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

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

On the criteria for the best bogoliubov quasi-particle

Vedene H. Smith

Published Apr 1, 1967• 3 citations
Publisher
DOI
10.1007/bf02712205

Related papers

Self-energy of the bogoliubov quasi particle

Donald H. Kobe

Annals of Physics•Jul 1, 1964•10 citations

Self-energy of the bogoliubov quasi particle

Donald H. Kobe

Annals of Physics•May 1, 1964•0 citations

Origins of bright soliton transparency to Bogoliubov quasi-particles

Zaijong Hwang, Andrew Koller, Maxim Olshanii

Bulletin of the American Physical Society•Jun 8, 2012•0 citations

Criteria for the Best Bogoliubov Quasiparticle

Donald H. Kobe

The principle of compensation of dangerous diagrams has previously been the only general criterion for determining the coefficients in the Bogoliubov canonical transformation to quasiparticles. In this paper it is shown that the criterion of maximum overlap of the true ground state with the BCS ground state gives the same condition for determining the coefficients. The criterion of diagonalizing the quadratic part of the reaction operator, which is a generalization of the Brillouin-Brueckner condition, is also equivalent to the above criteria. Finally these criteria are evaluated from the standpoint of "least labor for the most accuracy."

Physical Review•Nov 1, 1965•14 citations

Derivation of the Principle of Compensation of Dangerous Diagrams

Donald H. Kobe

The principle of compensation of dangerous diagrams (PCDD) postulated by Bogoliubov to determine the coefficients in the canonical transformation to quasi-particles in superconducting systems is derived from four different criteria (1) the expected number of quasi-particles in the true ground state is a minimum, (2) the one-particle density matrix and the two-particle amplitude determined from the BCS ground state are equated to the true ones, (3) the expectation value of an arbitrary operator is simplified by diagonalizing its quadratic part, and (4) the starting point for the dressing of the quasi-particle is chosen in the most convenient way. The condition obtained for the PCDD is then expressed in terms of quasi-particle Green's functions. The ladder diagrams are eliminated by examining an integral equation for the Green's function describing the creation of two quasi-particles from the vacuum. Finally, the condition obtained here for the PCDD is compared with the condition obtained previously.

Journal of Mathematical Physics•Jun 1, 1967•11 citations

On the “strong-coupling” generalization of the Bogoliubov model

A.Yu. Cherny, Arkady A Shanenko

arXiv:cond-mat/9811405•Physics Letters A•Dec 1, 1998•6 citations
The principle of compensation of dangerous diagrams has previously been the only general criterion for determining the coefficients in the Bogoliubov canonical transformation to quasiparticles. In this paper it is shown that the criterion of maximum overlap of the true ground state with the BCS ground state gives the same condition for determining the coefficients. The criterion of diagonalizing the quadratic part of the reaction operator, which is a generalization of the Brillouin-Brueckner condition, is also equivalent to the above criteria. Finally these criteria are evaluated from the standpoint of "least labor for the most accuracy."
The principle of compensation of dangerous diagrams (PCDD) postulated by Bogoliubov to determine the coefficients in the canonical transformation to quasi-particles in superconducting systems is derived from four different criteria (1) the expected number of quasi-particles in the true ground state is a minimum, (2) the one-particle density matrix and the two-particle amplitude determined from the BCS ground state are equated to the true ones, (3) the expectation value of an arbitrary operator is simplified by diagonalizing its quadratic part, and (4) the starting point for the dressing of the quasi-particle is chosen in the most convenient way. The condition obtained for the PCDD is then expressed in terms of quasi-particle Green's functions. The ladder diagrams are eliminated by examining an integral equation for the Green's function describing the creation of two quasi-particles from the vacuum. Finally, the condition obtained here for the PCDD is compared with the condition obtained previously.