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13 papers · 1 filter
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…
Quantum walks driven by quantum coins with two multiple eigenvalues
Norio Konno, Iwao Sato, Etsuo Segawa +1
We consider a spectral analysis on the quantum walks on graph with the local coin operators and the flip flop shift. The quantum coin operators have co…
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…
The first order expansion of a ground state energy of the model with cutoffs
Toshimitsu Takaesu
In this paper, we investigate the model with cutoffs. By introducing a spatial cutoff and a momentum cutoff, the total Hamiltonian is a self-adjoint operator on a boson Fock…
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…