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

arXiv:1206.1645 · Progress of Theoretical Physics

A Role of the Quasiparticle in the Conservation of the Fermion Number: -- An Example Illustrative of the Deformation of the Cooper Pair --

Y. Tsue, Constança Providência, João da Providência, M. Yamamura

Published Oct 1, 2012• 1 citation
arXivHTMLPDF

Abstract

The role of the “quasiparticle" introduced in the previous paper by the present authors is discussed. It serves as a guide for the deformation of the Cooper-pair in the BCS-Bogoliubov approach. As an illustrative example, a certain case is treated. This case produces the su(1,1)-like behavior in the su(2)-algebraic many-fermion system.

DOI
10.1143/ptp.128.717

Related papers

The BCS-Bogoliubov and the su(2)-Algebraic Approach to the Pairing Model in Many-Fermion System: -- The Quasiparticle in the Conservation of the Fermion Number --

Y. Tsue, Constança Providência, João da Providência +1 more

The relation between two approaches to the su(2)-algebraic many-fermion model is discussed: (1) the BCS-Bogoliubov approach in terms of the use of the quasiparticles representing all the degrees of freedom except those related to the Cooper-pairs and (2) the conventional algebraic approach in terms of the use of the minimum weight states, from which the Cooper-pairs are excluded. In order to arrive at the goal, the idea of the quasiparticles is brought up in the conservation of the fermion number. Under the c-number replacement for the three su(2)-generators, the quasiparticles suggested in this paper are reduced to those in the BCS-Bogoliubov approach. It is also shown that the two approaches are equivalent through the c-number replacement. Further, a certain modification of the BCS-Bogoliubov approach is discussed.

arXiv:1206.1644•Progress of Theoretical Physics•Oct 1, 2012•1 citation

A pseudo su(1,1)-algebraic deformation of the Cooper pair in the su(2)-algebraic many-fermion model

Y. Tsue, Constança Providência, João da Providência +1 more

A pseudo su(1,1)-algebra is formulated as a possible deformation of the Cooper pair in the su(2)-algebraic many-fermion system. With the aid of this algebra, it is possible to describe the behavior of individual fermions which are generated as the result of interaction with the external environment. The form presented in this paper is a generalization of a certain simple case developed recently by the authors. The basic idea follows the su(1,1) algebra in the Schwinger boson representation for treating energy transfer between the harmonic oscillator and the external environment. The Hamiltonian is given following the idea of phase space doubling in the thermo-field dynamics formalism, and the time-dependent variational method is applied to this Hamiltonian. Its trial state is constructed in the frame deformed from the BCS-Bogoliubov approach to superconductivity. Several numerical results are shown.

arXiv:1306.3282•Progress of Theoretical and Experimental Physics•Oct 18, 2013•0 citations

QUANTUM GROUP SU Q(2) AND PAIRING IN NUCLEI

S. Shelly Sharma, Naresh Kumar Sharma

A scheme for treating the pairing of nucleons in terms of generators of Quantum Group SU_{q}(2) is presented. The possible applications to nucleon pairs in a single orbit, multishell case, pairing vibrations and superconducting nuclei are discussed. The formalism for performing BCS calculations with q-deformed nucleon pairs is constructed and the role played by deformation parameter q analyzed in the context of nucleons in a single orbit and for Sn Isotopes.

arXiv:nucl-th/0009048•Feb 1, 2001•0 citations

Microscopic Model of Quasiparticle Wave Packets in Superfluids, Superconductors, and Paired Hall States

S. A. Parameswaran, Steven Allan Kivelson, R. Shankar +2 more

We study the structure of Bogoliubov quasiparticles, bogolons, the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: in a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.

arXiv:1202.3444•Physical Review Letters•Dec 5, 2012•9 citations

Cooper Pair with Nonzero Momentum in System with Spin Dependent Mass of Quasiparticles

Jan Kaczmarczyk, Józef Spałek

We consider a single Cooper pair with the spin dependent quasiparticle masses, with and without applied magnetic field.Such situation takes place for the strongly correlated electron systems, where a relatively strong Hubbard interaction differentiates the quasiparticle states in the majorityand the minority-spin subbands.In that situation, the two spin subbands in an applied magnetic field are not only shifted one with respect to the other, but also distorted differently, which results from the electronic correlations.Under these circumstances, the fermionic particles composing the Cooper pair, are quantum mechanically distinguishable.In result, the Cooper pair has a nonzero momentum (i.e.produces a stationary current in a similar manner as electron in the Bloch state), and there exists a critical value of the attractive interaction, below which the bound Cooper-pair state is not formed.The presence of the applied field (included via the Zeeman term) does not alter the picture qualitatively.Importance of these results for the formation of the Fulde-Ferrell-Larkin-Ovchinnikov phase in strongly correlated systems is mentioned.

Acta Physica Polonica A•Apr 1, 2007•3 citations

What is a Cooper pair ?

Gerardo Ortíz, J. Dukelsky

Recently, the nature of Cooper pairs in the BCS-BEC crossover has regained attention due to the observation of a large fraction of preformed fermion pairs on the BCS side of the Feshbach resonance in ultracold atomic Fermi gases. While several theoretical explanations were proposed, the interpretations are still controversial. The root of the controversy is understanding what represents a Cooper pair in a correlated Fermi system. This paper discusses these issues at the most elementary level.

arXiv:cond-mat/0604236•Apr 9, 2006•0 citations
The role of the “quasiparticle" introduced in the previous paper by the present authors is discussed. It serves as a guide for the deformation of the Cooper-pair in the BCS-Bogoliubov approach. As an illustrative example, a certain case is treated. This case produces the su(1,1)-like behavior in the su(2)-algebraic many-fermion system.
The relation between two approaches to the su(2)-algebraic many-fermion model is discussed: (1) the BCS-Bogoliubov approach in terms of the use of the quasiparticles representing all the degrees of freedom except those related to the Cooper-pairs and (2) the conventional algebraic approach in terms of the use of the minimum weight states, from which the Cooper-pairs are excluded. In order to arrive at the goal, the idea of the quasiparticles is brought up in the conservation of the fermion number. Under the c-number replacement for the three su(2)-generators, the quasiparticles suggested in this paper are reduced to those in the BCS-Bogoliubov approach. It is also shown that the two approaches are equivalent through the c-number replacement. Further, a certain modification of the BCS-Bogoliubov approach is discussed.
A pseudo su(1,1)-algebra is formulated as a possible deformation of the Cooper pair in the su(2)-algebraic many-fermion system. With the aid of this algebra, it is possible to describe the behavior of individual fermions which are generated as the result of interaction with the external environment. The form presented in this paper is a generalization of a certain simple case developed recently by the authors. The basic idea follows the su(1,1) algebra in the Schwinger boson representation for treating energy transfer between the harmonic oscillator and the external environment. The Hamiltonian is given following the idea of phase space doubling in the thermo-field dynamics formalism, and the time-dependent variational method is applied to this Hamiltonian. Its trial state is constructed in the frame deformed from the BCS-Bogoliubov approach to superconductivity. Several numerical results are shown.
We study the structure of Bogoliubov quasiparticles, bogolons, the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: in a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.
We consider a single Cooper pair with the spin dependent quasiparticle masses, with and without applied magnetic field.Such situation takes place for the strongly correlated electron systems, where a relatively strong Hubbard interaction differentiates the quasiparticle states in the majorityand the minority-spin subbands.In that situation, the two spin subbands in an applied magnetic field are not only shifted one with respect to the other, but also distorted differently, which results from the electronic correlations.Under these circumstances, the fermionic particles composing the Cooper pair, are quantum mechanically distinguishable.In result, the Cooper pair has a nonzero momentum (i.e.produces a stationary current in a similar manner as electron in the Bloch state), and there exists a critical value of the attractive interaction, below which the bound Cooper-pair state is not formed.The presence of the applied field (included via the Zeeman term) does not alter the picture qualitatively.Importance of these results for the formation of the Fulde-Ferrell-Larkin-Ovchinnikov phase in strongly correlated systems is mentioned.