dorsal/arxiv
View SchemaZero-Energy Flows and Vortex Patterns in Quantum Mechanics
| Authors | Tsunehiro Kobayashi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302148 |
| URL | https://arxiv.org/abs/quant-ph/0302148 |
| DOI | 10.1088/0031-8949/70/6/001 |
Abstract
We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zero-energy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. %, i.e., $-m \gamma^2 (x^2+y^2)/2$. We point out three interesting properties of the zero-energy flows; (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the absolute stability of the vortex patterns .
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"abstract": "We show that zero-energy flows appear in many particle systems as same as in\nsingle particle cases in 2-dimensions. Vortex patterns constructed from the\nzero-energy flows can be investigated in terms of the eigenstates in conjugate\nspaces of Gel\u0027fand triplets. Stable patterns are written by the superposition\nof zero-energy eigenstates. On the other hand vortex creations and\nannihilations are described by the insertions of unstable eigenstates with\ncomplex-energy eigenvalues into the stable patterns. Some concrete examples are\npresented in the 2-dimensional parabolic potential barrier case. %, i.e., $-m\n\\gamma^2 (x^2+y^2)/2$. We point out three interesting properties of the\nzero-energy flows; (i) the absolute economy as for the energy consumption, (ii)\nthe infinite variety of the vortex patterns, and (iii) the absolute stability\nof the vortex patterns .",
"arxiv_id": "quant-ph/0302148",
"authors": [
"Tsunehiro Kobayashi"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0031-8949/70/6/001",
"title": "Zero-Energy Flows and Vortex Patterns in Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0302148"
},
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