In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usual...In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators＇ commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.展开更多
In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and it...In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.展开更多
We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representatio...We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representation for describing electrons in uniform magnetic field is used.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10574060
文摘In the literature about mesoscopic Josephson devices the magnetic flux is considered as an operator, the fundamental commutative relation between the magnetic flux operator and the Cooper-pair charge operator is usually preengaged. In this paper we show that such a relation can be deduced from the basic Bose operators＇ commutative relation through the entangled state representation. The Faraday formula in bosonic form is then equivalent to the second Josephson equation. The current operator equation for LC mesoscopic circuit is also derived.
基金Supported by the National Natural Science Foundation of China under Grant No.10874174 the Specialized Reserach Fund for The Doctoral Progress of Higher Education of China under Grant No.20070358009
文摘In this paper we set up quantum mechanical correspondence of the Poisson integral formula.We show that Poisson kernel function existing in the transformation between the continuum entangled state representation and its induced state,i.e.the number-difference-correlated amplitude entangled state representation.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representation for describing electrons in uniform magnetic field is used.
