  Solutions of the scalar Helmholtz wave equation are derived for the analysis
of the transport and thermodynamic properties of the two-dimensional disk and
three-dimensional infinitely long straight wire in the external uniform
longitudinal magnetic field $\bf B$ under the assumption that the Robin
boundary condition contains extrapolation length $\Lambda$ with nonzero
imaginary part $\Lambda_i$. As a result of this complexity, the
self-adjointness of the Hamiltonian is lost, its eigenvalues $E$ become complex
too and the discrete bound states of the disk characteristic for the real
$\Lambda$ turn into the corresponding quasibound states with their lifetime
defined by the eigenenergies imaginary parts $E_i$. Accordingly, the
longitudinal flux undergoes an alteration as it flows along the wire with its
attenuation/amplification being $E_i$-dependent too. It is shown that, for zero
magnetic field, the component $E_i$ as a function of the Robin imaginary part
exhibits a pronounced sharp extremum with its magnitude being the largest for
the zero real part $\Lambda_r$ of the extrapolation length. Increasing
magnitude of $\Lambda_r$ quenches the $E_i-\Lambda_i$ resonance and at very
large $\Lambda_r$ the eigenenergies $E$ approach the asymptotic real values
independent of $\Lambda_i$. The extremum is also wiped out by the magnetic
field when, for the large $B$, the energies tend to the Landau levels.
Mathematical and physical interpretations of the obtained results are provided;
in particular, it is shown that the finite lifetime of the disk quasibound
states stems from the $\Lambda_i$-induced currents flowing through the sample
boundary. Possible experimental tests of the calculated effect are discussed;
namely, it is argued that it can be observed in superconductors by applying to
them the external electric field $\cal E$ normal to the surface.
