# 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:

- 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}

}