High-gradient approximation

This is the high-gradient approximation [Ran2]. It corresponds to a truncation of all spin interactions including moderate quadrupole interactions. 

The local density approximation is highly successful and has been used in density functional calculations for many years now. There were several difficulties in implementing better approximations, but in 1991 Perdew et al. successfully parametrised a potential known as the generalised gradient approximation (GGA) which expresses the exchange and correlation potential as a function of both the local density and its gradient ... 

More recently, Zhao et al. (2001a) employed the FLAPW method within the generalized gradient approximation (GGA) to investigate further electronic and magnetic properties of ordered Gai xMnxAs alloys with low and high Mn concentrations, 0.031 x 0.5. 

In essence, dispersion forces arise from the correlation between dynamic charge density fluctuations in two different systems or in distant parts of one system. The difficulty [228] in describing vdW forces in the static LDA or gradient approaches is therefore not surprising since in a highly inhomogeneous system (exemplified by, but not limited to, a pair of separated subsystems) these correlations may be quite different from those in the uniform or near-uniform electron gas upon which the LDA and the various gradient approximations are bas. ... 

In the high-field approximation the space-dependent thermodynamic-equilibrium density matrix po(r) is proportional to l fr) (cf. eqn (2.2.58)). A 90° pulse converts this density matrix into p (0+, r) oc U(r) = [l+(r) -I- l (r)] /2, where U is the x-component of the spin operator, 1+ = 1 + il>-, and L = 1 — il. In the subsequent free-precession period the density matrix evolves for a time t under the spin Hamiltonian Hx(r) (cf. eqn (3.1.1)) and under the influence of the applied gradient, which introduces a phase evolution given by kr = —yGrti, where k is the experimental variable,... 

The plot shows that the signal has a high gradient at 2.5 V of approximately 50mV/°C and a span of more than 4 V. Nonhnearities are compensated in the subsequent digital processing if required. With a 10-bit ADC resolutions of 1°C and better are possible. 

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