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L. Sprung, M. Girlanda, and M. Macucci H (43) Hi + H%, N N tf ^ = E ( - 2m ^ 7 V? + Vin)) = J > ( * ) , (44) i=i =1 with Ho gin, fj) = g(rj,fi). 067mo, mo being the free electron mass). We then consider a numerable complete basis {y>i(q)}, where with q we indicate both the spatial and the spin coordinates, over which the singleparticle wave function for our problem can be expanded. We define the elements of such a basis "spin-orbitals". 2) fnNk{qi)

Although cells can be coupled by aligning them along the horizontal direction, 46 J. Martorell, D. W. L. Sprung, M. Girlanda, and M. Macucci no lateral branching is possible, because the space above and below the cell is occupied by the leads needed to bias the individual gates. 14 Furthermore, the adjustment of the gate voltages required to symmetrize a cell can be performed on a circuit containing just a few cells, but is unthinkable for a large array of cells. In particular, we must consider that the tuning of one cell also depends on the bias voltages applied to the neighboring cells, as will be discussed more in detail at the end of the present chapter.

L. Sprung, M. Girlanda, and M. Macucci mapped onto a second plane, the z plane, where we write z = x + iy. The profile of the etched surface is defined by the following points (which are the vertices of an open Schwarz Christoffel (SC) polygon that will be used for the conformal mapping): tu0 = —oo+iO, w\ = —W/2+iO, 102 = —W/2+ice, W3 = +W/2 + ice , w4 = +W/2 + iO and w$ — +00 + iO. We are going to map the part of the upper half plane above this polygon into the upper half of the z plane. We map the sides of the polygon onto the x axis, choosing the images of the IUJ as follows: yi = 0 and xo = — 00, x\ = —a, xi = — 1, X3 ~ 1, x^ = a, £5 — 00.

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