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Magnetoresonances on a lasso graph
Pavel Exner
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9701007
- categories:
- quant-ph cond-mat funct-an math.FA
- comments:
- 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
- doi:
- 10.1007/BF02550448
- arxiv_id:
- quant-ph/9701007
- journal_ref:
- Found.Phys. 27 (1997) 171-190
- created:
- 1997-01-06
Full article ▸
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