A Pseudo su(1,1)-Algebraic Deformation of the Cooper-Pair in the su(2)-Algebraic Many-Fermion Model

TL;DR

This paper introduces a pseudo su(1,1)-algebraic deformation of the Cooper-pair model to describe fermion behavior interacting with an environment, extending previous models with a phase space doubling approach.

Contribution

It formulates a novel pseudo su(1,1)-algebraic deformation of the Cooper-pair in the su(2)-algebraic fermion system, incorporating environment interactions and phase space doubling.

Findings

Numerical results demonstrating the model's behavior

Extension of previous simple models

Application of time-dependent variational method

Abstract

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 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 present authors. 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. Hamiltonian is given under the idea of the 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 the superconductivity. Several numerical results are shown.