Diamagnetic spectrum and oscillations in an elliptic shell

The ballistic electronic motion in a two-dimensional multiconnected system of varying width, threaded by a magnetic field, is considered. The quantum states are classified according to their classical counterparts. The variable width leads to new types of states, in addition to those found in a constant-width (circular) geometry. The feature peculiar to these states is a classical spatial confinement at the wider regions, which leads to quenching of the Aharonov-Bohm oscillations and the diamagnetic current. In particular, the degeneracy of the spectrum pertaining to the circular geometry is lifted in the varying-width geometry, and irregularly situated gaps appear. The spectrum and wave functions are analyzed as a function of the magnetic-field strength.