By C. Truesdell

Whilst, after the agreeable fatigues of solicitation, Mrs Millamant set out an extended invoice of stipulations topic to which she could via levels dwindle right into a spouse, Mirabell provided in go back the situation that he would possibly not thereby be past degree enlarged right into a husband. With age and event in learn come the dual hazards of dwindling right into a thinker of technology whereas being enlarged right into a dotard. The philosophy of technology, i feel, shouldn't be the shield of senile scientists and of lecturers of philosophy who've themselves by no means quite a bit as understood the contents of a textbook of theoretical physics, not to mention performed just a little mathematical learn or maybe loved the arrogance of a growing scientist. at the latter count number I run no hazard: Any reader will see that i'm untrained (though no longer altogether unread) in school room philosophy. Of no lack of expertise of mine do I boast, certainly I remorse it, yet neither do i locate this one lack of knowledge deadly the following, for few certainly of the good philosophers to explicate whose works hodiernal professors of phil osophy break forests of pulp have been themselves so commonly and especially knowledgeable as are their scholiasts. In try and palliate the previous count number i've got selected to gather works written during the last thirty years, a few of them no longer released ahead of, and that i contain just a couple of very fresh essays.

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**Example text**

Notice here that Uxx /Uxy is always larger than 3 for numerical computations with the lattice Wannier functions References 1. Isacsson A, Girvin SM (2005) Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice. Phys Rev A 72(5):053604 2. Pinheiro F, Martikainen J-P, Larson J (2012) Confined p-band Bose-Einstein condensates. Phys Rev A 85(3):033638 3. Larson J, Collin A, Martikainen J-P (2009) Multiband bosons in optical lattices. Phys Rev A 79(3):033603 4. Pinheiro F, Martikainen J-P, Larson J (2015) Phases of d-orbital bosons in optical lattices.

This is in agreement with mean-field results obtained for the Bose-Hubbard model in the ground band. At higher fillings when the typical interaction energy becomes considerably larger than the gap between the E x y and E α bands, we expect that the dx y orbital will also become populated. Indeed, as we checked numerically, for the same parameters used in Fig. 7). Here, however, due to the higher truncation required in the number of particles, computations are considerably more costly than for the system at low densities, and are thus carried out for a fixed value of the chemical potential μ/U and for varying t/U .

We will use α ={x, y, z} whenever studying the p-band system with the pα orbital states in the 3D lattice; and α = {x 2 , y2 , xy} whenever studying the d-band system in 2D. As an additional point, let us stress here that the orbital states are not eigenstates of the single-particle Hamiltonian. We illustrate this by considering the explicit expression of the p-orbital wave-functions of a separable lattice, constructed with the site-localized Wannier functions,25 wν,j (α), with ν = 1, 2 and α a spatial direction,26 that are given by wx,j (r) = w2,jx (x)w1,jy (y)w1,jz (z) wy,j (r) = w1,jx (x)w2,jy (y)w1,jz (z) wz,j (r) = w1,jx (x)w1,jy (y)w2,jz (z).