Duality in perturbation theory and the quantum adiabatic approximation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 5, 1998, Pages 3439-3442

  Frasca, Marco ^a  

^a NONE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; NAVIER STOKES EQUATIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; REYNOLDS NUMBER; THEOREM PROVING;

DUALITY; DYSON SERIES; PERTURBATION THEORY; QUANTUM ADIABATIC APPROXIMATION; SCHRODINGER EQUATION;

QUANTUM THEORY;

EID: 0032209605     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.3439     Document Type: Article

References (19)

1. D. Pnueli and C. Gutfinger, Fluid Mechanics (Cambridge University Press, Cambridge, 1992);
2. V. L’vov and I. Procaccia, e-print chao-dyn/9502010.
3. Euler equations do not have second-order derivatives, while Navier-Stokes equations do: This originates the well-known boundary layer problem in perturbation theory. See, e.g., J. Kevorkian and J.D. Cole, Perturbation Methods in Applied Mathematics (Springer-Verlag, New York, 1985).
4. M. Frasca, Phys. Rev. A 45, 43 (1992); PLRAAN
5. Phys. Rev. AM. Frasca47, 2374 (1993);
6. Phys. Rev. AM. Frasca56, 1548 (1997).
7. M. Frasca, e-print hep-th/9406075;
8. M. Frascae-print hep-th/9406119;
9. M. FrascaNuovo Cimento B 111, 957 (1996);
10. Nuovo Cimento BM. Frasca112, 1073 (1997);
11. A. Joye, Ann. Inst. Henri Poincaré: Phys. Theor. 63, 231 (1995).AIPTEO
12. A. Mostafazadeh, Phys. Rev. A 55, 1653 (1997).PLRAAN
13. A.H. Nayfeh, Introduction to Perturbation Techniques (Wiley, New York, 1981), Chap. 14.
14. I do not aim to cite all the work about this fundamental problem of quantum mechanics. From the earlier to the latest works I cite just C.M. Bender and T.T. Wu, Phys. Rev. 184, 1231 (1969); PHRVAO
15. C.M. BenderT.T. WuPhys. Rev. D 7, 1620 (1973);
16. J. Zinn-Justin, Phys. Rep. 70, 109 (1981), and references therein; PRPLCM
17. W. Janke and H. Kleinert, Phys. Rev. Lett. 75, 2787 (1995). However, this is a very active field of physics for its implications in quantum field theory.PRLTAO
18. G. Parisi, Statistical Field Theory (Addison-Wesley, New York, 1988), p. 264ff.
19. B. Simon, Ann. Phys. (N.Y.) 58, 76 (1970). APNYA6