PreprintCC BY 4.0arXiv
A simple derivation of the zero-temperature BCS functional from the reduced BCS Hamiltonian
Abstract
We consider a grand-canonical reduced BCS Hamiltonian on the full fermionic Fock space with an attractive pairing interaction supported in an energy shell around the Fermi surface. For fixed chemical potential, we prove that the exact finite-volume ground-state energy differs from the minimum of the corresponding finite-volume BCS functional by a volume-independent error. As a consequence, the BCS variational principle is exact for the ground-state energy density in the thermodynamic limit.
Related
- Hamiltonian dynamics with nonconservative forces on extended phase space: An analytical mechanics derivation
- A simple derivation of the Kalman filter
- On the Minimum Number of Hamilton Cycles in Hamiltonian Threshold Graphs: A Simple Proof
- Reduced Solutions of Toda Systems for Arbitrary Complex Simple Lie Algebras
- Hamiltonian Interface Dynamics for Reduced-Order Optimization of Incompressible Mixing
BibTeX
@misc{hainzl2026simple,
title = {{A simple derivation of the zero-temperature BCS functional from the reduced BCS Hamiltonian}},
author = {Christian Hainzl and Riccardo Panza},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04060},
eprint = {2609.04060},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04060},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A simple derivation of the zero-temperature BCS functional from the reduced BCS Hamiltonian
AU - Christian Hainzl
AU - Riccardo Panza
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04060
UR - https://arxiv.org/abs/2609.04060
AB - We consider a grand-canonical reduced BCS Hamiltonian on the full fermionic Fock space with an attractive pairing interaction supported in an energy shell around the Fermi surface. For fixed chemical potential, we prove that the exact finite-volume ground-state energy differs from the minimum of the corresponding finite-volume BCS functional by a volume-independent error. As a consequence, the BCS variational principle is exact for the ground-state energy density in the thermodynamic limit.
ER -