Isospectraiity of spherical MHD dynamo operators: Pseudo-hermiticity and a no-go theorem

Journal of Mathematical Physics

Volumn 44, Issue 7, 2003, Pages 3097-3111

  Günther, Uwe ^a   Stefani, Frank ^a  

^a INSTITUTE OF ION BEAM PHYSICS AND MATERIALS RESEARCH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037661020     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1573741     Document Type: Article

References (48)

1. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting fluids (Cambridge University Press, Cambridge, 1978); F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Akademie-Verlag, Berlin and Pergamon, Oxford, 1980); Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (Gordon & Breach, New York, 1983).
2. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting fluids (Cambridge University Press, Cambridge, 1978); F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Akademie-Verlag, Berlin and Pergamon, Oxford, 1980); Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (Gordon & Breach, New York, 1983).
3. H. K. Moffatt, Magnetic Field Generation in Electrically Conducting fluids (Cambridge University Press, Cambridge, 1978); F. Krause and K.-H. Rädler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Akademie-Verlag, Berlin and Pergamon, Oxford, 1980); Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (Gordon & Breach, New York, 1983).
4. A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000); 86, 3024 (2001); U. Müller and R. Stieglitz, Phys. Fluids 13, 561 (2001); A. Gailitis et al., Rev. Mod. Phys. 74, 973 (2002).
5. A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000); 86, 3024 (2001); U. Müller and R. Stieglitz, Phys. Fluids 13, 561 (2001); A. Gailitis et al., Rev. Mod. Phys. 74, 973 (2002).
6. A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000); 86, 3024 (2001); U. Müller and R. Stieglitz, Phys. Fluids 13, 561 (2001); A. Gailitis et al., Rev. Mod. Phys. 74, 973 (2002).
7. A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000); 86, 3024 (2001); U. Müller and R. Stieglitz, Phys. Fluids 13, 561 (2001); A. Gailitis et al., Rev. Mod. Phys. 74, 973 (2002).
8. F. Stefani and G. Gerbeth, Astron. Nachr. 321, 235 (2000).
9. F. Stefani and G. Gerbeth, Phys. Earth Planet. Inter. 128, 109 (2001); Phys. Rev. E 67, 027302 (2003).
10. F. Stefani and G. Gerbeth, Phys. Earth Planet. Inter. 128, 109 (2001); Phys. Rev. E 67, 027302 (2003).
11. O. L. De Lange and R. E. Raab, Operator Methods in Quantum Mechanics (Clarendon, Oxford, 1991).
12. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer-Verlag, Berlin, 1991).
13. D. L. Pursey, Phys. Rev. D 33, 2267 (1986); A. Anderson, Phys. Rev. A 43, 4602 (1991).
14. D. L. Pursey, Phys. Rev. D 33, 2267 (1986); A. Anderson, Phys. Rev. A 43, 4602 (1991).
15. A. Gonzalez-Lopez and N. Kamran, J. Geom. Phys. 26, 202 (1998).
16. E. Witten, Nucl. Phys. B 202, 253 (1982); L. E. Gendenstein and I. V. Krive, Sov. Phys. Usp. 28, 645 (1985); F. Cooper, A. Khare, and U. Sukhatme, Phys. Reports 251, 267 (1995).
17. E. Witten, Nucl. Phys. B 202, 253 (1982); L. E. Gendenstein and I. V. Krive, Sov. Phys. Usp. 28, 645 (1985); F. Cooper, A. Khare, and U. Sukhatme, Phys. Reports 251, 267 (1995).
18. E. Witten, Nucl. Phys. B 202, 253 (1982); L. E. Gendenstein and I. V. Krive, Sov. Phys. Usp. 28, 645 (1985); F. Cooper, A. Khare, and U. Sukhatme, Phys. Reports 251, 267 (1995).
19. A. Mostafazadeh, J. Math. Phys. 43, 205 (2002).
20. A. Mostafazadeh, Nucl. Phys. B 640, 419 (2002).
21. F. Gesztesy, J. Funct. Anal. 117, 401 (1993); F. Gesztesy and G. Teschl, Proc. Am. Math. Soc. 124, 1831 (1996); F. Gesztesy and G. Teschl, J. Diff. Eqns. 128, 252 (1996).
22. F. Gesztesy, J. Funct. Anal. 117, 401 (1993); F. Gesztesy and G. Teschl, Proc. Am. Math. Soc. 124, 1831 (1996); F. Gesztesy and G. Teschl, J. Diff. Eqns. 128, 252 (1996).
23. F. Gesztesy, J. Funct. Anal. 117, 401 (1993); F. Gesztesy and G. Teschl, Proc. Am. Math. Soc. 124, 1831 (1996); F. Gesztesy and G. Teschl, J. Diff. Eqns. 128, 252 (1996).
24. M. Proctor, Astron. Nachr. 298, 19 (1977).
25. T. Ya. Azizov and I. S. Iokhvidov, Linear Operators in Spaces with an Indefinite Metric (Wiley-Interscience, New York, 1989).
26. H. Langer and C. Tretter, Operator Theory: Advanced Applications (Birkhauser-Verlag, Basel, 2001), Vol. 122, p. 331.
27. A. Mostafazadeh, J. Math. Phys. 44, 974 (2003); C. M. Bender, D. C. Brody, and H. F. Jones, "Must a Hamiltonian be hermitian?," hep-th/0303005.
28. A. Mostafazadeh, J. Math. Phys. 44, 974 (2003); C. M. Bender, D. C. Brody, and H. F. Jones, "Must a Hamiltonian be hermitian?," hep-th/0303005.
29. A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002); 43, 3944 (2002); Mod. Phys. Lett. A 17, 1973 (2002); J. Math. Phys. 43, 6343 (2002).
30. A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002); 43, 3944 (2002); Mod. Phys. Lett. A 17, 1973 (2002); J. Math. Phys. 43, 6343 (2002).
31. A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002); 43, 3944 (2002); Mod. Phys. Lett. A 17, 1973 (2002); J. Math. Phys. 43, 6343 (2002).
32. A. Mostafazadeh, J. Math. Phys. 43, 2814 (2002); 43, 3944 (2002); Mod. Phys. Lett. A 17, 1973 (2002); J. Math. Phys. 43, 6343 (2002).
33. S. Albeverio, F. Gesztesy, R. H. Krohn, and H. Holden, Solvable Models in Quantum Mechanics (Springer-Verlag, New York, 1988).
34. V. I. Gorbachuk and M. L. Gorbachuk, Boundary Value Problems for Operator Differential Equations (Kluwer Academic, Dordrecht, 1991); E. M. Russakovskii, Linear Algebra Appl. 212/213, 437 (1994).
35. V. I. Gorbachuk and M. L. Gorbachuk, Boundary Value Problems for Operator Differential Equations (Kluwer Academic, Dordrecht, 1991); E. M. Russakovskii, Linear Algebra Appl. 212/213, 437 (1994).
36. A. Dijksma and H. Langer, "Operator theory and ordinary differential operators," Lectures on Operator Theory and its Applications, American Mathematical Society Fields Institute Monographs. (American Mathematical Society, Providence, RI, 1996), Vol. 3, p. 75.
37. A. S. Markus, Introduction to the Spectral Theory of Polynomial Operator Pencils, Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1988), Vol. 71; Yu. S. Abramov, Variational Methods in the Theory of Operator Pencils - Spectral Optimization (Leningrad University Press, Leningrad, 1983).
38. A. S. Markus, Introduction to the Spectral Theory of Polynomial Operator Pencils, Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1988), Vol. 71; Yu. S. Abramov, Variational Methods in the Theory of Operator Pencils - Spectral Optimization (Leningrad University Press, Leningrad, 1983).
39. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1969), Vol. 18; T. Kato, Perturbation Theory of Linear Operators (Springer-Verlag, Berlin, 1980); H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators (Akademie-Verlag, Berlin, 1984), and Operator Theory: Advanced Applications (Birkhäuser-Verlag, Basel, 1985), Vol. 15.
40. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1969), Vol. 18; T. Kato, Perturbation Theory of Linear Operators (Springer-Verlag, Berlin, 1980); H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators (Akademie-Verlag, Berlin, 1984), and Operator Theory: Advanced Applications (Birkhäuser-Verlag, Basel, 1985), Vol. 15.
41. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1969), Vol. 18; T. Kato, Perturbation Theory of Linear Operators (Springer-Verlag, Berlin, 1980); H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators (Akademie-Verlag, Berlin, 1984), and Operator Theory: Advanced Applications (Birkhäuser-Verlag, Basel, 1985), Vol. 15.
42. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs (American Mathematical Society, Providence, RI, 1969), Vol. 18; T. Kato, Perturbation Theory of Linear Operators (Springer-Verlag, Berlin, 1980); H. Baumgärtel, Analytic Perturbation Theory for Matrices and Operators (Akademie-Verlag, Berlin, 1984), and Operator Theory: Advanced Applications (Birkhäuser-Verlag, Basel, 1985), Vol. 15.
43. M. I. Zelikin, Control Theory and Optimization I. Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Springer-Verlag, Berlin, 2000).
44. R. L. Anderson, J. Harnad, and P. Winternitz, J. Math. Phys. 24, 1062 (1983); S. Shnider and P. Winternitz, ibid. 25, 3155 (1984); S. Lafortune and P. Winternitz, J. Math. Phys. 37, 1539 (1996).
45. R. L. Anderson, J. Harnad, and P. Winternitz, J. Math. Phys. 24, 1062 (1983); S. Shnider and P. Winternitz, ibid. 25, 3155 (1984); S. Lafortune and P. Winternitz, J. Math. Phys. 37, 1539 (1996).
46. R. L. Anderson, J. Harnad, and P. Winternitz, J. Math. Phys. 24, 1062 (1983); S. Shnider and P. Winternitz, ibid. 25, 3155 (1984); S. Lafortune and P. Winternitz, J. Math. Phys. 37, 1539 (1996).
47. P. Camiz et al., J. Math. Phys. 12, 2040 (1971).
48. M. Jodeit and B. M. Levitan, Lett. Math. Phys. 43, 117 (1998).