FINITE INTEGRAL FORMULA INVOLVING ALEPH-FUNCTION AND GENERALIZED MITTAG-LEFFLER FUNCTION

The aim of this paper is to establish general definite integrals involving product of the Aleph function and the generalized Mittag-Leffler function with general arguments. This integral yields a number of known results as special cases. For the sake of illustration, several corollaries are also presented as special case of our main results

Communication of Spin Directions with Product States and Finite Measurements

Total spin eigenstates can be used to intrinsically encode a direction, which can later be decoded by means of a quantum measurement. We study the optimal strategy that can be adopted if, as is likely in practical applications, only product states of $N$-spins are available. We obtain the asymptotic behaviour of the average fidelity which provides a proof that the optimal states must be entangled. We also give a prescription for constructing finite measurements for general encoding eigenstates.Comment: 4 pages, minor changes, version to appear in PR

The Elliptic Billiard: Subtleties of Separability

Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem can be solved. A geometric picture is given revealing why levels of a separable system cross. It is shown that the repulsions found by Ayant and Arvieu are computational effects and that the method used by Traiber et al. is related to the present picture which explains the crossings they find. An asymptotic formula for the energy-levels is derived and it is found that the statistical quantities of the spectrum P(s) and \Delta(L) have the form expected for an integrable system.Comment: 10 pages, LaTeX, 3 Figures (postscript). Submitted to European Journal of Physic

Adiabatic description of nonspherical quantum dot models

Within the effective mass approximation an adiabatic description of spheroidal and dumbbell quantum dot models in the regime of strong dimensional quantization is presented using the expansion of the wave function in appropriate sets of single-parameter basis functions. The comparison is given and the peculiarities are considered for spectral and optical characteristics of the models with axially symmetric confining potentials depending on their geometric size making use of the total sets of exact and adiabatic quantum numbers in appropriate analytic approximations

Fonction de corrélation d'une variable quantique

Les théories des effets de relaxation dus au couplage spin-milieu dans les diverses techniques font apparaitre une analogie entre une fonction aléatoire stationnaire du temps et une variable quantique, quand on a affaire à un grand nombre de systèmes, formant un ensemble de Gibbs. Pour préciser cette analogie, on essaie de définir l'analogue d'une fonction de corrélation pour une variable quantique. On montre que cette fonction s'avère commode pour la résolution de certains problèmes d'élargissement de raies

L'élargissement par échange des raies R.P.E. des radicaux libres en solution

In a diffusional process, one replaces the time by a quantity, the so called fictitious time which is defined through an integral along the diffusing particle's path. The cloud of diffusing particles taken at the same fictitious time has a density satisfying a partial differential equation, which is applied to the theory of the exchange broadening in E.P.R. of free radicals (with hyperfine splitting) in solution, for the case where the exchange integral depends upon the distance between radical center (for instance, with an exponential law). There is a good agreement with experimental results in the case of tanone in methanol from — 30 °C to 90 °C. Another model admitting the formation of a short-lived dimer is also discussed.Dans un processus diffusionnel, on remplace le temps par une quantité définie au moyen d'une intégrale sur la trajectoire parcourue par le point migrant, le temps, fictif. Le nuage de points migrants pris au même instant fictif a une densité obéissant à une équation aux dérivées partielles, que l'on applique à la théorie de l'élargissement par échange des raies R.P.E. des radicaux libres azotés en solution, dans le cas où l'intégrale d'échange est fonction de la distance entre les centres des radicaux, par exemple, une fonction exponentielle. On a un bon accord avec l'expérience dans le cas du tanone dans le méthanol entre — 30° et + 90 °C. Un autre modèle, basé sur la possibilité de formation fugitive d'un biradical, est également traité