dorsal/arxiv
View SchemaA particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
| Authors | C. W. Gardiner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9703005 |
| URL | https://arxiv.org/abs/quant-ph/9703005 |
| DOI | 10.1103/PhysRevA.56.1414 |
Abstract
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is generalized to apply to a gas with an exact large number $ N$ of particles. This generalization yields a description of the Schr\"odinger picture field operators as the product of an annihilation operator $A$ for the total number of particles and the sum of a ``condensate wavefunction'' $\xi(x)$ and a phonon field operator $\chi(x)$ in the form $\psi(x) \approx A\{\xi(x) + \chi(x)/\sqrt{N}\}$ when the field operator acts on the N particle subspace. It is then possible to expand the Hamiltonian in decreasing powers of $\sqrt{N}$, an thus obtain solutions for eigenvalues and eigenstates as an asymptotic expansion of the same kind. It is also possible to compute all matrix elements of field operators between states of different N.
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"abstract": "The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is\ngeneralized to apply to a gas with an exact large number $ N$ of particles.\nThis generalization yields a description of the Schr\\\"odinger picture field\noperators as the product of an annihilation operator $A$ for the total number\nof particles and the sum of a ``condensate wavefunction\u0027\u0027 $\\xi(x)$ and a phonon\nfield operator $\\chi(x)$ in the form $\\psi(x) \\approx A\\{\\xi(x) +\n\\chi(x)/\\sqrt{N}\\}$ when the field operator acts on the N particle subspace. It\nis then possible to expand the Hamiltonian in decreasing powers of $\\sqrt{N}$,\nan thus obtain solutions for eigenvalues and eigenstates as an asymptotic\nexpansion of the same kind. It is also possible to compute all matrix elements\nof field operators between states of different N.",
"arxiv_id": "quant-ph/9703005",
"authors": [
"C. W. Gardiner"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.56.1414",
"title": "A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas",
"url": "https://arxiv.org/abs/quant-ph/9703005"
},
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