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VOLUME 84 (2006) | ISSUE 8 | PAGE 508
Bound states in the continuum in open Aharonov-Bohm rings
PACS: 03.65.-w, 05.60.Gg, 72.20.Dp
Abstract
Using formalism of effective Hamiltonian we consider bound states in continuum (BIC). They are those eigen states of non-hermitian effective Hamiltonian which have real eigen values. It is shown that BICs are orthogonal to open channels of the leads, i.e. disconnected from the continuum. As a result BICs can be superposed to transport solution with arbitrary coefficient and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are opened by attaching single-channel leads to them allow exact consideration of BICs. BICs occur at discrete values of energy and magnetic flux however it's realization strongly depend on a way to the BIC's point.