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Integrable model for interacting electrons in metallic grains.

L Amico¹, A Di Lorenzo, A Osterloh

¹Dipartimento di Metodologie Fisiche e Chimiche, Università di Catania, viale Andrea Doria 6, I-95125 Catania, Italy.

Physical Review Letters

|June 21, 2001

Summary

We present an integrable Bardeen-Cooper-Schrieffer (BCS) model with nonuniform interactions. This model, solvable via Bethe ansatz, offers insights into quantum systems like superconducting grains.

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Area of Science:

Condensed Matter Physics
Quantum Many-Body Systems
Superconductivity

Background:

The Bardeen-Cooper-Schrieffer (BCS) model is foundational for understanding conventional superconductivity.
Investigating integrable models provides exact solutions and deeper insights into complex quantum phenomena.
Nonuniform interactions are crucial for understanding mesoscopic superconducting systems.

Purpose of the Study:

To introduce and solve an integrable generalization of the BCS model.
To explore the role of nonuniform Coulomb and pairing interactions.
To discuss potential applications in mesoscopic superconductivity.

Main Methods:

Constructing a Hamiltonian based on commuting operators, ensuring integrability.
Utilizing the Bethe ansatz for the exact diagonalization of the Hamiltonian.

Related Experiment Videos

Analyzing the 'isotropic limit' to recover uniform interaction cases.

Main Results:

An integrable BCS model with nonuniform Coulomb and pairing interactions was derived.
The model's Hamiltonian is a functional of commuting operators, acting as constants of motion.
Exact solutions were obtained through the diagonalization of anisotropic Gaudin Hamiltonians via Bethe ansatz.

Conclusions:

The developed integrable model provides an exact solution framework for BCS systems with spatial variations.
The model's framework is applicable to understanding superconductivity in single and few interacting grains.
This work extends the applicability of integrable models to more realistic condensed matter scenarios.