dorsal/arxiv
View SchemaMagnetoresonances on a lasso graph
| Authors | Pavel Exner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9701007 |
| URL | https://arxiv.org/abs/quant-ph/9701007 |
| DOI | 10.1007/BF02550448 |
| Journal | Found.Phys. 27 (1997) 171-190 |
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.
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"abstract": "We consider a charged spinless quantum particle confined to a graph\nconsisting of a loop to which a halfline lead is attached; this system is\nplaced into a homogeneous magnetic field perpendicular to the loop plane. We\nderive the reflection amplitude and show that there is an infinite ladder of\nresonances; analyzing the resonance pole trajectories we show that half of them\nturn into true embedded eigenvalues provided the flux through the loop is an\ninteger or halfinteger multiple of the flux unit $hc/e$. We also describe a\ngeneral method to solve the scattering problem on graphs of which the present\nmodel is a simple particular case. Finally, we discuss ways in which a state\nlocalized initially at the loop decays.",
"arxiv_id": "quant-ph/9701007",
"authors": [
"Pavel Exner"
],
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"quant-ph",
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"doi": "10.1007/BF02550448",
"journal_ref": "Found.Phys. 27 (1997) 171-190",
"title": "Magnetoresonances on a lasso graph",
"url": "https://arxiv.org/abs/quant-ph/9701007"
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