We discuss the discrete spectrum induced by bulges on threadlike mesoscopic objects, using two models, a continuous hard-wall waveguide and a discrete tight-binding model with two sorts of atomic orbitals. We show that elongated bulges induce numerous quasibound states. In the discrete model we also evaluate the probability of transition between the localized states and extended ones of the valence band. We suggest this as a mechanism governing the porous-silicon luminescence. In addition, the model reproduces the dominance of nonradiative transitions, blueshift for finer textures, and luminiscence suppression at low temperatures.

We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit N. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart from the resonances coming from the decoupled-surface eigenvalues, such scatterers exhibit the high-energy behavior typical for the interaction for the physically interesting couplings.

The paper is devoted to a model of a mesoscopic system consisting of a pair of parallel planar waveguides separated by an infinitely thin semitransparent boundary modeled by a transverse interaction. We develop the BirmanSchwinger theory for the corresponding generalized Schrdinger operator. The spectral properties become nontrivial if the barrier coupling is not invariant with respect to longitudinal translations, in particular, there are bound states if the barrier is locally more transparent in the mean and the coupling parameter reaches the same asymptotic value in both directions along the guide axis. We derive the weak-coupling expansion of the ground-state eigenvalue for the cases when the perturbation is small in the supremum and the <b>L</b>¹-norms. The last named result applies to the situation when the support of the leaky part shrinks: the obtained asymptotics differs from that of a double guide divided

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