S-Wave Bound- and Resonant States of Two Fermions in Simple Cubic Lattice

• Authors: M. Bak
• Languages of publication: EN

Abstracts

EN

Resonant two-electron states are examined in attractive Hubbard model on simple cubic lattice and exact formula for scattering cross section in the limit of low density (empty lattice) is calculated. S-wave pair is considered by means of lattice Green functions (LGF). Analytical form of these functions found by Joyce is used facilitating calculations, which were greatly hindered before by the necessity of using LGF's tabulated values. It is found that the actual peak of scattering cross-section is formed on the lower band boundary in discrepancy with formulae of the theory of scattering in solids.

Keywords

EN

02.30.Gp; 03.65.Ge; 31.15.ac; 71.10.Fd

Discipline

• 71.10.Fd: Lattice fermion models (Hubbard model, etc.)
• 03.65.Ge: Solutions of wave equations: bound states
• 02.30.Gp: Special functions
• 31.15.ac: High-precision calculations for few-electron (or few-body) atomic systems

• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 4
• Pages: 808-811

Dates

published

2012-04

Contributors

author

M. Bak

• Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

References

• 1. J. Callaway, J. Math. Phys. 5, 783 (1964)
• 2. F. Dyson, Phys. Rev. 102, 1207 (1965)
• 3. M. Wortis, Phys. Rev. 132, 85 (1963)
• 4. R. Friedberg, T.D. Lee, H.C. Ren, Phys. Rev. B 50, 10190 (1994)
• 5. R. Micnas, J. Ranninger, S. Robaszkiewicz, Rev. Mod. Phys. 62, 113 (1990)
• 6. M. Bak, R. Micnas, Mol. Phys. Rep. 24, 168 (1999)
• 7. M. Bak, R. Micnas, Acta Phys. Pol. A 97, 209 (2000)
• 8. M. Bak, Acta Phys. Pol. A 106, 637 (2004)
• 9. M. Bak, Phys. Status Solidi B 242, 420 (2005)
• 10. M. Bak, Phys. Status Solidi B 244, 2421 (2007)
• 11. M. Bak, Acta Phys. Pol. A 114, 275 (2008)
• 12. B. Tobijaszewska, M. Bak, Acta Phys. Pol. A 115, 135 (2009)
• 13. F. Pistolesi, Ph Nozieres, Phys. Rev. B 66, 054501 (2002)
• 14. P. Kornilovitch, Phys. Rev. B 69, 235110 (2004)
• 15. S. Basu, R.J. Gooding, Phys. Status Solidi B 242, 1431 (2005)
• 16. M.Yu. Kagan, I.V. Brodsky, D.V. Efremov, A.V. Klaptsov, Phys. Rev. A 70, 023607 (2004)
• 17. Y.L. Wang, E. Manousakis, C.D. Wentworth, Phys. Rev. B 41, 7061 (1990)
• 18. A. Morris-Andrews, R.J. Gooding, J. Phys. Condens. Matter 19, 386216 (2007)
• 19. A.S. Blaer, H.C. Ren, O. Tchernyshyov, Phys. Rev. B 55, 6035 (1997)
• 20. M. Valiente, D. Petrosyan, J. Phys. B: At. Mol. Opt. Phys. 42, 121001 (2009)
• 21. M. Greiner, C.A. Regal, D.S. Jin, Nature 426, 537 (2003)
• 22. G. Modugno, F. Ferlaino, R. Heidemann, G. Roati, M. Inguscio, Phys. Rev. A 68, 011601 (2003)
• 23. G.S. Joyce, J. Phys. A: Math. Gen. 35, 9811 (2002)
• 24. R. Silberglitt, A.B. Harris, Phys. Rev. 174, 640 (1968)
• 25. G.F. Koster, Phys. Rev. 95, 1436 (1954)
• 26. E.N. Economou, Green's Functions in Quantum Physics, Springer-Verlag, 2006
• 27. T. Wolfram, J. Callaway, Phys. Rev. 130, 2207 (1963)

Identifiers

DOI

10.12693/APhysPolA.121.808