Fictitious magnetic field

The transformation can be made by applying Eq. 11.16, with a Hamiltonian appropriate to a fictitious magnetic field (see Section 2.8) that would cause procession at a frequency of — r ... 

In Fig. 21, the result from numerical calculations using a mean-field theory is depicted. It indicates that the fictitious magnetic field produces current roughly given by... 

When both real magnetic field B = V x A and the fictitious magnetic field Bgc = V X Afic are present, the electric current becomes... 

Fig. 2.2.7 Magnetic fields in the rotating frame. Depending on the offset S2o of the NMR frequency from the rotation frequency a>rt of the rotating frame, a fictitious magnetic field of magnitude = —Qaly acts along the z-direction. Along the y-direction the rf magnetic field of amplitude B = —a> ly is applied. The vector sum of both forms the effective field B ts< around which the magnetization is rotating with frequency o>eff = —...

The equivalence of any two-level problem to the problem of a particle of spin 1/2 in magnetic field is well known [10] and has been used to treat the one-electron part of a two-orbital problem in terms of a fictitious spin of 1/2 in a fictitious magnetic field. The equivalence is obvious from the fact that any 2x2 matrix is fully characterized by its four complex elements and therefore can be written as a linear combination of the unit matrix (a /3) and the three Pauli matrices Oy, a ). The one-electron part Hi of a... 

In this short review, a brief overview of the underlying principles of TDDFT has been presented. The formal aspects for TDDFT in the presence of scalar potentials with periodic time dependence as well as TD electric and magnetic fields with arbitrary time dependence are discussed. This formalism is suitable for treatment of interaction with radiation in atomic and molecular systems. The Kohn-Sham-like TD equations are derived, and it is shown that the basic picture of the original Kohn-Sham theory in terms of a fictitious system of noninteracting particles is retained and a suitable expression for the effective potential is derived. 

This potential is often written in terms of a fictitious exchange-correlation magnetic field Bxc... 

The two principle modes of the magnetostriction (A -° and As or Xy-2) introduced above are illustrated in fig. 2. With respect to the non-magnetic fictitious state, a spherical, isotropic sample exhibits a relative volume change AV/V = A" 0, when it becomes magnetic. In addition, when one forces the moments to be directed along an applied magnetic field B, an anisotropic deformation is induced, which transfers the sphere into an ellipsoid with the same volume. 

If a Type I superconductor such as lead is placed in a small magnetic field (e.g. a few mT) and cooled, then at 7[. the magnetic field is expelled from the interior of the specimen. This is the Meissner effect, which is fundamental to the superconducting state it is not simply characteristic of a material which happens to be a (fictitious) perfect conductor. The total absence of an electric field in a... 

Features (l)-(3) can be explained when we consider a fictitious, totally rigid biradical with a S-T splitting of 27. In this model, MFEs due to the LCM are possible to occur, where the magnetic field dependence of reaction products is shown in Fig. 6-2(d). The B ax value corresponds to the Blc value given by Eq. (6-5). 

The Nernst signal is measured by an experimental setup shown in Fig. 23a a temperature gradient VF is created in the x-direction, and a magnetic field B is applied in the z-direction. Due to the flow of loop currents, Efic appears in the y-direction and exerts force on electrons then, a real electric field develops to balance the fictitious electric field (E = -Egc) as in the Hall effect measurement. The Nernst signal is defined as the developed electric field in the j-direction, Ey, divided by... 

Thus, except for a constant term 2ho geminal space (hQ = 0 for the spin space), it is clear that the additive "one-electron part Hi(l,2) of the total Hamiltonian operator H in either the spin space or the geminal space corresponds to a Zeeman-like interaction of a particle of spin 1 with a field h, either a real magnetic field By with 2h = gPe fictitious field B, with 2h - g ... 

We have thus shown that magnetoelastic composites can be simply modelled as elastic continuum distributions of induced elastic and magnetic multipoles. It was shown also that the magnetization field in the composites can be determined therefrom by introducing fictitious constrained currents, eq (39) and the elastic displacement by introducing fictitious constrained body forces, eqs (38). Assuming that AC is negligible, the results of... 

In the absence of an RF field, H = Hq. At resonance, therefore, the fictitious field w/y exactly cancels H, and Heff becomes zero. When the static magnetic field is in the z direction and the RF field Hi is applied along the x direction (in other words. Hi is rotating clockwise in the x-y plane), the total magnetic field H is... 

In the rotating frame of reference for an on-resonance peak, the B0 field is exactly canceled by a fictitious field created by the rotation of the axes, so that for nuclei that are on-resonance the only field present is the B field during the spin lock (Z eff =B i). If we place the sample magnetization on the y axis of the rotating frame with a 90° hard pulse (phase —jc), the spin lock can be placed on the y axis (phase y). While the spin lock is on, the sample magnetization is locked on the y axis and will not undergo precession, as the only field present is the B field and the sample magnetization is on the same axis as the B field (Fig. 8.37). 

Fig. 9.2.7 Illustration of the fast adiabatic passage through resonance. The magnetization M follows the direction of the effective field The effective field in the rotating frame is the vector sum of the fictitious field Sbc and rf excitation field B. Both fields are applied in orthogonal directions. Because the fictitious field is proportional to the resonance offset S2, the magnitude of the fictitious field and thus the direction of the effective field can be changed by adjusting the resonance offset frequency S2.

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