Abstract:
We test the ability of semiclassical theory to describe quantitatively the revival of quantum wave packets-a long time phenomena-in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wave function up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times. © 2009 The American Physical Society.
Registro:
Documento: |
Artículo
|
Título: | Semiclassical description of wave packet revival |
Autor: | Toscano, F.; Vallejos, R.O.; Wisniacki, D. |
Filiación: | Instituto de Física, Universidade Federal Do Rio de Janeiro, CP 68528, 21941-972 Rio de Janeiro, RJ, Brazil Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil Departamento de Física J. J. Giambiagi, FCEN, Ciudad Universitaria, C1428EGA Buenos Aires, Argentina
|
Palabras clave: | Autocorrelation functions; Quantum wave packets; Semiclassical theories; Time-dependent; Wave packet revivals; Regression analysis; Wave functions; Wave packets; Waves; Automobile exhibitions |
Año: | 2009
|
Volumen: | 80
|
Número: | 4
|
DOI: |
http://dx.doi.org/10.1103/PhysRevE.80.046218 |
Título revista: | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|
Título revista abreviado: | Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
|
ISSN: | 15393755
|
CODEN: | PLEEE
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v80_n4_p_Toscano |
Referencias:
- Maslov, V.P., Fedoriuk, M.V., (1981) Semiclassical Approximations in Quantum Mechanics, , Reidel, Dordrecht
- Brack, M., Bhaduri, R.K., (2003) Semiclassical Physics, Frontiers in Physics, 96, , Westview, Boulder, CO
- Van Vleck, J.H., (1928) Proc. Natl. Acad. Sci. U.S.A., 14, p. 178. , 10.1073/pnas.14.2.178
- Gutzwiller, M.C., (1967) J. Math. Phys., 8, p. 1979. , 10.1063/1.1705112
- Tomsovic, S., Heller, E.J., (1991) Phys. Rev. Lett., 67, p. 664. , 10.1103/PhysRevLett.67.664;
- Tomsovic, S., Heller, E.J., (1993) Phys. Rev. e, 47, p. 282. , 10.1103/PhysRevE.47.282
- Mallalieu, M., Stroud, Jr.C.R., (1994) Phys. Rev. A, 49, p. 2329. , 10.1103/PhysRevA.49.2329
- Suarez Barnes, I.M., Nauenberg, M., Nockleby, M., Tomsovic, S., (1993) Phys. Rev. Lett., 71, p. 1961. , 10.1103/PhysRevLett.71.1961;
- Suarez Barnes, I.M., Nauenberg, M., Nockleby, M., Tomsovic, S., (1994) J. Phys. A, 27, p. 3299. , 10.1088/0305-4470/27/9/039
- Maia, R.N.P., Nicacio, F., Toscano, F., Vallejos, R.O., (2008) Phys. Rev. Lett., 100, p. 184102. , 10.1103/PhysRevLett.100.184102
- Littlejohn, R.G., (1992) J. Stat. Phys., 68, p. 7. , 10.1007/BF01048836
- Miller, W.H., (2001) J. Phys. Chem. A, 105, p. 2942. , 10.1021/jp003712k
- Robinett, R.W., (2004) Phys. Rep., 392, p. 1. , 10.1016/j.physrep.2003.11.002
- Yeazell, J.A., Mallalieu, M., Stroud, Jr.C.R., (1990) Phys. Rev. Lett., 64, p. 2007. , 10.1103/PhysRevLett.64.2007;
- Vrakking, M.J.J., Villeneuve, D.M., Stolow, A., (1996) Phys. Rev. A, 54, p. 37. , 10.1103/PhysRevA.54.R37;
- Rempe, G., Walther, H., Klein, N., (1987) Phys. Rev. Lett., 58, p. 353. , 10.1103/PhysRevLett.58.353;
- Diedrich, F., Krause, J., Rempe, G., Scully, M.O., Walther, H., (1988) IEEE J. Quantum Electron., 24, p. 1314. , 10.1109/3.968
- Yurke, B., Stoler, D., (1986) Phys. Rev. Lett., 57, p. 13. , 10.1103/PhysRevLett.57.13;
- Gantsong, Ts., Tanaś, R., (1991) Quantum Opt., 3, p. 33. , 10.1088/0954-8998/3/1/004;
- Tara, K., Agarwal, G.S., Chaturvedi, S., (1993) Phys. Rev. A, 47, p. 5024. , 10.1103/PhysRevA.47.5024
- Braunstein, S.L., Van Look, P., (2005) Rev. Mod. Phys., 77, p. 513. , 10.1103/RevModPhys.77.513
- Wang, Z., Heller, E.J., (2009) J. Phys. A: Math. Theor., 42, p. 285304. , 10.1088/1751-8113/42/28/285304
- Novaes, M., (2005) J. Math. Phys., 46, p. 102102. , 10.1063/1.2038608
- Cohen-Tannoudji, C., Diu, B., Laloë, F., (1977) Quantum Mechanics, 1. , Wiley, New York
- Walls, D.F., Milburn, G., (1995) Quantum Optics, , Springer, Berlin
- Schleich, W.P., (2001) Quantum Optics in Phase Space, , Wiley-VCH, Berlin
- Ozorio De Almeida, A.M., (1998) Phys. Rep., 295, p. 265. , 10.1016/S0370-1573(97)00070-7
- Whittaker, E.T., Watson, G.N., (1927) A Course of Modern Analysis, , Cambridge University Press, Cambridge
- Mumford, D., (1983) Tata Lectures on Theta i, , Birkhäuser, Boston
- Weisstein, E.W., http://mathworld.wolfram.com/JacobiThetaFunctions.html; Littlejohn, R.G., (1986) Phys. Rep., 138, p. 193. , 10.1016/0370-1573(86)90103-1
- Huber, D., Heller, E.J., Littlejohn, R.G., (1988) J. Chem. Phys., 89, p. 2003. , 10.1063/1.455714;
- Maslov, V.P., (1994) The Complex WKB Method for Nonlinear Equations i, , Birkhäuser, Basel
- De Aguiar, M.A.M., Baranger, M., Jaubert, L., Parisio, F., Ribeiro, A.D., (2005) J. Phys. A, 38, p. 4645. , 10.1088/0305-4470/38/21/010
- Child, M.S., (1991) Semiclassical Mechanics with Molecular Applications, , Oxford University Press, Oxford
Citas:
---------- APA ----------
Toscano, F., Vallejos, R.O. & Wisniacki, D.
(2009)
. Semiclassical description of wave packet revival. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 80(4).
http://dx.doi.org/10.1103/PhysRevE.80.046218---------- CHICAGO ----------
Toscano, F., Vallejos, R.O., Wisniacki, D.
"Semiclassical description of wave packet revival"
. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 80, no. 4
(2009).
http://dx.doi.org/10.1103/PhysRevE.80.046218---------- MLA ----------
Toscano, F., Vallejos, R.O., Wisniacki, D.
"Semiclassical description of wave packet revival"
. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 80, no. 4, 2009.
http://dx.doi.org/10.1103/PhysRevE.80.046218---------- VANCOUVER ----------
Toscano, F., Vallejos, R.O., Wisniacki, D. Semiclassical description of wave packet revival. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2009;80(4).
http://dx.doi.org/10.1103/PhysRevE.80.046218