dorsal/arxiv
View SchemaExact coherent states in one-dimensional quantum many-body systems with inverse-square interactions
| Authors | Dae-Yup Song |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0102022 |
| URL | https://arxiv.org/abs/quant-ph/0102022 |
| DOI | 10.1103/PhysRevA.63.032104 |
| Journal | Phys. Rev. A 63, 032104 (2001) |
Abstract
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of different timescale is found. If the interactions can be written in terms of the differences between positions of two particles, it is also shown that the Schr\"{o}dinger equation is invariant under a unitary transformation. These unitary relations can be used not only in finding coherent states from the given stationary states in a system, but also in finding exact wave functions of the Hamiltonian systems of time-dependent parameters from those of time-independent Hamiltonian systems. Both operators are invariant under the exchange of any pair of particles. The transformations are explicitly applied for some of the Calogero-Sutherland models to find exact coherent states.
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"abstract": "For the models of $N$-body identical harmonic oscillators interacting through\npotentials of homogeneous degree -2, the unitary operator that transforms a\nsystem of time-dependent parameters into that of unit spring constant and unit\nmass of different timescale is found. If the interactions can be written in\nterms of the differences between positions of two particles, it is also shown\nthat the Schr\\\"{o}dinger equation is invariant under a unitary transformation.\nThese unitary relations can be used not only in finding coherent states from\nthe given stationary states in a system, but also in finding exact wave\nfunctions of the Hamiltonian systems of time-dependent parameters from those of\ntime-independent Hamiltonian systems. Both operators are invariant under the\nexchange of any pair of particles. The transformations are explicitly applied\nfor some of the Calogero-Sutherland models to find exact coherent states.",
"arxiv_id": "quant-ph/0102022",
"authors": [
"Dae-Yup Song"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.63.032104",
"journal_ref": "Phys. Rev. A 63, 032104 (2001)",
"title": "Exact coherent states in one-dimensional quantum many-body systems with inverse-square interactions",
"url": "https://arxiv.org/abs/quant-ph/0102022"
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