14 citations · 71 across the 18 of their papers we have counts for
18 papers
The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition
Shuji Watanabe
We deal with a type I superconductor in a constant external magnetic field. We obtain the BCS-Bogoliubov gap equation with external magnetic field and apply the implicit function t…
Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity
Shuji Watanabe
In the preceding papers, imposing certain complicated and strong conditions, the present author showed that the solution to the BCS-Bogoliubov gap equation in superconductivity is…
An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature
Shuji Watanabe
In the preceding papers the present author gave another proof of the existence and uniqueness of the solution to the BCS-Bogoliubov gap equation for superconductivity from the view…
An operator-theoretical study of the specific heat and the critical magnetic field in the BCS-Bogoliubov model of superconductivity
Shuji Watanabe
In the preceding paper, introducing a cutoff, the present author gave a proof of the statement that the transition to a superconducting state is a second-order phase transition in…
An operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity (final version)
Shuji Watanabe
We show that the transition from a normal conducting state to a superconducting state is a second-order phase transition in the BCS-Bogoliubov model of superconductivity from the v…
Smoothness and monotone decreasingness of the solution to the BCS-Bogoliubov gap equation for superconductivity
Shuji Watanabe, Ken Kuriyama
We show the temperature dependence such as smoothness and monotone decreasingness with respect to the temperature of the solution to the BCS-Bogoliubov gap equation for superconduc…
An operator theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity
Shuji Watanabe
We first show some properties such as smoothness and monotone decreasingness of the solution to the BCS-Bogoliubov gap equation for superconductivity. Moreover we give the behavior…
Lipschitz continuity and monotone decreasingness of the solution to the BCS gap equation for superconductivity
Shuji Watanabe, Ken Kuriyama
In the preceding work \cite{watanabe3}, it is shown that the solution to the BCS gap equation for superconductivity is continuous with respect to both the temperature and the energ…
Landau-Lifshitz's conjecture about the motion of a quantum mechanical particle under the inverse square potential
Motohiro Sobajima, Shuji Watanabe
Landau and Lifshitz [4, Section 35] conjectured that for an arbitrary , there exists the motion of a quantum mechanical particle under the inverse square potential…
The solution to the BCS gap equation for superconductivity and its temperature dependence
Shuji Watanabe
From the viewpoint of operator theory, we deal with the temperature dependence of the solution to the BCS gap equation for superconductivity. When the potential is a positive const…
Characterization of point transformations in quantum mechanics
Yoshio Ohnuki, Shuji Watanabe
We characterize point transformations in quantum mechanics from the mathematical viewpoint. To conclude that the canonical variables given by each point transformation in quantum m…
An operator-theoretical treatment of the Maskawa-Nakajima equation in the massless abelian gluon model
Shuji Watanabe
The Maskawa-Nakajima equation has attracted considerable interest in elementary particle physics. From the viewpoint of operator theory, we study the Maskawa-Nakajima equation in t…
Is the solution to the BCS gap equation continuous in the temperature ?
Shuji Watanabe
One of long-standing problems in mathematical studies of superconductivity is to show that the solution to the BCS gap equation is continuous in the temperature. In this paper we a…
Smoothness of the Gap Function in the BCS-Bogoliubov Theory of Superconductivity
Shuji Watanabe
We deal with the gap equation in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature only. We show that the squared gap func…
Superconductivity and the BCS-Bogoliubov Theory
Shuji Watanabe
First, we reformulate the BCS-Bogoliubov theory of superconductivity from the viewpoint of linear algebra. We define the BCS Hamiltonian on , where is a po…
The solution to the BCS gap equation and the second-order phase transition in superconductivity
Shuji Watanabe
The existence and the uniqueness of the solution to the BCS gap equation of superconductivity is established in previous papers, but the temperature dependence of the solution is n…
The BCS Gap Equation on a Banach Space Consisting of Functions both of the Temperature and of the Wave Vector
Shuji Watanabe
In previous mathematical studies of the BCS gap equation of superconductivity, the gap function was regarded as an element of a space consisting of functions of the wave vector onl…
A mathematical proof that the transition to a superconducting state is a second-order phase transition
Shuji Watanabe
We deal with the gap function and the thermodynamical potential in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature only.…