Moment cinétique (mécanique quantique)

Résumé

En mécanique quantique le moment cinétique est défini comme un opérateur vectoriel (noté \hat\vec J) à trois composantes, correspondant chacune aux différentes dimensions de l'espace (opérateurs « scalaires »). Celles-ci obéissent entre elles à certaines relations de commutation. Ainsi, alors qu'en mécanique classique les trois composantes du moment cinétique peuvent être simultanément mesurées, ceci est impossible dans le cadre quantique. En fait, seuls peuvent être déterminés les états propres communs à l'opérateur {\hat J}^2 donnant la somme des carrés des différentes composantes d'une part, et à une composante particulière donnée (par exemple {\hat J}_z ). Par ailleurs, la définition quantique du moment cinétique généralise la notion « ordinaire » de moment cinétique à des situations n'ayant pas d'équivalent classique. Ceci amène en fait à distinguer le moment cinétique défini par analogie classique, en fonction des diverses composantes des o

Source officielle

https://fr.wikipedia.org/wiki/Moment_cin%C3%A9tique_(m%C3%A9canique_quantique)

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Electron Energy Loss Spectrometry (EELS) in Transmission Electron Microscopy (TEM) is a powerful tool for the investigation of the electronic structure of materials. In the low loss regime, one can access the optical properties which are governed by the dielectric function ε(ω), which may be retrieved thanks to the so-called "loss function". The energy range covered by EELS goes from the infrared (less than 1 eV) to the hard X-rays (about 3 keV), each region having its own interest. The low loss region (0–100 eV) serves to investigate the valence electron structure and the inter-band transition behavior. Using angular resolved EELS gives further information about the dispersion behavior of the investigated material. This work is a part of a large project aiming a closer agreement between theory and experiment in angular resolved EELS by improving the state of the art in both fields. The purpose of this work is to set up a reliable experimental technique to retrieve the momentum transfer resolved single scattering distribution at very low energy with good accuracy and resolutions. One of the main challenges was to use the newly installed JEOL 2200 FS transmission electron microscope that is equipped with an in-column Ω filter for retrieval of the loss function in diffraction energy filtered TEM. Issues such as the angular resolution, contamination, image-coupling in diffraction mode and plural scattering have been solved. Several optical alignments and operational modes of the JEOL 2200 FS have been tested, and finally nano-beam diffraction was found to be the optimal running mode. This work provides for the first time a full 3D energy loss data cube in diffraction mode with energy and angular resolutions of 1 eV and 0.5 nm−1 respectively. After processing, the energy and angular relevant data span an energy loss range from 2.75 eV to 40.25 eV and the angular momentum transfer up to 12.5 nm−1. Although theoretically, without CCD camera binning and the maximum available camera length of the JEOL (250 cm), a momentum transfer resolution of 0.04 nm−1 would have been possible, the effective angular resolution was limited by the smallest obtainable beam convergence as well as by the remaining aberrations of the microscope. The presented technique can be reproduced on any transmission electron microscope equipped with an in-column energy filter. Furthermore, it is demonstrated that the proposed method provides working ranges in energy, spatial and angular resolutions limited only by the perfor- mance of the microscope. Previous techniques did not provide experimental results showing an energy resolution independent of the spatial and angular resolutions.

EPFL2013

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An on/off Berry phase switch in circular graphene resonators

Donat Fabian Natterer, Yue Zhao

The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wave function may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a relatively small critical magnetic field is reached. This behavior results from turning on a p Berry phase associated with the topological properties of Dirac fermions in graphene. The Berry phase can be switched on and off with small magnetic field changes on the order of 10 millitesla, potentially enabling a variety of optoelectronic graphene device applications.

American Association for the Advancement of Science2017

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Pseudomomentum: origins and consequences

Harmeet Singh

The balance of pseudomomentum is discussed and applied to simple elasticity, ideal fluids, and the mechanics of inextensible rods and sheets. A general framework is presented in which the simultaneous variation of an action with respect to position, time, and material labels yields bulk balance laws and jump conditions for momentum, energy, and pseudomomentum. The example of simple elasticity of space-filling solids is treated at length. The pseudomomentum balance in ideal fluids is shown to imply conservation of vorticity, circulation, and helicity, and a mathematical similarity is noted between the evaluation of circulation along a material loop and the J-integral of fracture mechanics. Integration of the pseudomomentum balance, making use of a prescription for singular sources derived by analogy with the continuous form of the balance, directly provides the propulsive force driving passive reconfiguration or locomotion of confined, inhomogeneous elastic rods. The conserved angular momentum and pseudomomentum are identified in the classification of conical sheets with rotational inertia or bending energy.

2021

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EPFL2013