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Title: Coupled-cluster theory for systems of bosons in external traps

Abstract

A coupled-cluster approach for systems of N bosons in external traps is developed. In the coupled-cluster approach the exact many-body wave function is obtained by applying an exponential operator exp{l_brace}T{r_brace} to the ground configuration [{phi}{sub 0}>. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of [{phi}{sub 0}>, the appearance of excitation operators T={sigma}{sub n=1}{sup N}T{sub n} for bosons is much simpler than for fermions. We can treat very large numbers of bosons with coupled-cluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupled-cluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupled-cluster expansions are size consistent, for bosons the answer to this question depends on the choice of ground configuration. Utilizing the natural ground configuration, working equations for the truncated coupled-cluster with T=T{sub 1}+T{sub 2}, i.e., coupled-cluster singles doubles are explicitly derived. Finally, an illustrative numerical example for a condensate with up to N=10 000 bosons in an harmonic trap is provided and analyzed. The results are highly promising.

Authors:
; ;  [1]
  1. Theoretische Chemie, Physikalisch-Chemisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)
Publication Date:
OSTI Identifier:
20787144
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.73.043609; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; BOSE-EINSTEIN CONDENSATION; BOSONS; CLUSTER EXPANSION; EXCITATION; FERMIONS; MANY-BODY PROBLEM; MATHEMATICAL OPERATORS; TRAPS; WAVE FUNCTIONS

Citation Formats

Cederbaum, Lorenz S., Alon, Ofir E., and Streltsov, Alexej I.. Coupled-cluster theory for systems of bosons in external traps. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Cederbaum, Lorenz S., Alon, Ofir E., & Streltsov, Alexej I.. Coupled-cluster theory for systems of bosons in external traps. United States. doi:10.1103/PHYSREVA.73.0.
Cederbaum, Lorenz S., Alon, Ofir E., and Streltsov, Alexej I.. Sat . "Coupled-cluster theory for systems of bosons in external traps". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20787144,
title = {Coupled-cluster theory for systems of bosons in external traps},
author = {Cederbaum, Lorenz S. and Alon, Ofir E. and Streltsov, Alexej I.},
abstractNote = {A coupled-cluster approach for systems of N bosons in external traps is developed. In the coupled-cluster approach the exact many-body wave function is obtained by applying an exponential operator exp{l_brace}T{r_brace} to the ground configuration [{phi}{sub 0}>. The natural ground configuration for bosons is, of course, when all reside in a single orbital. Because of this simple structure of [{phi}{sub 0}>, the appearance of excitation operators T={sigma}{sub n=1}{sup N}T{sub n} for bosons is much simpler than for fermions. We can treat very large numbers of bosons with coupled-cluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupled-cluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupled-cluster expansions are size consistent, for bosons the answer to this question depends on the choice of ground configuration. Utilizing the natural ground configuration, working equations for the truncated coupled-cluster with T=T{sub 1}+T{sub 2}, i.e., coupled-cluster singles doubles are explicitly derived. Finally, an illustrative numerical example for a condensate with up to N=10 000 bosons in an harmonic trap is provided and analyzed. The results are highly promising.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 4,
volume = 73,
place = {United States},
year = {Sat Apr 15 00:00:00 EDT 2006},
month = {Sat Apr 15 00:00:00 EDT 2006}
}
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