Magnetostriction and anisotropy of CoxFe3xO4 (x≤0.1) single crystals

Using the strain gauge technique, the magnetostriction constants λ_[100] and λ_[111] have been measured on single crystals of Co_xFe_3-xO₄ with compositions 0.0005≤x≤0.1 in the temperature range between 100 and 300 K and using magnetic fields up to 23 kOe. The presence of Co²⁺-ions gives rise to a very large negative value of λ_[100] and a fairly large positive value of λ_[111]. A linear relationship is found between the magnetostriction constants and the cobalt concentration.Some conclusions about the anisotropic beheviour of the samples can be made, based on the magnetostriction measurements. The change of the direction of easy magnetization from [111] to [100] in the temperature range just above the Verwey transition, is illustrated and discussed. It turned out to be possible to determine an effective anisotropy constant K'₁ through a curve fitting procedure. It is found that 1n K'₁ varies linearly with T.     

Investigation of isotopic shift in the 4d' subconfiguration of neon using doppler-free two-photon spectroscopy

We have measured the same isotopic shift ²⁰Ne²²Ne for all the two-photon transitions between the 3s[$\text{3}\text{2}$]2 level and the 4d' levels except for the transition reaching the 4d'[$\text{3}\text{2}$]1 level. We explain this difference using specific-mass shift theory.     

Wave-function transformations by general SU(1, 1) single-mode squeezing and analogy to Fresnel transformations in wave optics

Following Dirac’s assertion: “… for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”, we find that the general SU(1, 1) single-mode squeezing operator F just corresponds to the generalized Fresnel transform (GFT) in wave optics. We derive the normal product form and canonical coherent state representation of F, whose matrix element in the coordinate representation is just the GFT. It is shown that F is a faithful representation of symplectic group which indicates that two successive GFTs is still a GFT. Applications of F in some other optical transforms, such as the Fresnel-wavelet transform, are presented.     

Laser spectroscopy of the A[16.4]8.5-X7.5, A[16.4]8.5-Y[0.15]8.5, and A[16.4]8.5-Z[0.85]7.5 transitions of dysprosium monochloride

Laser-induced fluorescence spectra have been obtained at low resolution using a laser ablation source and pulsed dye laser, and at high resolution using a Broida oven and cw ring dye laser. Dispersed fluorescence spectra from two different excited states, A[16.4]8.5 and B[15.4]Ω (unknown Ω) (the states are labelled [10⁻³T₀]Ω according to their energy and Ω assignment) showed transitions to the same four low lying electronic states, X7.5, Y[0.15]8.5, Z[0.85]7.5, and an unassigned state at 970 cm⁻¹. High resolution excitation spectra of the A-X 0-0, A-Y 0-0 and 0-1, and A-Z 0-0 and 0-1 transitions were obtained and a global fit to all the data yielded rotational constants for both ¹⁶²Dy³⁵Cl and ¹⁶⁴Dy³⁵Cl. From the band origins, vibrational frequencies of 291 and 284 cm⁻¹ were obtained for the Y[0.15]8.5 and Z[0.85]7.5 states, respectively, suggesting that these two states originate from the Dy⁺(4f¹⁰6s)Cl⁻ configuration. The ¹⁶²Dy-¹⁶⁴Dy and ³⁵Cl-³⁷Cl isotope effects were studied and both indicated a ground state, X7.5, vibrational frequency of ∼230 cm⁻¹ which was reinforced by the observation, in dispersed fluorescence from the B[15.4] state, of a weak transition to a state 233 cm⁻¹ above the ground state. The observed electronic states and their configurational origin are discussed in terms of ligand field theory predictions.     

A Remark on Pople's Induced Current Theory

A very widely known and widely used ^[1] expression to calculate a nuclear magnetic shielding constant by combining the effect of diamagnetic and paramagnetic atomic currents on each atom was given by Pople. ^[2,3] In the present article, we will present a remark on a restriction to the applicablity of Pople's induced current theory. ^[2,3] To simplify the discussion, we will deal with a simple hydride MH, in which paramagnetic circulation can occur only in the atom M. The rectangular coordinates x, y and z are taken as Fig. 1.     

Prony's method applied to estimate noise source locations and their sound powers

An application of Prony's method for evaluating the acoustic power and location of sound sources from spatially sampled data is described. A sound source considered as a point source has an intensity proportional to the inverse square of the distance between source and observation point. The Fourier transform of this intensity function is an exponential function with a real exponent. The shift property of the Fourier transform results in a spectral change in the phase angle, which is expressed in the transform domain by a multiplicative exponential function of pure imaginary exponent. In this paper the usual time axis of the Fourier pair of time and frequency is treated as a variable denoting the location of the sound source. Accordingly, each spectral component of spatially sampled sound intensity generated by n point sources can be expressed as a linear combination of n complex exponentials. By applying Prony's method to the spectral data, these unknown exponents can be calculated numerically. This paper deals with an estimation procedure to find the location and power of a noise source. The estimation is done by minimizing the sum of the squares of the errors between the model and measured data. The proposed method has general applicability to problems where the so-called inverse square law for intensity can be assumed to be valid.     

Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations

We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.     

Geometric Quantization, Parallel Transport and the Fourier Transform

In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle over the space of compatible complex structures on a symplectic vector space. This bundle is equipped with a projectively flat connection. We show that parallel transport along a geodesic in the bundle is a rescaled orthogonal projection or Bogoliubov transformation. We then construct the kernel for the integral parallel transport operator. Finally, by extending geodesics to the boundary (for which the metaplectic correction is essential), we obtain the Segal-Bargmann and Fourier transforms as parallel transport in suitable limits.     

Nonlinear science abstracts

The class of exactly integrable non-linear evolution equations (NLEE) related to the general first order n × n linear problem is studied. The set of independent scattering data $\text{J}$ is determined and trace identities are obtained. Next we use a special integro-differential operator Λ and obtain the expansions of the potential and its variation in the eigenfunctions of Λ. These enable us to consider the inverse scattering method as a generalized Fourier transform and to write down in a compact form the integrals of motion. We prove that there exist a hierarchy of Hamiltonian structures generated by Λ. At the end we calculate the symplectic form in terms of the scattering data variations.     

Three-body forces in the lattice dynamics of some hcp metals

The consideration of paired interionic forces cannot explain the lattice dynamics of Be, Tb and Ho. In the present work, a phenomenological force constant model has been developed which considers three-body forces in addition to the usual forces of paired character. This approach explains the correct ordering of dispersion branches and the experimental degeneracy of the K-point in Be, Tb and Ho. Further good agreement is found between the theoretical curves and the neutron data of three high symmetry directions $\text{[0001], [01}\text{1}\text{0] and [11}\text{2}\text{0]}$ for all the three hcp metals.     

Fourier transform spectrometer remote sensing of O2 A-band electric quadrupole transitions

We observed electric quadrupole transitions in the O₂ A-band, b¹Σ_g⁺←X³Σ_g^?(0,0), in high solar zenith angle atmospheric spectra recorded with the high-resolution solar-viewing Fourier transform spectrometer at Park Falls, WI. We identified 12 ΔN=±3 transitions for the first time, including the first detection of ^NO-branch transitions and extended the ^TS-branch observations of Brault [J Mol Spectrosc 1980;80:384–8] up to N″=23. Additionally, we observed six electric quadrupole transitions of the ΔN=?1 ^PO-branch. These observations demonstrate the excellent sensitivity and long-term stability of the new generation of solar-viewing Fourier transform spectrometers.     

Critical principal connections and gauge-invariance

Let p:P→X be a principal G-bundle over an oriented manifold. As suggested by the classical Yang-Mills field theory, a certain class of variational problems for connections on P is defined. Global equations are derived for the corresponding critical connections and for the Jacobi fields along a critical connection, which are a very adequate tool for the study of the symplectic theory associated with the said variational problems.     

Rovibrational laser control targeting a dark state in acetylene. Simulation in the Ns = 1, Nr = 5 polyad

Optimal control theory in the Liouville space is used to perform rovibrational control by means of a laser pulse in a polyad of acetylene in order to populate a dark vibrational state. The initial mixed state is a truncated Boltzmann distribution of rotational levels from J=27 to J=31 of the ground vibrational state. The target state is a rotational equidistribution of levels ranging from J=28 to J=32 of the first excited vibrational dark state including quanta of energy in each bending modes, with positive vibrational angular momenta. The simulation is performed by using a manifold of eigenstates of a full-dimensional Hamiltonian calibrated by high precision spectroscopy known as the global acetylene Hamiltonian [B. Amyay et al., J. Chem. Phys. 131, 114301 (2009)]. The control is successful as an Uhlmann's fidelity of 0.98 is reached.     

A study of fermions coupled to gauge and gravitational fields on a cylinder

Fermions on a cylinder coupled to background gravitation and gauge fields are examined by studying the geometric action associated with the symmetries of such a system. We are able to show that the gauge coupling constant is constrained to a value of 1/N where N is an integer. Furthermore, in direct analogy with a Yang-Mills theory a new gravitational theory is introduced which couples to the fermions by promoting the coadjoint vector of the diffeomorphism sector to a dynamical variable. The classical dynamics of this theory are examined by displaying its symplectic structure and showing that it is equivalent to a one-dimensional system.     

Complex extension of the representation of the symplectic group associated with the canonical commutation relations

The aim of the investigation is to extend the representation of the real symplectic group associated with the canonical commutation relations into the complex symplectic group. It is shown that an extension exists to a semigroup S such that Sp(2n, R) ? S ? Sp(2n, C). The construction of the extension is achieved by extensive use of Bargmann's reproducing kernel space. We are able to give a simple geometric model for the semigroup S: it is exactly the semigroup of all complex symplectic transformations which increase the U(n, n) “length”.     

Symplectic capacities and the geometry of uncertainty: The irruption of symplectic topology in classical and quantum mechanics

This paper aims at conducting an analysis of various uncertainty principles from a topological point of view where the notion of symplectic capacity plays a key role. The existence of symplectic capacities follows from a deep theorem of symplectic topology, Gromov’s non-squeezing theorem, which was discovered in the mid 1980’s, and which has led to numerous developments whose applications to Physics are not fully understood or exploited at the time of writing. We will show that the notion of symplectic non-squeezing contains, as a watermark, not only the Robertson–Schrödinger uncertainty relations (and a classical version thereof), but also Hardy’s uncertainty principle for a function and its Fourier transform. This observation will allow us to formulate the characterization of positivity for density matrices in a topological way. We also address some open questions and conjectures, whose solution cannot be given at the present time due to the lack of a sufficiently developed mathematical theory.     

Time constants of radiative transitions from the 5<Emphasis Type="Italic">d</Emphasis>[3/2]<Subscript>1</Subscript> level of a xenon atom

Integral yields of spontaneous emission at wavelengths of 1.73, 2.03, and 2.65 μm have been measured upon excitation of pure xenon by a pulsed electron beam. These yields have been analyzed and experimental data have been obtained on time constants of radiative transitions 5d[3/2]₁ → 6p[5/2]₂, 5d[3/2]₁ → 6p[3/2]₁, and 5d[3/2]₁ → 6p[1/2]₀ of XeI, which appeared to be equal to (2300 ± 400) × 10^?9, (300 ± 40) × 10^?9, and (1300 ± 200) × 10^?9 s, respectively. It is shown that the experimental data are in a qualitative agreement with the results of computational and theoretical investigations. The results of averaging the experimental and calculated data are proposed for use as recommended values of the corresponding constants.     

Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

The Ising model is considered on a simple cubic lattice, with a coupling constant J along one axis and coupling constants J’ along the remaining two axes. The transfer-matrix technique and an extended phenomenological renormalization group theory [18, 19] are applied to obtain two-sided bounds on the critical temperature for the model with J′/J≤1. The bounds monotonically converge with decreasing J′/J and provide improved estimates for the phase-transition temperature in anisotropic three-dimensional Ising model, as compared with those available from the literature.     

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.