dorsal/arxiv
View SchemaN identical particles under quantum confinement: A many-body dimensional perturbation theory approach II, the lowest-order wave function II
| Authors | M. Dunn, D. K. Watson, J. G. Loeser |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607135 |
| URL | https://arxiv.org/abs/quant-ph/0607135 |
Abstract
In this paper, the second in a series of two, we complete the derivation of the lowest-order wave function of a dimensional perturbation theory (DPT) treatment for the N-body quantum-confined system. Taking advantage of the symmetry of the zeroth-order configuration, we use group theoretic techniques and the FG matrix method from quantum chemistry to obtain analytic results for frequencies and normal modes. This method directly accounts for each two-body interaction, rather than an average interaction so that even lowest-order results include beyond-mean-field effects. It is thus appropriate for the study of both weakly and strongly interacting systems and the transition between them. While previous work has focused on energies, lowest-order wave functions yield important information such as the nature of excitations and expectation values of physical observables at low orders including density profiles. Higher orders in DPT also require as input the zeroth-order wave functions. In the earlier paper we presented a program for calculating the analytic normal-mode coordinates of the large-D system and illustrated the procedure by deriving the two simplest normal modes. In this paper we complete this analysis by deriving the remaining, and more complex, normal coordinates of the system.
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"abstract": "In this paper, the second in a series of two, we complete the derivation of\nthe lowest-order wave function of a dimensional perturbation theory (DPT)\ntreatment for the N-body quantum-confined system. Taking advantage of the\nsymmetry of the zeroth-order configuration, we use group theoretic techniques\nand the FG matrix method from quantum chemistry to obtain analytic results for\nfrequencies and normal modes. This method directly accounts for each two-body\ninteraction, rather than an average interaction so that even lowest-order\nresults include beyond-mean-field effects. It is thus appropriate for the study\nof both weakly and strongly interacting systems and the transition between\nthem. While previous work has focused on energies, lowest-order wave functions\nyield important information such as the nature of excitations and expectation\nvalues of physical observables at low orders including density profiles. Higher\norders in DPT also require as input the zeroth-order wave functions. In the\nearlier paper we presented a program for calculating the analytic normal-mode\ncoordinates of the large-D system and illustrated the procedure by deriving the\ntwo simplest normal modes. In this paper we complete this analysis by deriving\nthe remaining, and more complex, normal coordinates of the system.",
"arxiv_id": "quant-ph/0607135",
"authors": [
"M. Dunn",
"D. K. Watson",
"J. G. Loeser"
],
"categories": [
"quant-ph"
],
"title": "N identical particles under quantum confinement: A many-body dimensional perturbation theory approach II, the lowest-order wave function II",
"url": "https://arxiv.org/abs/quant-ph/0607135"
},
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