Adiabatic theorems for quantum resonances

Communications in Mathematical Physics

Volumn 273, Issue 3, 2007, Pages 651-675

  Salem, Walid K Abou ^a,b   Fröhlich, Jürg ^a  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34347214455     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0198-2     Document Type: Article

References (36)

1. Dalfovo, F., Giorgini, S., Pitaevskii, L.P.: Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463-512 (1999)
2. Simon, B.: Resonances in N-body quantum systems with dilation analytic potentials and the foundations of time-dependent perturbation theory. Ann. Math. 97, 247 (1973)
3. Simon, B.: Resonances and complex scaling: a rigorous overview. Int. J. Quant. Chem. 14, 529 (1978)
4. Hunziker, W.: Resonances, metastable states and exponential decay laws in perturbation theory. Commun. Math. Phys. 132, 177 (1990)
5. Orth, A.: Quantum mechanical resonances and limiting absorption: the many body problem. Commun. Math. Phys. 126, 559 (1990)
6. Herbst, I.: Exponential decay in the Stark effect. Commun. Math. Phys. 87, 429 (1982/3)
7. Cattaneo, L., Graf, G.M., Hunziker, W.: A general resonance theory based on Mourre's inequality. Annales Henri Poincare 7, 583-601 (2006)
8. Pfeifer, P., Fröhlich, J.: Generalized time-energy uncertainty relations and bounds on lifetimes of resonances. Rev. Mod. Phys. 67, 759 (1995)
9. Soffer, A., Weinstein, M.I.: Time-dependent resonance theory. Geom. Funct. Anal. 8, 1086 (1998)
10. Merkli, M., Sigal, I.M.: A time-dependent theory of quantum resonances. Commun. Math. Phys. 201, 549 (1999)
11. Jensen, A., Nenciu, G.: On the Fermi Golden Rule: Degenerate Eigenvalues, http://mpej.unige.ch/mp-arc/html/html/c/06/06-157.pdf,2006
12. Davies, E.B.: An adiabatic theorem applicable to the Stark effect. Commun. Math. Phys. 89, 329-339 (1983)
13. Chakrabarti, B.K., Ascharyya, M.: Dynamical Transitions and Hysteresis. Rev. Mod. Phys. 71, 847-859 (1999)
14. Cohen-Tannoudji, C.: Manipulating atoms with photons. Rev. Mod. Phys. 70, 707-719 (1998)
15. Phillips, W.D.: Laser cooling and trapping of neutral atoms. Rev. Mod. Phys. 70, 721-741 (1998)
16. Kato, T.: On the adiabatic theorem of quantum mechanics. Phys. Soc. Jap. 5, 435-439 (1958)
17. Balslev, E., Combes, J.M.: Spectral properties of Schrödinger operators with dilation analytic interactions. Commun. Math. Phys. 22, 280 (1971)
18. Abou Salem, W.: On the quasi-static evolution of nonequilibrium steady states. http://arxiv.org/list/math-ph/060104, 2006. To appear in Annales Henri Poincare (2007)
19. Hagedorn, G., Joye, A.: Elementary exponential error estimates for the adiabatic approximation. J. Math. Anal. Appl. 267, 235-246 (2002)
20. Joye, A.: General adiabatic evolution with a gap condition. http://arxiv.org/list/math-ph/0608059, 2006
21. Nenciu, G.: Linear adiabatic theory, exponential estimates. Commun. Math. Phys. 152, 479-496 (1993)
22. Bach, V., Fröhlich, J., Sigal, I.M.: Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field. Commun. Math. Phys. 207, 249-290 (1999)
23. Bach, V., Fröhlich, J., Sigal, I.M.: Mathematical Theory of nonrelativistic matter and radiation. Lett. Math. Phys. 34, 183-201 (1995)
24. Bach, V., Fröhlich, J., Sigal, I.M.: Quantum electrodynamics of confined nonrelativistic particles. Adv. in Math. 137, 299-395 (1998)
25. Teufel, S.: A note on the adiabatic theorem without a gap condition. Lett. Math. Phys. 58, 261-266 (2002)
26. Teufel, S.: Adiabatic perturbation theory in quantum dynamics. Lecture Notes in Mathematics 1821, Heidelberg, New York: Springer-Verlag (2003)
27. Avron, J.E., Elgart, A.: Adiabatic theorem without a gap condition, Commun. Math. Phys. 203, 445-463 (1999)
28. Avron, J.E., Elgart, A.: An adiabatic theorem without a spectral gap. In: Mathematical results in quantum mechanics (Prague 1998), Oper. Theory Adv. Appl. 108, Basel: Birkhäuser, (1999), pp. 3-12
29. Abou Salem, W., Fröhlich, J.: Adiabatic theorems and reversible isothermal processes. Lett. Math. Phys. 72, 153-163 (2005)
30. Abou Salem, W., Fröhlich. J.: In preparation
31. Combes, J.M., Thomas, L.: Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators. Commun. Math. Phys. 34, 251 (1973)
32. Hunziker, W.: Notes on asymptotic perturbation theory for Schrödinger eigenvalue problems. Helv. Phys. Acta. 61, 257-304 (1988)
33. Herbst, I., Simon, B.: Dilation analyticity in constant electric field II. Commun. Math. Phys. 80, 181-216 (1981)
34. Aguilar, J., Combes, J.M.: A class of analytic perturbations for one-body Schrödinger Hamiltonians. Commun. Math. Phys. 22, 269-279 (1971)
35. Kato, T.: Perturbation theory for linear operators, Berlin: Springer (1980)
36. Reed, M., Simon, B.: Methods of Modern Mathematical Physics, Vol. I (Functional Analysis), Vol. II (Fourier Analysis, Self-Adjointness). New York: Academic Press (1975)