Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics

Ground-State Energy of a System of Interacting Bose Particles

Masahiko HIROOKA, Shuichiro Yamasaki

Published Oct 1, 1982• 1 citation
Publisher

Abstract

The ground-state energy of a system of interacting N-bosons is investigated in a collective formalism. Ultraviolet divergences in perturbation calculations are eliminated by the introduction of quasi-particle operators which are related by a nonlinear canonical transformation to the collective variables, i.e., the density fluctuation operators and their canonical conjugates. The transformation is presented in terms of a series in powers of N−1/2. The ground-state energy appears as a series in powers of N−1. The perturbation contributions of order N−2 to the ground-state energy are calculated. Most of these contributions can be incorporated into the lower order ones which agree with the previously obtained results.

DOI
10.1143/ptp.68.1050

Related papers

GROUND-STATE ENERGY DENSITY OF A DILUTE BOSE GAS IN THE CANONICAL TRANSFORMATION

Sang‐Hoon Kim, CHUL KU KIM, Mukunda P. Das

The ground-state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order na3 in the particle depletion and ground-state energy density of a dilute Bose gas system, which corresponds to the density fluctuation resulting from the excited states. Considering a two-body interaction only, the coefficient of the na3 term is shown to be 2(π-8/3) for the particle depletion, and 16(π-8/3) for the ground-state energy density.

arXiv:cond-mat/0603479•International Journal of Modern Physics B•Dec 30, 2007•0 citations

A Method of a Quasi-Linear Canonical Transformation for the Many-Body Problem. II

Shokichi Kanno

We apply the method of quasi-linear canonical transformation proposed in a previous paper to the system of N interacting bosons, and we calculate the excitation energy for the dilute hard-sphere Bose gas. In our formulation the total number of the particles are exactly conserved in contrast with the Bogoliubov theory. There appears no logarithmic divergent term in the physical quantities which correspond to the self-energy operators Σ11 and Σ02 appearing in the method of Green's function.

Progress of Theoretical Physics•May 1, 1969•1 citation

Ground State Energy of Bose Particle System

Ryuzo Abe

The ground state energy of the Bose particle system at low densities is investigated by using the method which is based on summing up the terms of the conventional perturbation series giving rise to the lowest order with respect to the density. The summation is shown to be greatly simplified if the scattering matrix is introduced, and a simple example is demonstrated for the repulsive square well potential by calculating a few terms of the series first directly and secondly with the aid of scattering matrix. The final result is shown to be valid both for weak and strong interactions and the calculation is carried out analytically for some types of potential function. The connection of the present method with the pseudopotential method and with the Brueckner theory is investigated and some problems associated with the attractive interactions are discussed.

Progress of Theoretical Physics•Dec 1, 1958•2 citations

Ground-state energy of the spinor Bose-Einstein condensate

Wen-Jui Huang, Shih-Chuan Gou

It is known that for a weakly interacting Bose-Einstein condensate (BEC), the assumption of a two-body $\ensuremath{\delta}$ interaction described by a constant coupling strength gives rise to a divergent ground-state energy. A similar divergence occurs in the spinor condensate in which the spin-spin interaction is included in addition to the repulsive $\ensuremath{\delta}$ interaction. In this paper, we examine, in the standard Bogoliubov approximation, the ground-state energy of a homogeneous spinor BEC with hyperfine spin $f=1.$ The renormalized coupling constants are calculated and expressed in terms of the bare ones using the standard second-order perturbation method. With these renormalized coupling constants, we show that the ultraviolet divergence of the ground-state energy can be exactly eliminated.

arXiv:cond-mat/9809153•Physical Review A•Jun 1, 1999•22 citations

Ground-State Energy of a Many-Particle Boson System

Deok Kyo Lee

The ground state of a many-particle boson system is studied for two closely related limits: the uniform limit and the weak coupling limit. The former is defined by $\ensuremath{\alpha}=1\ensuremath{-}g(0)\ensuremath{\ll}1$ and the latter by $\ensuremath{\beta}=\frac{(N\ensuremath{-}{N}_{0})}{N}\ensuremath{\ll}1$, where $g(r)$ is the radial distribution function and ${N}_{0}$ is the mean occupation number of the zero-momentum state. In the uniform limit the variation-perturbation approach based on (a) the method of correlated basis functions and (b) the series expansion in powers of $\ensuremath{\alpha}$ is found to be equivalent to the field-theoretic treatment given by Brueckner (for the charged-boson gas) in the weak coupling limit. In particular, it is shown that the variation-perturbation energy obtained for the uniform limit in the momentum representation is identical through second order to the ground-state energy evaluated for $\ensuremath{\beta}\ensuremath{\ll}1$ by summing one- and two-ring diagrams in the Bogoliubov occupation-number representation. The charged-boson gas and the one-dimensional boson system with a $\ensuremath{\delta}$-function interaction are considered to examine some of the interesting features of the uniform-limit procedure.

Physical Review A•Oct 1, 1971•29 citations

Three-Particle Correlations in the Ground State of a Bose Fluid

Shuichiro Yamasaki, Masahiko HIROOKA

The three-particle structure function in the ground state of a boson system is studied in a formalism which establishes phonon type quasi-particles coupled to each other by the residual interaction preserving the linearity of the spectrum. The leading order results agree with those from the unquantized theories of Bogoliubov-Zubarev and Feenberg, et al. The next order corrections are calculated, and one of them is found to bear a strong resemblance to the result of Lee and Lee. Possible relations of the present formalism to the correlated basis function method in the uniform limit are discussed on a phenomenological level.

Progress of Theoretical Physics•Oct 1, 1981•2 citations
The ground-state energy of a system of interacting N-bosons is investigated in a collective formalism. Ultraviolet divergences in perturbation calculations are eliminated by the introduction of quasi-particle operators which are related by a nonlinear canonical transformation to the collective variables, i.e., the density fluctuation operators and their canonical conjugates. The transformation is presented in terms of a series in powers of N−1/2. The ground-state energy appears as a series in powers of N−1. The perturbation contributions of order N−2 to the ground-state energy are calculated. Most of these contributions can be incorporated into the lower order ones which agree with the previously obtained results.
The ground-state energy density of an interacting dilute Bose gas system is studied in the canonical transformation scheme. It is shown that the transformation scheme enables us to calculate a higher order correction of order na3 in the particle depletion and ground-state energy density of a dilute Bose gas system, which corresponds to the density fluctuation resulting from the excited states. Considering a two-body interaction only, the coefficient of the na3 term is shown to be 2(π-8/3) for the particle depletion, and 16(π-8/3) for the ground-state energy density.
The ground state energy of the Bose particle system at low densities is investigated by using the method which is based on summing up the terms of the conventional perturbation series giving rise to the lowest order with respect to the density. The summation is shown to be greatly simplified if the scattering matrix is introduced, and a simple example is demonstrated for the repulsive square well potential by calculating a few terms of the series first directly and secondly with the aid of scattering matrix. The final result is shown to be valid both for weak and strong interactions and the calculation is carried out analytically for some types of potential function. The connection of the present method with the pseudopotential method and with the Brueckner theory is investigated and some problems associated with the attractive interactions are discussed.
It is known that for a weakly interacting Bose-Einstein condensate (BEC), the assumption of a two-body $\ensuremath{\delta}$ interaction described by a constant coupling strength gives rise to a divergent ground-state energy. A similar divergence occurs in the spinor condensate in which the spin-spin interaction is included in addition to the repulsive $\ensuremath{\delta}$ interaction. In this paper, we examine, in the standard Bogoliubov approximation, the ground-state energy of a homogeneous spinor BEC with hyperfine spin f=1.f=1.f=1. The renormalized coupling constants are calculated and expressed in terms of the bare ones using the standard second-order perturbation method. With these renormalized coupling constants, we show that the ultraviolet divergence of the ground-state energy can be exactly eliminated.
The ground state of a many-particle boson system is studied for two closely related limits: the uniform limit and the weak coupling limit. The former is defined by $\ensuremath{\alpha}=1\ensuremath{-}g(0)\ensuremath{\ll}1$ and the latter by $\ensuremath{\beta}=\frac{(N\ensuremath{-}{N}_{0})}{N}\ensuremath{\ll}1$, where g(r)g(r)g(r) is the radial distribution function and N0{N}_{0}N0​ is the mean occupation number of the zero-momentum state. In the uniform limit the variation-perturbation approach based on (a) the method of correlated basis functions and (b) the series expansion in powers of $\ensuremath{\alpha}$ is found to be equivalent to the field-theoretic treatment given by Brueckner (for the charged-boson gas) in the weak coupling limit. In particular, it is shown that the variation-perturbation energy obtained for the uniform limit in the momentum representation is identical through second order to the ground-state energy evaluated for $\ensuremath{\beta}\ensuremath{\ll}1$ by summing one- and two-ring diagrams in the Bogoliubov occupation-number representation. The charged-boson gas and the one-dimensional boson system with a $\ensuremath{\delta}$-function interaction are considered to examine some of the interesting features of the uniform-limit procedure.
The three-particle structure function in the ground state of a boson system is studied in a formalism which establishes phonon type quasi-particles coupled to each other by the residual interaction preserving the linearity of the spectrum. The leading order results agree with those from the unquantized theories of Bogoliubov-Zubarev and Feenberg, et al. The next order corrections are calculated, and one of them is found to bear a strong resemblance to the result of Lee and Lee. Possible relations of the present formalism to the correlated basis function method in the uniform limit are discussed on a phenomenological level.