Long-range hopping parameters in H″ between site A in the unit cell (m, n) and site B in the unit cell (m0, n0) are denoted with \(t_{ab}^{m,n;m_0,n_0}\) and equivalently for A–C coupling (Methods). We analytically find that the zero-energy state, residing solely on ...
conditionWe consider symmetry properties of minimizers in the variational characterization of the best constant in the trace inequality in the ball Bρ of radius ρ. When p is fixed, minimizers in this problem can be radial or non-radial depending on the parameters q and ρ. We prove that ...
d Same as in (c), but the optimal geometry of the fast layer is estimated as a function of c and η for L = 1. The black dashed line is identified by the condition rc = L; the white dashed line is given by Eq. (10). Full size image We remind that the problem is ...
So, for the Left condition, \(\varGamma _{1}\) and \(\varGamma _{2}\) cannot both have nonzero matrix elements in the same row. This has the physical consequence that each doublet \(Q^0_{Li}\) couples to one and only one doublet \(\varPhi _{k}\). Moreover, we find ...
(3.10) In this way, the F -term condition for symmetric N and Ω, N Ω = ΩN , is also the consistency condition of S-transformation. When (N Ω)T = N Ω, (N B)T = N B and (N B)kk ∈ 2Z for k = 1, 2, 3 are fulfilled, Ti-transformation of zero-modes can ...
(18) as a subsidiary condition. Therefore we use it to eliminate the divergence of the current from Eq. (22b). After that we put Eq. (22a) in Eq. (22b) to eliminate the second term (this is called the ‘supplementary theorem’ of Gyarmati [27]). Because time is a parameter and ...
1. When one replaces the condition of nonnegativity and zero boundary condition by a periodic boundary condition, however, one encounters an additional degeneracy; for instance the functions depicted in Fig. 2, Fig. 3 are not equal to their Steiner symmetrizations even though they satisfy (1.5)...
Hello, I am working on a EHD problem. In a this problem I have to use symmetry Boundary condition. So should I use symmetry or symmetryPlane Boundary
{H,S}=0. (2) Hence, the sublattice symmetrySand chiral symmetry Π usually are not distinguished in the literature3,4,5,7,8,9,10,11,12,13,14, and the two terms, “sublattice” and “chiral”, have been used interchangeably. Furthermore, the topological classification for sublattice ...
The complete non-coplanar spin configuration actually contains three or more sets of collinear configurations (for instance, another two sets may be located at two inequivalent 24 g Wyckoff positions) with the condition that the directions of different sets of spins are mutually unparallel. Hence,...