Coupledcluster theory for systems of bosons in external traps
Abstract
A coupledcluster approach for systems of N bosons in external traps is developed. In the coupledcluster approach the exact manybody 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 coupledcluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupledcluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupledcluster 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 coupledcluster with T=T{sub 1}+T{sub 2}, i.e., coupledcluster 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, PhysikalischChemisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 229, D69120 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; BOSEEINSTEIN CONDENSATION; BOSONS; CLUSTER EXPANSION; EXCITATION; FERMIONS; MANYBODY PROBLEM; MATHEMATICAL OPERATORS; TRAPS; WAVE FUNCTIONS
Citation Formats
Cederbaum, Lorenz S., Alon, Ofir E., and Streltsov, Alexej I.. Coupledcluster 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.. Coupledcluster 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 .
"Coupledcluster theory for systems of bosons in external traps". United States.
doi:10.1103/PHYSREVA.73.0.
@article{osti_20787144,
title = {Coupledcluster theory for systems of bosons in external traps},
author = {Cederbaum, Lorenz S. and Alon, Ofir E. and Streltsov, Alexej I.},
abstractNote = {A coupledcluster approach for systems of N bosons in external traps is developed. In the coupledcluster approach the exact manybody 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 coupledcluster expansions. In a substantial part of this work, we address the issue of size consistency for bosons and enquire whether truncated coupledcluster expansions are size consistent. We show that, in contrast to the familiar situation for fermions for which coupledcluster 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 coupledcluster with T=T{sub 1}+T{sub 2}, i.e., coupledcluster 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}
}

In this series, the recently developed explicit formalism of orthogonally spinadapted Hibert space (or state universal), multireference (MR) coupledcluster (CC) theory, exploiting the model space spanned by two closedshelltype reference configurations, is applied to a simple minimumbasisset fourelectron model system consisting of two interacting hydrogen molecules in various geometrical arrangements. In this paper, we examine the nonplanar geometries of this system, generally referred to as the T4 models, and their special cases designated as P4 and V4 models. They correspond to different cross sections of the H[sub 4] potentialenergy hypersurface, involving the dissociation or simultaneous stretching of two HH bonds.more »

THEORY OF STRONGLY COUPLED MANYFERMION SYSTEMS. I. CONVERGENCE OF LINKED CLUSTER EXPANSIONS
A strongly coupled systemthe limiting case of a highly degenerate manyfermion system for which the variation of the kinetic energy is neglected, and the interaction restricted to a region of momentam space neighboring the Fernd surfaceis analyzed with no assumptions concerning the convergence of power series expansions or on partial summations of infinite series. The vacuum expectation value of the resolvent operator, /sub 0/, is expressed as the Laplace transform of the exponential of a function linearly dependent on the volume of the system. It is shown that the linkedcluster expansion of the vacuum expectation value of the resolvent operatormore » 
Orthogonallyspinadapted coupledcluster theory for closedshell systems including triexcited clusters
The orthogonallyspinadapted form of the nonlinear system of equations for the extended coupledpair manyelectron theory, which involves the monoexcited, biexcited, and triexcited states and cluster components, is derived. A diagrammatic approach, based on second quantization, the timeindependent Wick theorem, and the graphical methods of spin algebras, is employed. The advantages of using the orthogonallyspinadapted states and cluster components, rather than the nonorthogonallyspinadapted ones which have been previously employed, particularly in the triexcited case, are also discussed. It is also shown that the formulas for the direct configurationinteraction method can easily be obtained in compact form from the linear part ofmore » 
Translationally invariant coupled cluster theory for simple finite systems
The widely used coupled cluster method (CCM) in quantum manybody theory has recently provided very accurate descriptions of a large number of extended systems. Although its earlier applications to closedshell and neighboring finite nuclei were also very successful, they have been shrouded in algebraic and technical complexity. Furthermore, they are difficult to compare with more traditional calculations of generalized shellmodel theory since, at least at the important level of twobody correlations, they have been largely implemented in relativecoordinate space rather than the more usual oscillator configuration space. The CCM is reviewed here in the precise context of applications to simplemore » 
Application of relativistic coupledcluster theory to heavy atomic systems with strongly interacting configurations: Hyperfine interactions in {sup 207}Pb{sup +}
We report the results of our calculations of the magnetic dipole hyperfine constants for the ground and lowlying excited states of Pb{sup +} using the relativistic coupledcluster theory. The spectacular role of correlation effects particularly for the 6p{sub 3/2} state is highlighted. The relative importance of core polarization and pair correlation effects have been studied and the result obtained for the ground state is different from that of Ba{sup +}, which has a single s valence electron.