Magnetoresonances on a lasso graph

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.

To appear in the February issue of "Foundations of Physics" dedicated to the 65th birthday of L.P. Horwitz; 17 LaTeX pages with 2 ps figures

References in corpus (3)

• Contact interactions on graph superlattices
• Weakly coupled states on branching graphs
• Band spectra of rectangular graph superlattices

Cited by in corpus (8)

• Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
• Scattering theory on graphs
• Convergence of resonances on thin branched quantum wave guides
• Scattering theory on graphs (2): the Friedel sum rule
• Cross-section Fluctuations in Open Microwave Billiards and Quantum Graphs: The Counting-of-Maxima Method Revisited
• On the Effective Size of a Non-Weyl Graph
• Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards
• Escape behaviour of a quantum particle in a loop coupled to a lead