Related papers: The solution to the BCS gap equation for supercond…
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 address this problem. We regard the BCS gap equation as a…
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 not discussed. In this paper, in order to show how the…
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 only. But we regard it as an element of a Banach space…
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 energy under the restriction that the temperature is very small.…
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 viewpoint of operator theory, and showed that the solution is…
It was recently shown that the BCS formalism leads to several solutions for the energy gap and the equilibrium quasiparticle distribution, with a phase transition temperature which depends on the position of the chemical potential within…
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 twice differentiable only on the neighborhoods of absolute…
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 viewpoint of operator theory. Here we have no magnetic field.…
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 superconductivity. Here the temperature belongs to the closed interval…
We deal with the gap equation in the BCS-Bogoliubov theory of superconductivity, where the gap function is a function of the temperature $T$ only. We show that the squared gap function is of class $C^2$ on the closed interval…
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 of the solution with respect to the temperature near the…
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 $T$ only. We show that the squared gap function is of class $C^2$ on…
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 the BCS-Bogoliubov model of superconductivity on the basis…
In the standard theory of superconductivity a quasiparticle excitation changes the energy of the system by the quasiparticle energy. But the number of excitations determine also the gap energy which further determines the energy of the…
Lately, there has been much interest in high temperature superconductors, and more recently hydrogen-based superconductors. This work offers a simple model which explains the behavior of the superconducting gap based on BCS theory, and…
A General Theory of Superconductivity with points of view differing from those of the BCS Theory is presented in two parts. In the first part, a general equation for the superconductivity is obtained; based on the stable pairing of two…
We investigate superconductivity in a grand canonical ensemble with {\it fixed number parity} (even or odd). In the low temperature limit we find small corrections to the BCS gap equation and energy spectrum $E(k)$. The even-odd free energy…
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 theorem to it. We show that there is a unique magnetic field…
New calculation reveals that E is constant in a thin layer across the Fermi surface, befitting the definition of energy gap parameter, Delta varies dramatically. The BCS self-consistent equation has a simple and exact solution, showing that…
We show that the energy gap for the BCS gap equation is $ \Xi = \mu \left( 8 e^{-2} + o(1)\right) \exp\left( \frac{\pi}{2\sqrt{\mu} a}\right) $ in the low density limit $\mu \to 0$. Together with the similar result for the critical…