dorsal/arxiv
View SchemaGeometric phases for neutral and charged particles in a time-dependent magnetic field
| Authors | Qiong-gui Lin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201024 |
| URL | https://arxiv.org/abs/quant-ph/0201024 |
| DOI | 10.1088/0305-4470/35/2/314 |
| Journal | J. Phys. A 35 (2002) 377-391 |
Abstract
It is well known that any cyclic solution of a spin 1/2 neutral particle moving in an arbitrary magnetic field has a nonadiabatic geometric phase proportional to the solid angle subtended by the trace of the spin. For neutral particles with higher spin, this is true for cyclic solutions with special initial conditions. For more general cyclic solutions, however, this does not hold. As an example, we consider the most general solutions of such particles moving in a rotating magnetic field. If the parameters of the system are appropriately chosen, all solutions are cyclic. The nonadiabatic geometric phase and the solid angle are both calculated explicitly. It turns out that the nonadiabatic geometric phase contains an extra term in addition to the one proportional to the solid angle. The extra term vanishes automatically for spin 1/2. For higher spin, however, it depends on the initial condition. We also consider the valence electron of an alkaline atom. For cyclic solutions with special initial conditions in an arbitrary strong magnetic field, we prove that the nonadiabatic geometric phase is a linear combination of the two solid angles subtended by the traces of the orbit and spin angular momenta. For more general cyclic solutions in a strong rotating magnetic field, the nonadiabatic geometric phase also contains extra terms in addition to the linear combination.
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"abstract": "It is well known that any cyclic solution of a spin 1/2 neutral particle\nmoving in an arbitrary magnetic field has a nonadiabatic geometric phase\nproportional to the solid angle subtended by the trace of the spin. For neutral\nparticles with higher spin, this is true for cyclic solutions with special\ninitial conditions. For more general cyclic solutions, however, this does not\nhold. As an example, we consider the most general solutions of such particles\nmoving in a rotating magnetic field. If the parameters of the system are\nappropriately chosen, all solutions are cyclic. The nonadiabatic geometric\nphase and the solid angle are both calculated explicitly. It turns out that the\nnonadiabatic geometric phase contains an extra term in addition to the one\nproportional to the solid angle. The extra term vanishes automatically for spin\n1/2. For higher spin, however, it depends on the initial condition. We also\nconsider the valence electron of an alkaline atom. For cyclic solutions with\nspecial initial conditions in an arbitrary strong magnetic field, we prove that\nthe nonadiabatic geometric phase is a linear combination of the two solid\nangles subtended by the traces of the orbit and spin angular momenta. For more\ngeneral cyclic solutions in a strong rotating magnetic field, the nonadiabatic\ngeometric phase also contains extra terms in addition to the linear\ncombination.",
"arxiv_id": "quant-ph/0201024",
"authors": [
"Qiong-gui Lin"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/35/2/314",
"journal_ref": "J. Phys. A 35 (2002) 377-391",
"title": "Geometric phases for neutral and charged particles in a time-dependent magnetic field",
"url": "https://arxiv.org/abs/quant-ph/0201024"
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