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

Quantum Physics Letters

Recursive Construction of the Bosonic Bogoliubov Vacuum State

D. Portes, Marcos O Pinho, Hilário Rodrigues

Published Apr 1, 2013• 1 citation
Publisher

Abstract

Abstract: In this work we derive a novel procedure for obtaining the bosonic Bogoliubov vacuum states by using a recursive scheme. The vacuum state for the new creation and annihilation operators is explicitly constructed in terms of the number states of the old operators, which are connected by a Bogoliubov transformation. The coefficients of the ground state in Fock basis are thus obtained as exclusive functions of the parameters of the Bogoliubov transformations.

DOI
10.12785/qpl/020102

Related papers

The explicit determination of the linear boson transformation coefficients

K. Tanabe

The problem of determining the wavefunction is solved for the boson Bogoliubov transformation. The method of series expansion is applied to derive the general expression for the coefficients which connect the new Fock states of an arbitrary number of quasiparticles with the states before the transformation.

Journal of Mathematical Physics•May 1, 1973•25 citations

New results about the canonical transformation for boson operators

C. M. Raduta, A. A. Raduta

The Bogoliubov transformation for a monopole boson induces a unitary transformation connecting the Fock spaces of initial and correlated bosons. Here, we provide a very simple method for deriving the analytical expression for the overlap matrix of the basis states generating the two boson spaces.

arXiv:2012.05092•International Journal of Modern Physics E•Feb 10, 2021•0 citations

Some New Expressions for Vacuum Projection Operators of q -Deformed Boson Oscillators

Hong-Yi Fan, Sicong Jing

We derive some new expressions for the vacuum projection operator of q-deformed boson oscillators. A recursion method is essential to our derivation of the power series expansion of the vacuum projection operator in terms of the q-creation and q-annihilation operators.

Communications in Theoretical Physics•Oct 1, 1993•1 citation

Linear boson transformation coefficients

Arvind Narayan Vaidya

A simple expression for the coefficients which connect a Fock state containing an arbitrary number of quasiparticles with its tranformed state under a boson Bogoliubov transformation is obtained.

Journal of Mathematical Physics•Jun 1, 1976•0 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

Generalised Bogoliubov transformation coefficients for para-Bose states

H. E. De Meyer, Guido Vanden Berghe

Simple expressions are obtained for the coefficients which connect a para-Bose state containing an arbitrary number of quasiparticles with its transformed state under a real boson and a complex generalised Bogoliubov transformation.

Journal of Physics A Mathematical and General•Jan 1, 1980•8 citations
Abstract: In this work we derive a novel procedure for obtaining the bosonic Bogoliubov vacuum states by using a recursive scheme. The vacuum state for the new creation and annihilation operators is explicitly constructed in terms of the number states of the old operators, which are connected by a Bogoliubov transformation. The coefficients of the ground state in Fock basis are thus obtained as exclusive functions of the parameters of the Bogoliubov transformations.
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.