The approximation in the second plot is smoother than the approximation in the third plot.
The approximation in the second line of eq 6.27 neglects second-order terms in λD – λH.
We therefore start by describing the visualization techniques in the first part, and then move on to storage size reduction by sparse approximation in the second part of the results.
The cross-correlation of f and g at a shift (or distance) of d is (1) The approximation in the second line results from the summation in the first line not being taken over exactly the same values of b as the summations in the formulae for and.
In the same manner, we can obtain further approximations (v_{3} x,t), ldots) Setting (beta=1) in the first approximation (24) and the second approximation (25) and after some simplifications, we obtain the same approximations as (15) and (16) on returning to the original variable.
For the realistic choice of qubit and transmission line parameters, the figures of merit (beta= sqrt{E_{EM}/ Delta} sim30) and (nu= hbarmax(Gamma_{qb},Gamma_{TL})/Delta sim10^{-3}) (Ref. [18]) ensure that the continuum approximation is justified, and that in the first approximation the effects of decoherence can be neglected.
and from (17) we obtain an approximation to plasmon dispersion in the first order in the Coulomb interaction: Ω n 1 n 2 ( q ) ≈ E n 1 n 2 ( 0 ) + g V ( q ) F n 1 n 2 ( q ).
This is a good approximation to their movements in the first interval, since the viewing zone was narrow and oriented in this direction, but, of course, we had no control over the participant's movement in the second interval.
end{aligned} Results of numerical calculations are presented in Tables 1-3 for both the first and second order approximations in the cases (N=M=20, 40, 80) and 160.
The full correlation approximation assumes that all the terms, obtained in solution of the SBVP in the first approximation, are being considered, including those containing correlation functions of order higher than the second.
