Search results for "solution"

New approach to describe two coupled spins in a variable magnetic field

2021

We propose a method to describe the evolution of two spins coupled by hyperfine i nteraction in an external time- dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved exactly in a constant, appropriately oriented magnetic field. In order to t reat t he n onstationary d ynamical p roblem, we modify the time-dependent Schrödinger equation through a change of representation that, by exploiting an instantaneous (adiabatic) basis makes the time-dependent Hamiltonian diagonal at any time instant. The solution of the transformed time-dependent Schrödinger FRVBUJPO in the form of chronologically ordered exponents with transpar…

The rotational spectrum of trans-DCOOD: Lamb-dip measurements, THz spectroscopy and quantum-chemical calculations

2011

Abstract The rotational spectrum of the bi-deuterated isotopologue of trans-formic acid, trans-DCOOD, was recorded at sub-Doppler resolution in the millimeter- and sub-millimeter-wave region using the Lamb-dip technique. The hyperfine structure due to the deuterium nuclei could be resolved and accurate hyperfine constants were derived. The experimental determination of the deuterium quadrupole-coupling constants was supported by high-level quantum-chemical calculations at the coupled-cluster level using large atomic-orbital basis sets. The Lamb-dip measurements were also supplemented by THz Doppler-limited measurements in order to extend the predictive capability of the available spectrosco…

Quantum chemical calculations of KTN solid solutions

1998

Abstract The results of semi-empirical calculations for perovskite KNbxTa1−xO3 (KTN) solid solutions are presented for x = 0.04, 0.11, 0.89, and 0.96. Quantum chemical method of the Intermediate Neglect of the Differential Overlap (INDO) was combined with 135- and 320-atom supercells. Analysis of the optimised atomic and electronic structure has clearly demonstrated that several nearest Nb atoms substituting for Ta in KTaO3 — unlike Ta impurities in KNbO3 — reveal the self-ordering effect, which probably triggers the ferroelectricity observed in KTN.

Evolution of the $B$-Meson Light-Cone Distribution Amplitude in Laplace Space

2020

The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in $\Lambda_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tilde\phi_+(\eta)$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay $B^-\to\gamma\ell^-\bar\nu$ in terms of $\tilde\phi_+(\eta)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tilde\phi_+(\eta)$ in ter…

Hydrogen CARS thermometry in H2-N2 mixtures at high pressure and medium temperatures: influence of linewidths models

2000

International audience; In order to improve the accuracy of H2 CARS thermometry, H2 Q-branch CARS spectra have been recorded for various H2-N2 mixtures in a high-pressure cell at different pressures and temperatures (up to 40 bar and 875 K). Due to the low spectral resolution of broadband CARS experiments, the relevant spectral lineshape factor is the linewidth ratio G(Q(3))/G(Q(1)), since Q(1) and Q(3) are the most intense lines of the Q-branch spectrum in this temperature range. For the first time, the speed-inhomogeneous effects are accounted for in the simulation of the CARS profiles. The evaluated temperatures are in good agreement with reference values obtained by thermocouples. The s…

Dynamics of Phase Transition in 0.4NBT-0.4ST-0.2PT Solid Solution

2012

In this paper we present dielectric spectroscopy results of NBT-(0.6-x)ST-xPT with x = 0.2 solid solution. Dielectric investigations clearly showed a relaxor—normal ferroelectric phase transition at TPT = 419 K and low temperature and low frequency dispersion similar to coexistence of dipolar glass and ferroelectric phase. The mean relaxation time above the phase transition follows Vogel—Fulcher law with following parameters: E A = 0.179 eV, τ 0 = 3.39·10−14 s, T VF = 223 K.

On the existence of exotic and non-exotic multiquark meson states

2007

To obtain an exact solution of a four-body system containing two quarks and two antiquarks interacting through two-body terms is a cumbersome task that has been tackled with more or less success during the last decades. We present an exact method for the study of four-quark systems based on the hyperspherical harmonics formalism that allows us to solve it without resorting to further approximations, like for instance the existence of diquark components. We apply it to systems containing two heavy and two light quarks using different quark-quark potentials. While $QQ\bar n \bar n$ states may be stable in nature, the stability of $Q\bar Qn \bar n$ states would imply the existence of quark cor…

Mathematical models on the way from superstring to photon

2002

Aza–oxa macrocyclic ligands functionalised with naphthylmethyl fluorescent groups

2000

Abstract Compounds L 1 and L 2 were obtained by reaction of 2-(bromomethyl)naphthalene with 1,4,10-trioxa-7,13-diazacyclopentadecane and 1,4,7-trioxa-10-azacyclododecane, respectively. These receptors contain aza–oxa crowns attached covalently to fluorescent groups. The protonation and coordination behaviour of L 1 and L 2 against metal ions has been studied in dioxane:water (70:30 v/v, 25°C, 0.1 M potassium nitrate) using potentiometric methods. All metal ions studied form complexes with L 1 and L 2 with the logarithm of the formation constants L+M 2+ =[M(L)] 2+ in the sequence Cd 2+ ≅Pb 2+ , Zn 2+ 2+ for L 1 and Zn 2+ 2+ 2+ 2+ 2+ for L 2 . The fluorescent behaviour of L 1 and L 2 was stud…

Thermodynamic predictions of the formation of chalcogenide glasses

1985

The understanding of glass forming ability requires quantitative information on the stable and metastable phase equilibria of binary and multicomponent systems, particularly as a function of composition and temperature. This paper discusses the success of the use of Gibbs free energy curves for the supercooled liquid relative to the stable crystalline phases to describe glass forming ability. Applications are reported for the systems GeSe2-Se, Sb2Se3-Se and GeSe2-Sb2Se3 for which experimental minimal quenching rates are available. A strongly associated regular solution model for the liquid phase gives a predicted behaviour consistent with experimental data. The method is intended to apply t…