We study transport properties of an arbitrary two terminal Hermitian system within a tight-binding approximation and derive the expression for the transparency in the form, which enables one to determine exact energies of perfect (unity) transmittance, zero transmittance (Fano resonance) and bound state in the continuum (BIC). These energies correspond to the real roots of two energy-dependent functions that are obtained from two non-Hermitian Hamiltonians: the Feshbach's effective Hamiltonian and the auxiliary Hamiltonian, which can be easily deduced from the effective one. BICs and scattering states are deeply connected to each other. We show that transformation of a scattering state into a BIC can be formally described as a "phase transition" with divergent generalized response function. Design rules for quantum conductors and waveguides are presented, which determine structures exhibiting coalescence of both resonances and antiresonances resulting in the formation of almost rectangular transparency and reflection windows. The results can find applications in construction of molecular conductors, broad band filters, quantum heat engines and waveguides with controllable BIC formation.

We calculate and analyse S-wave resonances of helium up to an energy of-0.02 au applying the complex rotation technique. Rydkrg series converging to the hydrogenic thresholds of the Het ion are analysed by quantum defect theory. For moderately excited inner electrons the series converging to different thresholds begin to overlap resulting in perturbed Rydberg series. We find that approximate quantum numbers as well as propensity rules governing the decay of the resonances and the perturbation scheme of the Rydberg aeries prevail. With increasing excitation of the inner electran however, only series whose stiltes tend lo extreme interelectronic angles (cos0) = + I remain regular.

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Recent progress in the semiclassical description of two-electron atoms is reported herein. It is shown that the classical dynamics for the helium atom is of mixed phase space structure, i.e., regular and chaotic motion coexists. Semiclassically, both types of motion require separate treatment. Stability islands are quantized via a torus–quantization-type procedure, whereas a periodic-orbit cycle expansion approach accounts for the states associated with hyperbolic electron pair motion. The results are compared with highly accurate ab initio quantum calculations, most of which are reported here for the first time. The results are discussed with an emphasis on previous interpretations of doubly excited electron states

We show within the framework of quantum-defect theory that bound states in the continuum (BIC) can occur in systems of at least three coupled Coulombic channels due to the interference of resonances belonging to different channels, As a physical realization of such BIC, we discuss the Schrodinger equation describing a hydrogen atom in a uniform magnetic field. Below a well-defined continuum threshold, the solutions of a Schrodinger equation are square integrable and the energy eigenvalues are discrete. Above the threshold, the eigenvalues are distributed continuously and the eigenstates are generally not normalizable. ' Narrow resonances with large but finite lifetimes can occur if a slight modification of the Hamiltonian would lead to an effectively higher threshold. Examples are long-lived resonances behind a large potential barrier, or quasibound states in closed channels of a system with weakly coupled channels. However, in special cases, local potentials have been constructed where, for discrete energies above threshold, the Schrodinger equation -has square integrable solutions which have no obvious connection to bound eigenstates of such an approximate Hamiltonian. In examples given by Stillinger and Herrick and Fonda and Newton, nonseparability of the Hamiltonian or relatively strong coupling of channels are important for the occurrence of such bound states in the continuum (BIC). The aim of this Brief Report is to show how BIC can occur naturally in systems of coupled Coulombic channels and to present, for the first time, a physically real example of BIC. Coupled Coulombic channels are comprehensively described in the, framework of multichannel quantum-defect theory (MQDT) as developed by Seaton. 5 The basic equation of MQDT is det[ tan(n ];)5;, + R;, ] = 0, where the elements R"" define Seaton's real symmetric R matrix, and describe the dynamic effect of the short-range deviations of the true potential from the case of uncoupled pure Coulomb potentials. If all important channels are included, the R"" vary only weakly with energy. In closed channels, the quantity ]; in Eq. (1) is related to the energy E and the respective channe1 threshold I; by denly by m, and the width I is' (4) where E, is the turning point of 5(E). For three coupled channels, Eq. (1) becomes R ]2T3+R 3]T2 -2R ]2R 23R 3] tan5(E) = R ]]-T2T3 -R 23 with T2 and T3 as defined in Eq. (3). The phase shift 5(E) jumps by rr near poles of the right-hand side of Eq. (5). To understand the general behavior of 5(E), it is useful to study the zeros and poles of the fraction on the righthand side of Eq. (5). This quantity stays regular when either T2 or T3 has a pole. Poles of the fraction occur when the denominator D (E) = T2T3 -R p3 has zeros, and zeros occur when the numerator N (E) = R ]2T3+ R 3]T2 -2R ]2R 23R 3]vanishes.Near resonances, i.e. , near zeros of D, the derivative of the phase shift is d 5 D'(E) dE D(E) 0 N(E) In general, D(E) has no multiple zeros, so Eq. (8) shows that an infinite derivative of 5 corresponding to a vanishing width ...