Constante de structure fine | EPFL Graph Search

La est la associée à l'interaction électromagnétique. Elle est sans dimension et son interprétation reste un défi pour la physique moderne. La constante est ainsi désignée pour des raisons historiques par référence à la structure fine. Le physicien allemand Arnold Sommerfeld (-) l'a proposée en . Son symbole conventionnel est \alpha. Son expression est : :\alpha = \frac{e^2}{4 \pi \varepsilon_0 \hbar c} où : :e est la charge élémentaire, :\hbar = \frac{h}{2 \pi} est la constante de Planck réduite, :c est la célérité de la lumière dans le vide, :\varepsilon_0 est la permittivité du vide. Sa valeur recommandée par le Comité de données pour la science et la technologie, ajustée en , est : :\alpha = 7{,}297,352,566,4(17) \times 10^{-3}. Définitions La est la , sans dimension, associée à l'interaction électromagnétique

Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive delta-impurities symmetrically situated around the origin

Fabio Rinaldi

In this presentation, we wish to provide an overview of the spectral features for the self-adjoint Hamiltonian of the three-dimensional isotropic harmonic oscillator perturbed by either a single attractive delta-interaction centered at the origin or by a pair of identical attractive delta-interactions symmetrically situated with respect to the origin. Given that such Hamiltonians represent the mathematical model for quantum dots with sharply localized impurities, we cannot help having the renowned article by Bruning, Geyler and Lobanov [1] as our key reference. We shall also compare the spectral features of the aforementioned three-dimensional models with those of the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive delta'-interaction in one dimension, fully investigated in [2, 3], given the existence in both models of the remarkable spectral phenomenon called "level crossing". The rigorous definition of the self-adjoint Hamiltonian for the singular double well model will be provided through the explicit formula for its resolvent (Green's function). Furthermore, by studying in detail the equation determining the ground state energy for the double well model, it will be shown that the concept of "positional disorder", introduced in [1] in the case of a quantum dot with a single delta-impurity, can also be extended to the model with the twin impurities in the sense that the greater the distance between the two impurities is, the less localized the ground state will be. Another noteworthy spectral phenomenon will also be determined; for each value of the distance between the two centers below a certain threshold value, there exists a range of values of the strength of the twin point interactions for which the first excited symmetric bound state is more tightly bound than the lowest antisymmetric bound state. Furthermore, it will be shown that, as the distance between the two impurities shrinks to zero, the 3D-Hamiltonian with the singular double well (requiring renormalization to be defined) does not converge to the one with a single delta-interaction centered at the origin having twice the strength, in contrast to its one-dimensional analog for which no renormalization is required. It is worth stressing that this phenomenon has also been recently observed in the case of another model requiring the renormalization of the coupling constant, namely the one-dimensional Salpeter Hamiltonian perturbed by two twin attractive delta-interactions symmetrically situated at the same distance from the origin.

St Petersburg Natl Research Univ Information Technologies, Mech & Optics2016

Multifrequency ESR in ET2 MnCu[N(CN)(2)](4): A radical cation salt with quasi-two-dimensional magnetic layers in a three-dimensional polymeric structure

László Forró, Bálint Náfrádi, Krisztina Nagy

The radical cation salt, ET2MnCuN(CN)(2), [ET=bis(ethylenedithio)tetrathiafulvalene] with an unusual three-dimensional anionic polymeric network is studied by x-ray diffraction, static susceptibility measurements, and electron spin resonance (ESR) at frequencies between 9 and 420 GHz. The magnetic properties are determined by the alternating two-dimensional layers of the Mn2+ ions of the network and the partially charged ET molecules. At ambient temperature the overlap between Mn2+ ions and ET molecules is weak and an exchange integral vertical bar J(Mn-ET)vertical bar approximate to 4.10(-2) K is estimated from their resolved ESR lines. At lower temperatures, ET2MnCuN(CN)(2) is not a simple system of weakly interacting paramagnetic ions in spite of the isotropic, Curie-like static susceptibility. There are first-order phase transitions at 292 K and in the range of 120-180 K. One of the lattice constants shows anomalous temperature dependence below 292 K. Anisotropic ESR shifts appear below 150 K, which we explain by demagnetizing fields of the platelike crystals and an exchange-narrowed fine structure. The latter contributes significantly to the shift when the populations of Zeeman levels are altered in high magnetic fields at low temperatures. We estimated the exchange coupling between Mn2+ ions within a layer, J(Mn-Mn)approximate to-48 K and determined the fine structure parameters below 150 K, showing a distortion in the plane of the Mn2+ ions.

2009

Spectral properties of a symmetric three-dimensional quantum dot with a pair of identical attractive delta-impurities symmetrically situated around the origin

Fabio Rinaldi

St Petersburg Natl Research Univ Information Technologies, Mech & Optics2016