We derive closed analytical formulae for the power emitted by moving charged particles in a uniaxial wire medium by means of an eigenfunction expansion. Our analytical expressions demonstrate that, in the absence of material dispersion, the stopping power of the uniaxial wire medium is proportional to the charge velocity, and that there is no velocity threshold for the Cherenkov emission. It is...

We investigate the existence of principal eigenvalues, i.e., values of λ for which the corresponding eigenfunction is positive, for the problem −∆u(x) = λg(x)u(x) for x ∈ lR where g is a smooth function which may change sign, Unlike most previous studies the eigenfunction is not required to → 0 as |x| → ∞. It is shown that there may exist a closed interval of principal eigenvalues [λ∗, λ ] and ...

A bstract . We study in one dimension the semi-classical limit of the exact eigenfunction Ψh E(N,h) of the Hamiltonian H = − 1 2 h2∆ + V (x), for a potential V being analytic, bounded below and lim|x|→∞ V (x) = +∞. The main result of this paper is that for any given E > minx∈R1 V (x) with two turning points, the exact L2 normalized eigenfunction |Ψh E(N,h) (q)|2 converges to the classical proba...

We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bidirectional interaction is allowed, so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around the center, followed by power-law long tails at both spectrum edges. The largest eigenvalue lambda1 depends on system size N as lambda1 approximately N1/4 for l...