dorsal/arxiv
View SchemaPrecession and interference in the Aharonov-Casher and scalar Aharonov-Bohm effect
| Authors | Philipp Hyllus, Erik Sjöqvist |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210070 |
| URL | https://arxiv.org/abs/quant-ph/0210070 |
| DOI | 10.1023/A:1025637918269 |
| Journal | Found. Phys. 33, 1085 (2003). |
Abstract
The ideal scalar Aharonov-Bohm (SAB) and Aharonov-Casher (AC) effect involve a magnetic dipole pointing in a certain fixed direction: along a purely time dependent magnetic field in the SAB case and perpendicular to a planar static electric field in the AC case. We extend these effects to arbitrary direction of the magnetic dipole. The precise conditions for having nondispersive precession and interference effects in these generalized set ups are delineated both classically and quantally. Under these conditions the dipole is affected by a nonvanishing torque that causes pure precession around the directions defined by the ideal set ups. It is shown that the precession angles are in the quantal case linearly related to the ideal phase differences, and that the nonideal phase differences are nonlinearly related to the ideal phase differences. It is argued that the latter nonlinearity is due the appearance of a geometric phase associated with the nontrivial spin path. It is further demonstrated that the spatial force vanishes in all cases except in the classical treatment of the nonideal AC set up, where the occurring force has to be compensated by the experimental arrangement. Finally, for a closed space-time loop the local precession effects can be inferred from the interference pattern characterized by the nonideal phase differences and the visibilities. It is argued that this makes it natural to regard SAB and AC as essentially local and nontopological effects.
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"abstract": "The ideal scalar Aharonov-Bohm (SAB) and Aharonov-Casher (AC) effect involve\na magnetic dipole pointing in a certain fixed direction: along a purely time\ndependent magnetic field in the SAB case and perpendicular to a planar static\nelectric field in the AC case. We extend these effects to arbitrary direction\nof the magnetic dipole. The precise conditions for having nondispersive\nprecession and interference effects in these generalized set ups are delineated\nboth classically and quantally. Under these conditions the dipole is affected\nby a nonvanishing torque that causes pure precession around the directions\ndefined by the ideal set ups. It is shown that the precession angles are in the\nquantal case linearly related to the ideal phase differences, and that the\nnonideal phase differences are nonlinearly related to the ideal phase\ndifferences. It is argued that the latter nonlinearity is due the appearance of\na geometric phase associated with the nontrivial spin path. It is further\ndemonstrated that the spatial force vanishes in all cases except in the\nclassical treatment of the nonideal AC set up, where the occurring force has to\nbe compensated by the experimental arrangement. Finally, for a closed\nspace-time loop the local precession effects can be inferred from the\ninterference pattern characterized by the nonideal phase differences and the\nvisibilities. It is argued that this makes it natural to regard SAB and AC as\nessentially local and nontopological effects.",
"arxiv_id": "quant-ph/0210070",
"authors": [
"Philipp Hyllus",
"Erik Sj\u00f6qvist"
],
"categories": [
"quant-ph"
],
"doi": "10.1023/A:1025637918269",
"journal_ref": "Found. Phys. 33, 1085 (2003).",
"title": "Precession and interference in the Aharonov-Casher and scalar Aharonov-Bohm effect",
"url": "https://arxiv.org/abs/quant-ph/0210070"
},
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