tion of motion for (q2) and we obtain ih(a/at)(q2) + ! trQ l [R, p2] = N,,(p.) trQ q2 [P, R], ih(a/at)(q2) -ih(qp + pq) = N"(p.) tr. q2 [P, R], which becomesIn Sec. IV we need the equation of motion for (pq) which can be obtained from (qp + pq) sinceWe find the equation of motion for (pq + pq) by multiplying Eq. (3.10) by (pq + qp) and taking the trace. The result isEquations (A3), (A4) , and (A5) constitute three first-order, linear inhomogeneous equations for the three second moments of the electromagnetic field, (p2), (q2), and (pq). In general, if we go to nth order in "( N "( we find a set of first-order inhomogeneous linear equations for the nth moments. The inhomogeneities depend on moments of lower order than the nth.It is important to note that even if all the second moments are zero initially they will grow to nonzero values because the inhomogeneous terms depend on (p), (q), and (p.).The eigenfrequencies of the homogeneous equations for (q2), (p2), and (pq) are 0, ±2ifl. Since these frequencies are prominent in the inhomogeneous terms, the second moments are strongly coupled to the SCFA quantities (p), (q), and (p.).It is shown that for a wide class of nonlinear wave equations there exist no stable time-independent solutions of finite energy. The possibility is considered whether elementary particles might be oscillating solutions of some nonlinear wave equation, in which the wavefunction is periodic in the time though the energy remains localized.
The stability of time-dependent particlelike solutions of the form ψ=φ(r)e−iωt is examined for the nonlinear field ∇2ψ−c−2 ∂2ψ/∂t2=κ2ψ−μ2ψψ*ψ. It is found that such solutions are unstable for all ω.
We present both experimental and numerical data showing the absorption of unpolarized, normally incident light by a gold crossed grating having a shallow sinusoidal profile. We show furthermore that the total absorption of unpolarized light can be achieved for an angle of incidence of 30 degrees with a crossed grating having its period adjusted appropriately from the normal incidence case to preserve the plasmonic resonance responsible for the enhanced absorptance. We contrast the process for achieving high absorptance in the principal plane of incidence aligned with the grooves of one of the gratings, with that for the principal plane at 45 degrees to each grating.
The conductivities of body-centred (b. c. c.) and face-centred (f. c. c.) cubic lattices of spheres of a conducting material in a conducting matrix are calculated by using a method originally devised by Lord Rayleigh. Measurements of the conductivity of the b. c. c. lattice of perfectly conducting spheres are presented. Good agreement between theory and experiment is obtained. Our results are shown to be in agreement with asymptotic equations derived by other authors. A formula is given for the case of a disordered array.
For gratings having an arbitrary symmetric profile, we prove that when the period becomes much finer than the wavelength the grating becomes equivalent to a graded uniaxial layer . We show for one polarization that this quasi-static equivalence holds when the ratio of wavelength to grating period exceeds 40 . We also present a simple physical model which explains the anisotropic nature of the equivalent layer . We take the case of a finely-textured copper surface, and show that it can be a good selective absorber for polarized light, but that its performance in unpolarized' light is much less satisfactory .
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