Δ, θ, γ , B and b.