Geodesic
Energy and coherence loss rates in a one-dimensional vibrational system interacting with a bath
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 130-144 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the problem of the dynamics of a Gaussian wave packet in a one-dimensional harmonic ocsillator interacting with a bath. This problem arises in many chemical and biochemical applications related to the dynamics of chemical reactions. We take the bath–oscillator interaction into account in the framework of the Redfield theory. We obtain closed expressions for Redfield-tensor elements, which allows finding the explicit time dependence of the average vibrational energy. We show that the energy loss rate is temperature-independent, is the same for all wave packets, and depends only on the spectral function of the bath. We determine the degree of coherence of the vibrational motion as the trace of the density-matrix projection on a coherently moving wave packet. We find an explicit expression for the initial coherence loss rate, which depends on the wave packet width and is directly proportional to the intensity of the interaction with the bath. The minimum coherence loss rate is observed for a "coherent" Gaussian wave packet whose width corresponds to the oscillator frequency. We calculate the limiting value of the degree of coherence for large times and show that it is independent of the structural characteristics of the bath and depends only on the parameters of the wave packet and on the temperature. It is possible that residual coherence can be preserved at low temperatures.
Keywords: quantum dissipation, Redfield theory, density matrix, harmonic oscillator, degree of coherence, wave packet. 
@article{TMF_2007_153_1_a9,
     author = {V. V. Eremin and I. O. Glebov},
     title = {Energy and coherence loss rates in a~one-dimensional vibrational system interacting with a~bath},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {130--144},
     year = {2007},
     volume = {153},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a9/}
}
TY  - JOUR
AU  - V. V. Eremin
AU  - I. O. Glebov
TI  - Energy and coherence loss rates in a one-dimensional vibrational system interacting with a bath
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 130
EP  - 144
VL  - 153
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a9/
LA  - ru
ID  - TMF_2007_153_1_a9
ER  - 
%0 Journal Article
%A V. V. Eremin
%A I. O. Glebov
%T Energy and coherence loss rates in a one-dimensional vibrational system interacting with a bath
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 130-144
%V 153
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a9/
%G ru
%F TMF_2007_153_1_a9
V. V. Eremin; I. O. Glebov. Energy and coherence loss rates in a one-dimensional vibrational system interacting with a bath. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 130-144. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a9/

[1] V. Sundström, Progr. Quantum Electron., 24 (2000), 187 | DOI

[2] R. S. Knox, J. Photochem. Photobiol. B, 49 (1999), 81 | DOI

[3] C. E. Crespo-Hernandez, B. Cohen, P. M. Hare, B. Kohler, Chem. Rev., 104 (2004), 1977 | DOI

[4] S. K. Pal, A. H. Zewail, Chem. Rev., 104 (2004), 2099 | DOI

[5] X. Hu, T. Ritz, A. Damjanovic, K. Schulten, J. Phys. Chem. B, 101 (1997), 3854 | DOI

[6] D. Egorova, A. Kühl, W. Domcke, Chem. Phys., 268 (2001), 105 | DOI

[7] D. Egorova, W. Domcke, J. Photochem. Photobiol. A, 166 (2004), 19 | DOI

[8] A. Kühl, W. Domcke, J. Chem. Phys., 116 (2002), 263 | DOI

[9] V. I. Novoderezhkin, A. G. Yakovlev, R. van Grondelle, V. A. Shuvalov, J. Phys. Chem. B, 108 (2004), 7445 | DOI

[10] U. Weiss, Quantum Dissipative Systems, 2nd ed., World Sci. Publ., Singapore, 1999

[11] A. G. Redfield, Adv. Magn. Res., 1 (1965), 1 | DOI

[12] K. Blum, Teoriya matritsy plotnosti i ee prilozheniya, Mir, M., 1983 | MR | MR

[13] V. Yu. Golyshev, Pisma v ZhTF, 28:2 (2002), 50

[14] V. V. Eremin, I. M. Umanskii, N. E. Kuzmenko, L. D. Ievleva, Izv. RAN. Ser. khim., 2000, no. 12, 1991

[15] V. V. Eryomin, S. I. Vetchinkin, I. M. Umanskii, J. Chem. Phys., 101 (1994), 10730 | DOI

[16] R. P. Feinman, A. R. Khibbs, Kvantovaya mekhanika i integraly po traektoriyam, Mir, M., 1968 | MR | Zbl