ACCURACY OF ANALYTICAL CALCULATION OF THE HEAT DECAY RATE OF METASTABLE STATE IN THE ENERGY DIFFUSION MODE 

Chushnyakova Mariya Vladimirovna, Candidate of physical and mathematical sciences, senior lecturer, sub-department of physics, Omsk State Technical University (11, Mira avenue, Omsk, Russia), E-mail: maria.chushnyakova@gmail.com
Gonchar Igor' Ivanovich, Doctor of physical and mathematical sciences, professor, sub-department of physics and chemistry, Omsk State Transport University (35, Marksa avenue, Omsk, Russia), E-mail: vigichar@hotmail.com
Krokhin Sergey Nikolaevich, Candidate of physical and mathematical sciences, associate professor, head of the sub-department of physics and chemistry, Omsk State Transport University (35, Marksa avenue, Omsk, Russia), E-mail: krokhinsn@mail.ru
Maliy Ol'ga Vladimirovna, Engineer, sub-department of physics, Omsk State Technical University (11, Mira avenue, Omsk, Russia), E-mail: malij_olga@mail.ru com 

539.173 

10.21685/2072-3040-2019-3-9 

Background. The problem of the thermal decay of a metastable state appears in many branches of natural sciences: from chemistry and nuclear physics till electromagnetism and astrophysics. The energy diffusion regime (regime of week friction) is of the special interest since it is less intensively studied in the literature. The aim of the present research is the analysis of accuracy of approximate analytical formulas for the rate of a metastable state thermal decay in the energy diffusion regime
Materials and methods. The numerical modeling of a metastable state thermal decay is performed by means of the stochastic differential equations (Langevin equations).
Results. The quasistationary decay rate is calculated for the energy diffusion regime as well as for the spatial diffusion regime. The decay rates obtained using the numerical modeling are exact within the statistical errors. These dynamical (numerical) rates are compared with the approximate formulas for the energy diffusion regime in a wide range of friction parameter. All the results are presented in the dimensionless form in order to make them useful for a wider range of readers.
Conclusions. It is found that within the present model (parabolic potential, ratio of the barrier height to thermal energy is equal to 2.4), it is possible to choose such a value of a single free parameter of the approximate formula that the deviation of the approximate rate from the exact one does not exceed 5%. The obtained value of the free parameter does not depend upon the friction strength and does not contradict to the physical sense of the parameter intended by authors. 

thermal decay rate; Langevin equations; energy diffusion regime 

1. Kramers H. A. Physica. 1940, vol. 7, no. 4, pp. 284–304.
2. Weiss G. H. Journal of Statistical Physics. 1986, vol. 42, no. 1, pp. 3–36.
3. Hänggi P., Talkner P., Borkovec M. Review of Modern Physics. 1990, vol. 62, no. 2, pp. 251–341.
4. New Trends in Kramers' Reaction Rate Theory. P. Talkner, P. Hänggi (eds.). Berlin: Springer, 2012, 251 p.
5. Chandrasekhar S. Review of Modern Physics. 1943, vol. 15, no. 1, pp. 1–89.
6. Pontryagin L., Andronov A., Vitt A. On the statistical treatment of dynamical systems, Noise in Nonlinear Dynamical Systems Volume 1. Theory of Continuous Fokker-Planck Systems. Cambridge: Cambridge University Press, 2009, 356 p.
7. Challis K. J. Physical Review E. 2016, vol. 94, no. 6, p. 062123
8. Sharma A., Wittmann R., Brader J. M. Physicsal Review E. 2017, vol. 95, no. 1, p. 012115.
9. Zhou H.-X. Quarterly Reviews of Biophysics. 2010, vol. 43, no. 2, pp. 219–293.
10. Gontchar I. I., Fröbrich P. Nuclear Physics A. 1993, vol. 551, no. 3, pp. 495–507.
11. Ezin A. N., Samgin A. L. Physical Review E. 2010, vol. 82, no. 5, p. 056703.
12. Jiang Z., Smelyanskiy V. N., Boixo S., Neven H., Isakov S. V., Mazzola G., Troyer M. Physical Review A. 2017, vol. 95, no. 1, p. 012322.
13. Büttiker M., Harris E. P., Landauer R. Physical Review B. 1983, vol. 28, no. 3, pp. 1268–1275.
14. Gontchar I. I., Chushnyakova M. V., Aktaev N. E., Litnevsky A. L., Pavlova E. G. Physical Review C. 2010, vol. 82, no. 6, p. 064606.
15. Eccles C., Roy S., Gray T. H., Zaccone A. Physical Review C. 2017, vol. 96, no. 5, p. 054611.
16. Chushnyakova M. V., Gontchar I. I. Physical Review E. 2018, vol. 97, no. 3, p. 032107.
17. Karpov A. V., Nadtochy P. N., Ryabov E. G., Adeev G. D. Journal of Physics G: Nuclear and Particle Physics. 2003, vol. 29, no. 10, pp. 2365–2380.
18. Nadtochy P. N., Kelić A., Schmidt K.-H. Physical Review C. 2007, vol. 75, no. 6, pp. 064614.
19. Pavlova E. G., Aktaev N. E., Gontchar I. I. Physica A. 2012, vol. 391, no. 23, pp. 6084–6100.
20. Gontchar I. I., Krokhin S. N. Herald of Omsk University. 2012, vol. 4, pp. 84–87.
21. Gontchar I. I., Chushnyakova M. V. Pramana – Journal of Physics. 2017, vol. 88, no. 6, p. 90.