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

Collective Description of a System of Interacting Bose Particles. I

Sigenobu Sunakawa, Yoshimatsu Yokoo, Hiroshi Nakatani

Published Mar 1, 1962• 28 citations
Publisher

Abstract

The collective description of the one-dimensional interacting Bose system is studied. The exact canonical conjugate of the density operator is given explicitly. The Hamiltonian of the system is expressed in terms of the exact collective variables.
DOI
10.1143/ptp.27.589

Related papers

Collective Description of a System of Interacting Bose Particles. II

Sigenobu Sunakawa, Hiroshi Nakatani, Yoshimatsu Yokoo

The collective behavior of the three-dimensional Bose system is investigated. Along the line of reasoning of the preceding paper, the momentum density operator is modified and it is shown that the modified momentum density operator is equivalent to the velocity operator of the quantum hydrodynamics. The Hamiltonian is described in terms of the collective variables for the case of irrotational motion. The result is compared with other theories.

Progress of Theoretical Physics•Mar 1, 1962•11 citations

On the Phonon-Phonon Interaction in a System of Bose Particles

Sigenobu Sunakawa, Yoshimatsu Yokoo, Hiroshi Nakatani

The definite expression of the phonon-phonon interaction in a Bose system is derived up to the order of N-1 in terms of the density operator and its exact canonical conjugate which was introduced in the previous papers. We find some mathematical ambiguity in the course of calculation, and clarify the reason why the different results were obtained so far. The validity of our formalism is discussed from the physical point of view.

Progress of Theoretical Physics•Jul 1, 1962•7 citations

On the Exact Canonical Conjugate Momenta of Collective Motion in Many-Boson System

Masayoshi Nakamura, Ryō Suzuki

The exact canonical momenta conjugate to collective coordinates are proposed for the description of quantum-mechanical collective motion in a ment-boson system. The present procedure gives rise to the possibility of extension of Tomonaga's theory to the three-dimensional case.

Progress of Theoretical Physics•Sep 1, 1980•3 citations

One-Dimensional Many Boson System. III: Unitary Transformation and Exactly Dressed Bose Particle

Shosuke Sasaki, T. Kebukawa

A unitary operator, which transforms free states into the exact eigenstates for a one-dimensional many boson system with repulsive delta-function potential, is explicitly constructed. By the unitary operator, original bare creation and annihilation operators are transformed into new operators which are shown to create or annihilate the exactly dressed bosons with the interaction cloud. The total Hamiltonian, total number and total momentum in the system are expressed in the diagonalized form in terms of the dressed operators. It is shown that the exact ground state is the condensed state of all exactly dressed bosons with zero momentum.

Progress of Theoretical Physics•Jun 1, 1981•5 citations

Ideal bose gas in an oscillator potential (exact solution)

Е. А. Титов

Exact expressions for the statistical sum of the grand canonical ensemble and the one-particle density matrix are derived based on the definition of the density matrix for a system of N identical noninteracting Bose particles in an oscillator potential as a sum with respect to the symmetric exchange of the density matrix coordinates of distinguishable particles. A quasi-classical scenario is analyzed in detail.

Laser Physics•Jun 28, 2006•0 citations

On the Validity of Collective Variable Description of Bose Systems

Minoru Takahashi

The validity of Sunakawa, Yamasaki and Kebukawa's Hamiltonian and that of Bogoliubov and Zubarev's Hamiltonian are examined. Perturbational expansion of the ground state energy by these Hamiltonians disagrees with the exact solution of Lieb and Liniger for one-dimensional Bose system with repulsive delta-function interaction. This fact suggests that these Hamiltonians are not microscopic descriptions of the many-Boson system. Mathematical inconsistency in Bogoliubov and Zubarev's theory is also pointed out. Moreover analytic expression of high density expansion for the ground state energy density e0 is found out to be e0n-3=γ-(4/3π)γ3/2+(1/6-1/π2)γ2+O(γ5/2), γ≡c/n, for one-dimensional Bose system with delta function interaction (density n, strength 2c, ħ=2m=1) by the use of the correlated basis function method.

Progress of Theoretical Physics•Feb 1, 1975•33 citations
A unitary operator, which transforms free states into the exact eigenstates for a one-dimensional many boson system with repulsive delta-function potential, is explicitly constructed. By the unitary operator, original bare creation and annihilation operators are transformed into new operators which are shown to create or annihilate the exactly dressed bosons with the interaction cloud. The total Hamiltonian, total number and total momentum in the system are expressed in the diagonalized form in terms of the dressed operators. It is shown that the exact ground state is the condensed state of all exactly dressed bosons with zero momentum.
The validity of Sunakawa, Yamasaki and Kebukawa's Hamiltonian and that of Bogoliubov and Zubarev's Hamiltonian are examined. Perturbational expansion of the ground state energy by these Hamiltonians disagrees with the exact solution of Lieb and Liniger for one-dimensional Bose system with repulsive delta-function interaction. This fact suggests that these Hamiltonians are not microscopic descriptions of the many-Boson system. Mathematical inconsistency in Bogoliubov and Zubarev's theory is also pointed out. Moreover analytic expression of high density expansion for the ground state energy density e0 is found out to be e0n-3=γ-(4/3π)γ3/2+(1/6-1/π2)γ2+O(γ5/2), γ≡c/n, for one-dimensional Bose system with delta function interaction (density n, strength 2c, ħ=2m=1) by the use of the correlated basis function method.