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Model BCS Hamiltonian and Approximating Hamiltonian in the Case of Infinite Volume. IV. Two Branches of Their Common Spectra and States

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Abstract

We consider the model and approximating Hamiltonians directly in the case of infinite volume. We show that each of these Hamiltonians has two branches of the spectrum and two systems of eigenvectors, which represent excitations of the ground states of the model and approximating Hamiltonians as well as the ground states themselves. On both systems of eigenvectors, the model and approximating Hamiltonians coincide with one another. In both branches of the spectrum, there is a gap between the eigenvalues of the ground and excited states.

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REFERENCES

  1. D. Ya. Petrina, “Spectrum and states of the BCS Hamiltonian in a finite domain. I. Spectrum,” Ukr.Mat.Zh., 52, No. 5, 667–689 (2000).

    Google Scholar 

  2. D. Ya. Petrina, “Spectrum and states of the BCS Hamiltonian in a finite domain. II. Spectra of excitations,” Ukr.Mat.Zh., 53, No. 8, 1290–1315 (2001).

    Google Scholar 

  3. D. Ya. Petrina, “Spectrum and states of BCS Hamiltonian in a finite domain. III. BCS Hamiltonian with mean-field interaction,” Ukr.Mat.Zh., 54, No. 11, 1486–1504 (2002).

    Google Scholar 

  4. D. Ya. Petrina, “On Hamiltonians in quantum statistics and on a model Hamiltonian in the theory of superconductivity,” Teor.Mat.Fiz., 4, No. 3, 394–405 (1970).

    Google Scholar 

  5. D. Ya. Petrina and V. P. Yatsyshyn, “On a model Hamiltonian in the theory of superconductivity,” Teor.Mat.Fiz., 10, No. 2, 283–305 (1972).

    Google Scholar 

  6. D. Ya. Petrina, Mathematical Foundations of Quantum Statistical Mechanics.Continuos Systems, Kluwer, Dordrecht (1995).

    Google Scholar 

  7. N. N. Bogolyubov, On the Model Hamiltonian in the Theory of Superconductivity [in Russian], Preprint No. R-511, JINR, Dubna (1960).

  8. R. Haag, “The mathematical structure of the Bardeen–Cooper–Schrieffer model,” Nuovo Cim., 25, 287–299 (1962).

    Google Scholar 

  9. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, “Theory of superconductivity,” Phys.Rev., 108, 1175–1204 (1957).

    Google Scholar 

  10. N. Ilieva and W. Thirring, “A pair potential supporting a mixed mean-field/BCS-phase,” Nucl.Phys.B., 565, 629–640 (2000).

    Google Scholar 

  11. N. Ilieva and W. Thirring,“ A mixed mean-field/BCS-phase with an energy gap at high T c,” Particles, Nuclei B., 31, No. 7, 3083–3094 (2000).

    Google Scholar 

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  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    D. Ya. Petrina

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  1. D. Ya. Petrina
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Petrina, D.Y. Model BCS Hamiltonian and Approximating Hamiltonian in the Case of Infinite Volume. IV. Two Branches of Their Common Spectra and States. Ukrainian Mathematical Journal 55, 212–240 (2003). https://doi.org/10.1023/A:1025412228521

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  • DOI: https://doi.org/10.1023/A:1025412228521

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