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:cond-mat/0204432 · Annals of Physics

Electrostatic Analogy for Integrable Pairing Force Hamiltonians

Luigi Amico A, Antonio Di Lorenzo, A. Mastellone, A. Osterloh, R. Raimondi

Published Aug 1, 2002• 32 citations
arXivHTMLPDF
DOI
10.1006/aphy.2002.6277

Related papers

Exact eigenstates of the pairing-force Hamiltonian

R. W. Richardson, Noah Sherman

Nuclear Physics•Mar 1, 1964•484 citations

Exact Eigenstates of the Pairing-Force-Hamiltonian. I Fermion System

Ikuro Shimose, Yasumitsu Akiyoshi

•Oct 20, 1973•0 citations

Electrostatic analogy for integrable pairing force Hamiltonians

Luigi Amico A, Antonio Di Lorenzo, Andrea Mastellone +2 more

For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.

•Jan 1, 2002•19 citations

Integrability of the pairing hamiltonian

M. C. Cambiaggio, Alejandro M. F. Rivas, Marcos Saraceno

arXiv:nucl-th/9708031•Nuclear Physics A•Oct 1, 1997•166 citations

Non-skew-symmetric classical r-matrices, algebraic Bethe ansatz, and Bardeen–Cooper–Schrieffer–type integrable systems

T. Skrypnyk

We construct quantum integrable systems associated with non-skew-symmetric gl(2)-valued classical r-matrices. We find a new explicit multiparametric family of such the non-skew-symmetric classical r-matrices. We consider two classes of examples of the corresponding integrable systems, namely generalized Gaudin systems with and without an external magnetic field. In the case of arbitrary r-matrices diagonal in a standard gl(2)-basis, we calculate the spectrum of the corresponding quantum integrable systems using the algebraic Bethe ansatz. We apply these results to a construction of integrable fermionic models and obtain a wide class of integrable Bardeen–Cooper–Schrieffer (BCS)-type fermionic Hamiltonians containing the pairing and electrostatic interaction terms. We also consider special cases when the corresponding integrable Hamiltonians contain only pairing interaction term and are exact analogs of the “reduced BCS Hamiltonian” of Richardson.

Journal of Mathematical Physics•Mar 1, 2009•49 citations

Quantum simulation of pairing Hamiltonian

Nabeel Salim, P. Arumugam

Journal of subatomic particles and cosmology.•Oct 10, 2026•0 citations
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a wider class of integrable Hamiltonians with pairing force interactions. We apply it to obtain the exact thermodynamic limit of this class of models. To verify the analytical results, we compare them with numerical solutions of the Bethe ansatz equations for finite systems at half-filling for the ground state.
We construct quantum integrable systems associated with non-skew-symmetric gl(2)-valued classical r-matrices. We find a new explicit multiparametric family of such the non-skew-symmetric classical r-matrices. We consider two classes of examples of the corresponding integrable systems, namely generalized Gaudin systems with and without an external magnetic field. In the case of arbitrary r-matrices diagonal in a standard gl(2)-basis, we calculate the spectrum of the corresponding quantum integrable systems using the algebraic Bethe ansatz. We apply these results to a construction of integrable fermionic models and obtain a wide class of integrable Bardeen–Cooper–Schrieffer (BCS)-type fermionic Hamiltonians containing the pairing and electrostatic interaction terms. We also consider special cases when the corresponding integrable Hamiltonians contain only pairing interaction term and are exact analogs of the “reduced BCS Hamiltonian” of Richardson.