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Exactly Solvable Many-Body Systems and Pseudo-Hermitian Point Interactions

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Czechoslovak Journal of Physics Aims and scope

Abstract

We study Hamiltonian systems with point interactions and give a systematic description of the corresponding boundary conditions and the spectrum properties for self-adjoint, PT-symmetric systems and systems with real spectra. The integrability of one dimensional many-body systems with these kinds of point (contact) interactions are investigated for both bosonic and fermionic statistics.

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References

  1. C. M. Bender and S. Boettcher: Phys. Rev. Lett. 80 (1998) 5243. C.M. Bender and S. Boettcher, and P.N. Meisinger: J. Math. Phys. 40 (1999) 2201. C.M. Bender, D.C. Brody, and H.F. Jones: Phys. Rev. Lett. 89 (2002) 270401.

    Google Scholar 

  2. F.M. Fernández, R. Guardiola, J. Ros, and M. Znojil: J. Phys. A: Math. Gen 31 (1998) 10105.

    Google Scholar 

  3. S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and H. Holden: Solvable Models in Quantum Mechanics, Springer, New York, 1988.

    Google Scholar 

  4. M. Gaudin: La fonction d'onde de Bethe, Masson, 1983.

  5. S. Albeverio and R. Kurasov: Singular perturbations of differential operators and solvable Schrödinger type operators, London Mathematical Society Lecture Note Series, Vol. 271, Cambridge University Press, Cambridge, 2000.

    Google Scholar 

  6. P. Kurasov: J. Math. Analy. Appl. 201 (1996) 297.

    Google Scholar 

  7. J.B. McGuire: J. Math. Phys. 5 (1964) 622; 6 (1965) 432; 7 (1966) 123. J.B. McGuire and C.A. Hurst: J. Math. Phys. 13 (1972) 1595; 29 (1988) 155.

    Google Scholar 

  8. C.N. Yang: Phys. Rev. Lett. 19 (1967) 1312. C.N. Yang: Phys. Rev. 168 (1968) 1920.

    Google Scholar 

  9. C.H. Gu and C.N. Yang: Commun. Math. Phys. 122 (1989) 105.

    Google Scholar 

  10. P. Chernoff and R. Hughes: J. Func. Anal. 111 (1993) 97.

    Google Scholar 

  11. S. Albeverio, Z. Brzeźniak, and L Dabrowski: J. Phys. A 27 (1994) 4933.

    Google Scholar 

  12. S. Albeverio, S.M. Fei, and P. Kurasov: Lett. Math. Phys 59 (2002) 227.

    Google Scholar 

  13. Z.Q. Ma: Yang-Baxter Equation and Quantum Enveloping Algebras, World Scientific, 1993. V. Chari and A. Pressley: A Guide to Quantum Groups, Cambridge University Press, 1994. C. Kassel: Quantum Groups, Springer-Verlag, New York, 1995. S. Majid: Foundations of Quantum GroupThe ory, Cambridge University Press, 1995. K. Schmüdgen: Quantum Groups and Their Representations, Springer, 1997.

  14. S. Albeverio, L. D¸abrowski, and S.M. Fei: Int. J. Mod. Phys. B 14 (2000) 721.

    Google Scholar 

  15. S. Albeverio, S.M. Fei, and P. Kurasov: Rep. Math. Phys. 47 (2001) 157.

    Google Scholar 

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Fei, SM. Exactly Solvable Many-Body Systems and Pseudo-Hermitian Point Interactions. Czechoslovak Journal of Physics 54, 43–49 (2004). https://doi.org/10.1023/B:CJOP.0000014366.93476.92

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  • DOI: https://doi.org/10.1023/B:CJOP.0000014366.93476.92

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