Pavel Exner
Magnetoresonances on a lasso graph
(48K, LaTeX, with 2 ps figures)
ABSTRACT. We consider a charged spinless quantum particle confined to a
graph consisting of a loop to which a halfline lead is attached; this
system is placed into a homogeneous magnetic field perpendicular to
the loop plane. We derive the reflection amplitude and show that
there is an infinite ladder of resonances; analyzing the resonance
pole trajectories we show that half of them turn into true embedded
eigenvalues provided the flux through the loop is an integer or
halfinteger multiple of the flux unit $\,hc/e\,$. We also describe a
general method to solve the scattering problem on graphs of which the
present model is a simple particular case. Finally, we discuss ways
in which a state localized initially at the loop decays.