Theory of Resonant States. An Exact Analytical Approach for Open Quantum Systems.

Advances in Quantum Chemistry

Volumn 60, Issue C, 2010, Pages 407-455

  García Calderón, Gastón ^a  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77957883687     PISSN: 00653276     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0065-3276(10)60007-X     Document Type: Book

References (100)

1. Gamow G. Zur quantentheorie des atomkernes. Z. Phys. 1928, 51:204.
2. Gamow G., Critchfield C.L. Theory of Atomic Nucleus and Nuclear Energy-Sources 1949, Clarendon Press, Oxford, p. 156.
3. Siegert A.F.J. On the derivation of the dispersion formula for nuclear reactions. Phys. Rev. 1939, 56:750.
4. Humblet J., Rosenfeld L. Theory of nuclear reactions I. Resonant states and collision matrix. Nucl. Phys. 1961, 26:529.
5. Rosenfeld L. Theory of nuclear reactions II. The foundations of the optical model. Nucl. Phys. 1961, 26:594.
6. Humblet J. Theory of nuclear reactions III. Physical quantities and channel radii. Nucl. Phys. 1962, 31:544.
7. Humblet J. Theory of nuclear reactions IV. Coulomb interactions in the channels and penetration factors. Nucl. Phys. 1964, 50:1.
8. Jeukenne J.P. Theory of nuclear reactions V. Penetration factors for charged particles in low energy nuclear reactions. Nucl. Phys. 1964, 58:1.
9. Humblet J. Theory of nuclear reactions VI. Unitarity, open and closed channels. Nucl. Phys. 1964, 57:386.
10. Mahaux C. Theory of nuclear reactions VII. Photon channels. Nucl. Phys. 1965, 68:481.
11. Rosenfeld L. Theory of nuclear reactions VIII. Time evolution of scattering process. Nucl. Phys. 1965, 70:1.
12. Mahaux C. Theory of nuclear reactions IX. Few-level approximations. Nucl. Phys. 1965, 71:241.
13. Berggren T. On the use of resonant states and eigenfunction expansions of scattering and reaction amplitudes. Nucl. Phys. A 1968, 109:265.
14. Romo W.J. Inner product for resonant states and shell-model applications. Nucl. Phys. A 1968, 116:617.
15. More R.M. Theory of decaying states. Phys. Rev. 1971, 4:1782.
16. More R.M., Gerjuoy E. Properties of resonance wave functions. Phys. Rev. 1973, 7:1288.
17. Garcĺa-Calderón G., Peierls R. Resonant states and their uses. Nucl.Phys. A 1976, 265:443.
18. Garcĺa-Calderón G. An expansion of continuum wave functions in terms of resonant states. Nucl. Phys. A 1976, 261:130.
19. Zel'dovich Y.B. On the theory of unstable states. (Sov. Phys.)-JETP 1961, 12:542.
20. Moiseyev N. Quantum theory of resonances: Calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 1998, 302:211.
21. Giraud B.G., Kato K. Complex-scaled spectrum completeness for pedestrians. Ann. Phys. (N.Y.) 2003, 308:115.
22. J. Humblet, Thesis, University of Liège, 1952; Mém. Soc. Roy. Sc. de Liège (8°) 12 (4) (1952) 36.
23. A. Mattar, G. Garcĺa-Calderón, unpublished.
24. Berrondo M., Garcĺa-Calderón G.G. An eigenfunction expansion involving resonant states. Lett. Nuovo Cimento 1977, 20:34.
25. Garcĺa-Calderón G. Symmetries in Physics 1992, 252. Springer-Verlag, Berlin. A. Frank, K.B. Wolf (Eds.).
26. de la Madrid R., Garcĺa-Calderón G., Muga J.G. Resonance expansions in quantum mechanics, Czech. J. Phys. 2005, 55:1146.
27. Okolowicz J., Ploszajczak M., Rotter I. Dynamics of quantum systems embedded in a continuum. Phys. Rep. 2003, 374:271.
28. Michel N., Nazarewicz W., Ploszajczak M., Vertse T. Shell model in the complex energy plane. J. Phys. G Nucl. Part. Phys. 2009, 36:013101.
29. de la Madrid R. The resonance amplitude associated with the Gamow states. Nucl. Phys. A 2008, 812:13.
30. Tolstikhin O.I., Ostrovsky V.N., Nakamura H. Siegert pseudostate formulation of scattering theory: One-channel case. Phys. Rev. A 1998, 58:2077.
31. Tolstikhin O.I. Siegert-state expansion for nonstationary systems. III. Generalized Born-Fock equations and adiabatic approximation for transitions to the continuum. Phys. Rev. A 2008, 77:032711.
32. Fernández-Garcĺa N., Rosas-Ortiz O. Gamow-Siegert functions and Darboux-deformed short range potentials. Ann. Phys. 2008, 323:1397.
33. Ching E.S.C., Leung P.T., Maassen van den Brink A., Suen W., Tong S.S., Young K. Quasinormal-mode expansion for waves in open systems. Rev. Mod. Phys. 1998, 70:1545.
34. Settimi A., Severini S., Hoenders B.J. Quasi-normal-modes description of transmission properties for photonic bandgap structures. J. Opt. Soc. Am. B 2009, 26:876.
35. Garcĺa-Calderón G., Chaos-Cador L. Theory of coherent and incoherent processes in quantum corrals. Phys. Rev. B 2006, 73:195405.
36. Chaos-Cador L., Garcĺa-Calderón G. Theory of resonant scattering in two dimensions. J. Phys. A Math. Theor. 2010, 43:035301.
37. Garcĺa-Calderón G., Rubio A. Effect of inelastic processes on the elastic width in resonant structures. Phys. Rev. B 1992, 46:9784.
38. Bohm A., Bryant P., Sato Y. Quantal time asymmetry: mathematical foundation and physical interpretation. J. Phys. A Math. Theor. 2008, 41:304019.
39. Bender C.M. Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 2007, 70:947.
40. Peierls R.E. The Proceedings of the 1954 Glasgow Conference on Nuclear and Meson Physics 1955, 296. Pergamon Press, New York. E.H. Bellamy, R.G. Moorhouse (Eds.).
41. Newton R.G. Scattering Theory of Waves and Particles 2002, Dover Publications Inc, New York. Second ed.
42. Hernandez E., Jauregui A., Mondragon A. Degeneracy of resonances in a double barrier potential. J. Phys. A Math. Gen. 2000, 33:4507.
43. G. Garcĺa-Calderón, unpublished.
44. Garcĺa-Calderón G., Berrondo M. Note on the asymptotic energy behaviour of the Green function for a cut-off potential. Lett. Nuovo Cimento 1979, 26:562.
45. Romo W.J. Study of the completeness properties of resonant states. J. Math. Phys. 1980, 21:2704.
46. Bang J., Gareev F.A., Gitzzatkulov M.H., Goncharov S.A. Expansion of continuum functions on resonance wave functions and amplitudes. Nucl. Phys. A 1978, 309:381.
47. Garcĺa-Calderón G. On the overcompletness of the set of bound, antibound and resonant states. Lett. Nuovo Cimento 1982, 33:253.
48. del Campo A., Garcĺa-Calderón G., Muga J.G. Quantum transients. Phys. Rep. 2009, 476:1.
49. Moshinsky M. Diffraction in time. Phys. Rev. 1952, 88:625.
50. Faddeyeva V.N., Terentev M.N. Tables of values of the function ω(z)=e-z2(1+2iπ∫0zet2dt), for complex argument 1961, Pergamon Printing & Art Services Ltd, London, Academician. V.A. Fock (Ed.).
51. Abramowitz M., Stegun I.A. Handbook of Mathematical Functions 1972, Dover Publications, New York, p. 297.
52. G. Garcĺa-Calderón, I. Maldonado, J. Villavicencio, unpublished.
53. Garcĺa-Calderón G. The effect of asymmetry on resonant tunneling in one dimension. Solid State Commun. 1987, 62:441.
54. Garcĺa-Calderón G., Rubio A. Transient effects and delay time in the dynamics of resonant tunneling. Phys. Rev. A 1997, 55:3361.
55. Garcĺa-Calderón G., Romo R., Rubio A. Description of overlapping resonances in multibarrier tunneling structures. Phys. Rev. B 1993, 47:9572.
56. Garcĺa-Calderón G., Villavicencio J. Full time nonexponential decay in double-barrier quantum structures. Phys. Rev. A 2006, 73:062115.
57. Garcĺa-Calderón G., Romo R., Villavicencio J. Survival probability of multibarrier resonance systems: Exact analyical approach. Phys. Rev. B 2007, 76:035340.
58. Garcĺa-Calderón G., Romo R., Villavicencio J. Internal dynamics of multibarrier systems for pulsed quantum decay. Phys. Rev. A 2009, 79:052121.
59. Garcĺa-Calderón G., Rubio A. An expansion of continuum wave functions in terms of resonant states (II). Solvable models. Nucl. Phys. A 1986, 458:560.
60. Cordero S., Garcĺa-Calderón G. Transient effects and reconstruction of the energy spectra in the time evolution of transmitted wave packets. J. Phys. A Math. Theor. 2010, 43:185301.
61. Ferry D.K., Goodnick S.M. Transport in Nanostructures 1997, Cambridge University Press, Cambridge, UK.
62. Romo R., Garcĺa-Calderón G. Strong overlap and transmission in triple-barrier resonant structures. Phys. Rev. B 1994, 49:14016.
63. Garcĺa-Calderón G., Romo R., Rubio A. Effect of disorder in specific realizations of multibarrier random systems. Phys. Rev. B 1997, 56:4845.
64. Süli E E., Mayers D. An Introduction to Numerical Analysis. Cambridge University Press 2003, Cambridge, UK.
65. Thouless D.J. Electrons in disordered systems and the theory of localization. Phys. Rep. 1974, 13:93.
66. Romo R., Villavicencio J. Dynamical description of the buildup process in resonant tunneling: evidence of exponential and non-exponential contributions. Phys. Rev. B 1999, 60:R2142.
67. Garcĺa-Calderón G., Villavicencio J. Time dependence of the probability density in the transient regime or tunneling. Phys. Rev. A 2001, 64:012107.
68. Garcĺa-Calderón G., Villavicencio J., Delgado F., Muga J.G. Time scale for forerunners in quantum tunneling. Phys. Rev. A 2002, 66:042119.
69. Romo R. Buildup dynamics of transmission resonances in superlattices. Phys. Rev. B 2002, 66:245311.
70. Garcĺa-Calderón G., Villavicencio J. Delay time and tunneling transient phenomena. Phys. Rev. A 2002, 66:032104.
71. Romo R., Villavicencio J., Garcĺa-Calderón G. Transient tunneling effects of resonance doublets in triple barrier systems. Phys. Rev. B 2002, 66:033108.
72. Hernández A., Garcĺa-Calderón G. Quantum shutter transient solutions and the delay time for a delta potential. Phy. Rev. A 2003, 68:014104.
73. Garcĺa-Calderón G., Villavicencio J. Transient time-domain resonances and the time scale for tunneling. Phys. Rev. A 2003, 68:052107.
74. Garcĺa-Calderón G., Villavicencio J., Yamada N. Equivalence between the real-time Feynman histories and the quantum-shutter approaches for the ỳpassage time in tunneling. Phys. Rev. A 2003, 67:052106.
75. Yamada N., Garcĺa-Calderón G., Villavicencio J. Quantum-shutter approach to tunneling time scales with wave packets. Phys. Rev. A 2005, 72:012106.
76. Villavicencio J., Romo R., Cruz E. Tunneling and delay time of cutoff Gaussian wave packets. Phys. Rev. A 2007, 75:012111.
77. Gurney R.W., Condon E.U. Quantum mechanics and radioactive desintegration. Phys. Rev. 1929, 33:127.
78. Khalfin L.A. On the theory of the decay of a quasi-stationary state. Sov. Phys., Dokl. 1957, 2:340. Contribution to the decay theory of a quasi-stationary state, Sov. Phys.-JETP 6 (1958) 1053.
79. Wilkinson S.R., Bharucha C.F., Fischer M.C., Madison K.W., Morrow P.K., Niu Q., et al. Experimental evidence for non-exponential decay in quantum tunnelling. Nature 1997, 387:575.
80. Rothe C., Hintschich S.I., Monkman A.P. Violation of the exponential-decay law at long times. Phys. Rev. Lett. 2006, 96:163601.
81. Winter R.G. Evolution of a quasistationary state. Phys. Rev. 1961, 123:1503.
82. Jittoh T., Matsumoto S., Sato J., Sato Y., Takeda K. Nonexponential decay of an unstable quantum system: Small-Q-value s-wave decay. Phys. Rev. A 2005, 71:012109.
83. Exner P., Fraas M. The decay law can have an irregular character. J. Phys. A 2007, 40:1333.
84. Garcĺa-Calderón G., Mateos J.L., Moshinsky M. Resonant spectra and the time evolution of the survival and nonescape probabilities. Phy. Rev. Lett. 1995, 74:33.
85. Garcĺa-Calderón G., Maldonado I., Villavicencio J. Resonant-state expansions and the long-time behavior of quantum decay. Phys. Rev. A 2007, 76:012103.
86. Lewenstein M., Sanpera A., Ahufinger V., Bogdan D., Sen A., Sen U. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 2007, 56:243.
87. van Dijk W., Nogami Y. Novel expression for the wave function of a decaying quantum system. Phys. Rev. Lett. 1999, 83:2867.
88. Tsuchiya M., Matsusue T., Sakaki H. Tunneling escape rate of electrons from quantum well in double-barrier heterostructures. Phys. Rev. lett. 1987, 59:2356.
89. S. Cordero, G. Garcĺa-Calderón, unpublished.
90. Goldberger M.L., Watson K.W. Collision Theory 1964, Wiley, New York, p. 450.
91. Nicolaides C.A., Beck D.R. Possibility of observing nonexponential decay in autoinizing states. Phys. Rev. Lett. 1977, 38:683.
92. Garcĺa-Calderón G., Riquer V., Romo R. Survival probability of a single resonance. J. Phys. A:Mat. Theor. 2001, 34:4155.
93. Douvropoulos T.G., Nicolaides C.A. Nonexponential decay propagator and its differential equation for real and complex energy distributions of unstable states. Phys. Rev. A 2004, 69:032105.
94. Tsuchiya M., Matsusue T., Sakaki H. Tunneling escape rate of electrons from quantum-well in double-barrier heterostructures. Phys. Rev. Lett. 1987, 59:2356.
95. Leo K., Shah J., Göbel E.O., Damen T.C., Schmitt-Rink S., Schäfer W., et al. Coherent oscillations of a wave packet in a semiconductor double-quantum-well structure. Phys. Rev. Lett. 1991, 66:201.
96. Longhi S. Nonexponential decay via tunneling in tight-binding lattices and the optical Zeno effect. Phys. Rev. Lett. 2006, 97:110402.
97. Feynman R.P., Vernon F.L. The theory of a general quantum system interacting with a linear dissipative system. Ann. Phys. (N.Y.) 1963, 24:118.
98. Caldeira A.O., Leggett A.J. Influence of dissipation on quantum tunneling in macroscopic systems. Phys. Rev. Lett. 1981, 46:211.
99. Nicolaides C.A. Physical constraints on nonstationary states and nonexponential decay. Phys. Rev. A 2002, 66:022118.
100. Poppe G.P.M., Wijers C.M.J. More efficient computation of the complex error function. ACM Trans. Math. Softw. 1990, 16:38.