Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed-matter, atomic, and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed-matter, atomic, and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.

arXiv:cond-mat/0607600Physical Review ADec 5, 200613 citations

Fully Exponentially Correlated Wave Functions for Few-Body Systems

Frank E. Harris

Bulletin of the American Physical SocietyMar 2, 20150 citations

Analytic, Group-Theoretic Wave Functions for Confined N-Body Quantum Systems

W. Blake Laing, Martin Dunn, John G. Loeser +1 more

Systems involving N-identical interacting particles under quantum confinement appear in many areas of physics, including chemical, condensed matter, and atomic physics. We discuss a beyondmean- field perturbation method that is applicable to weakly, intermediate and strongly-interacting systems. Group theory is used to derive an analytic beyond-mean-field correlated wave function at zeroth order for a system under spherical confinement. We derive the corresponding zeroth-order analytic density profile and apply it to the example of a Bose-Einstein condensate.Systems involving N-identical interacting particles under quantum confinement appear in many areas of physics, including chemical, condensed matter, and atomic physics. We discuss a beyondmean- field perturbation method that is applicable to weakly, intermediate and strongly-interacting systems. Group theory is used to derive an analytic beyond-mean-field correlated wave function at zeroth order for a system under spherical confinement. We derive the corresponding zeroth-order analytic density profile and apply it to the example of a Bose-Einstein condensate.

arXiv:physics/0510177Oct 19, 20050 citations

A new variational wave function for interacting few-body systems

C. Ciofi degli Atti, Silvano Simula

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoSep 1, 198410 citations

Test of a general symmetry-derived N -body wave function

Martin Dunn, W. Blake Laing, Derrick Toth +1 more

The resources required to solve the general interacting quantum $N$ -body problem scale exponentially with $N$ , making the solution of this problem very difficult when $N$ is large. In a previous series of papers we develop an approach for a fully interacting wave function for a confined system of identical bosons with a general two-body interaction. This method tames the $N$ scaling by developing a perturbation series that is order-by-order invariant under a point group isomorphic with ${S}_{N}$ . Group theory and graphical techniques are then used to solve for the wave function exactly and analytically at each order, yielding a solution for the general $N$ -body problem which scales as ${N}^{0}$ at any given order. Recently this formalism has been used to obtain the first-order fully interacting wave function for a system of harmonically confined bosons interacting harmonically. In this paper, we report the application of this $N$ -body wave function to a system of $N$ fully interacting bosons in three dimensions. We derive an expression for the density profile for a confined system of harmonically interacting bosons. Choosing this simple interaction is not necessary or even advantageous for our method, however this choice allows a direct comparison of our exact results through first order with exact results obtained in an independent solution. Our density profile for the wave function through first order in three dimensions is indistinguishable from the first-order exact result obtained independently and shows strong convergence to the exact result to all orders.The resources required to solve the general interacting quantum $N$-body problem scale exponentially with $N$, making the solution of this problem very difficult when $N$ is large. In a previous series of papers we develop an approach for a fully interacting wave function for a confined system of identical bosons with a general two-body interaction. This method tames the $N$ scaling by developing a perturbation series that is order-by-order invariant under a point group isomorphic with ${S}_{N}$. Group theory and graphical techniques are then used to solve for the wave function exactly and analytically at each order, yielding a solution for the general $N$-body problem which scales as ${N}^{0}$ at any given order. Recently this formalism has been used to obtain the first-order fully interacting wave function for a system of harmonically confined bosons interacting harmonically. In this paper, we report the application of this $N$-body wave function to a system of $N$ fully interacting bosons in three dimensions. We derive an expression for the density profile for a confined system of harmonically interacting bosons. Choosing this simple interaction is not necessary or even advantageous for our method, however this choice allows a direct comparison of our exact results through first order with exact results obtained in an independent solution. Our density profile for the wave function through first order in three dimensions is indistinguishable from the first-order exact result obtained independently and shows strong convergence to the exact result to all orders.

Physical Review ADec 11, 200912 citations

Confined quantum systems involving

N

identical interacting particles are to be found in many areas of physics, including condensed-matter, atomic, and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.

The resources required to solve the general interacting quantum

N

-body problem scale exponentially with

N

, making the solution of this problem very difficult when

N

is large. In a previous series of papers we develop an approach for a fully interacting wave function for a confined system of identical bosons with a general two-body interaction. This method tames the

N

scaling by developing a perturbation series that is order-by-order invariant under a point group isomorphic with

{S}_{N}

. Group theory and graphical techniques are then used to solve for the wave function exactly and analytically at each order, yielding a solution for the general

N

-body problem which scales as

{N}^{0}

at any given order. Recently this formalism has been used to obtain the first-order fully interacting wave function for a system of harmonically confined bosons interacting harmonically. In this paper, we report the application of this

N

-body wave function to a system of

N

fully interacting bosons in three dimensions. We derive an expression for the density profile for a confined system of harmonically interacting bosons. Choosing this simple interaction is not necessary or even advantageous for our method, however this choice allows a direct comparison of our exact results through first order with exact results obtained in an independent solution. Our density profile for the wave function through first order in three dimensions is indistinguishable from the first-order exact result obtained independently and shows strong convergence to the exact result to all orders.