Search results for "Equations"
showing 10 items of 955 documents
Towards the time-optimal control of dissipative spin-1/2 particles in nuclear magnetic resonance
2011
International audience; We consider the time-optimal control of a spin 1/2 particle whose dynamics is governed by the Bloch equations with both longitudinal and transverse relaxation terms. We solve this control problem by using geometric optimal control techniques. We show the crucial role of singular extremals in the time-optimal synthesis. This role can mainly be attributed to the presence of dissipation. We also analyze the robustness of the optimal control sequence when both the maximum amplitude of the control field and the dissipative parameters are varied. Finally, we present an experimental implementation of the different solutions using techniques of Nuclear Magnetic Resonance.
Optical phonons and electron-phonon interaction in quantum wires.
1993
A unified macroscopic continuum theory for the treatment of optical-phonon modes in quantum-wire structures is established. The theory is based on a Lagrangian formalism from which the equations of motion are rigorously derived. They consist of four coupled second-order differential equations for the vibrational amplitude and electrostatic potential. The matching boundary conditions are obtained from the fundamental equations. It is shown that no incompatibility exists between mechanical and electrostatic matching boundary conditions when a correct mathematical treatment of the problem is given. The particular case of a GaAs quantum wire buried in AlAs, where the phonons can be considered c…
Nonlinear magneto-optical resonances atD1excitation ofRb85andRb87in an extremely thin cell
2010
Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the ${D}_{1}$ transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground-state total angular momentum ${F}_{g}$ was greater than or equal to the excited-state total angular momentum ${F}_{e}$. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from th…
Skyrmion Dynamics – from thermal diffusion to ultra-fast motion
2018
Summary form only given. Spintronics promises to be a paradigm shift from using the charge degree of freedom to using the spin degree of freedom. To this end three key requirements are: (i) stable spin structures for long term data retention; (ii) efficient spin manipulation for low power devices and (iii) ideally no susceptibility to stray fields as realized for antiferromagnets. We explore different materials classes to tackle these challenges and explore the science necessary for a disruptive new technology. To obtain ultimate stability, topological spin structures that emerge due to the Dzyaloshinskii-Moriya interaction (DMI), such as chiral domain walls and skyrmions are used. These po…
Nonlinear Critical Layers in Barotropic Stability
1991
Abstract Applying the method of matched asymptotic expansions (MAE) to the shallow water equations on a rotating sphere, the structure of critical layers that occur in the linear and inviscid analysis of neutral disturbances of barotropic zonal flows is investigated, assuming that the critical layers are controlled by nonlinearity rather than viscosity or nonparallel flow effects. It turns out that nonlinearity is insufficient to resolve the critical layer singularity completely. It suffices however to connect linear and nondissipative solutions across critical latitudes.
Ground-state magneto-optical resonances in cesium vapor confined in an extremely thin cell
2007
Experimental and theoretical studies are presented related to the ground-state magneto-optical resonance prepared in Cesium vapour confined in an Extremely Thin Cell (ETC, with thickness equal to the wavelength of the irradiating light). It is shown that the utilization of the ETC allows one to examine the formation of a magneto-optical resonance on the individual hyperfine transitions, thus distinguishing processes resulting in dark (reduced absorption) or bright (enhanced absorption) resonance formation. We report on an experimental evidence of the bright magneto-optical resonance sign reversal in Cs atoms confined in the ETC. A theoretical model is proposed based on the optical Bloch equ…
Analyzing dynamical gluon mass generation
2007
We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained so…
Restoring of A balance by electric pulses
2004
Restoring of the balance beam to its initial situation after a change of load can be effected by combination of forces of different kind. In former papers we discussed the possibility using the equation of motion of the balance to determine the mass to be measured. After the measurement the balance was restored by means of current pulses into the electromagnetic measuring system. In the present paper we discuss the application of electric pulses into an additional electrostatic system.
Convergence of Nuclear Magnetic Shieldings in the Kohn-Sham Limit for Several Small Molecules.
2015
Convergence patterns and limiting values of isotropic nuclear magnetic shieldings were studied for several small molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6, and C6H6) in the Kohn-Sham limit. Individual results of calculations using dedicated families of Jensen's basis sets (pcS-n and pcJ-n) were fitted toward the complete basis set limit (CBS) using a simple two-parameter formula. Several density functionals were used; calculated vibrational corrections (ZPV) applied; and, for comparison purposes, similar calculations performed using RHF, MP2, SOPPA, SOPPA(CCSD), and CCSD(T) methods and additionally, the aug-cc-pVTZ-J basis set. Finally, the CBS estimated results were critically com…
Angular shift of an electromagnetic beam reflected by a planar dielectric interface
1989
A mathematical procedure for obtaining theoretically an expression for the fields of a beam reflected by a planar interface separating two lossless, linear, isotropic, homogeneous media is presented. Comparison of this expression with that obtained when the beam undergoes reflection from a perfect conductor leads to the expression for the angular shift of the beam reflected by a planar dielectric interface. The cases of normal and parallel polarization of a microwave beam are considered. In the last case, a complete study for angles of incidence far and near the Brewster angle is made.