Skip to main content
SpringerLink
Log in

Exit dynamics from Morse potential under thermal fluctuations

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

We study the dynamics of a Brownian particle in Morse potential under thermal fluctuations, modelled by Gaussian white noise whose amplitude depends on absolute temperature. Dynamics of such a particle is investigated by numerically integrating the corresponding Langevin equation. From the mean first passage time (escape time), we study the dependence of Kramer’s rate on temperature and viscosity of the medium. An approximate analytical expression for the rate constant is found by solving differential equation for the mean first passage time. The expression shows a temperature dependent pre-factor for the Arrhenius equation. Our numerical simulations are in agreement with the analytical approximations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

References

  1. K J Laidler, Arch. Hist. Exact Sci. 32, 43 (1985)

    Article  MathSciNet  Google Scholar 

  2. L Farkas, Z. Phys. Chem. (Leipzig) 125, 236 (1927)

    Google Scholar 

  3. H A Kramers, Physica 7, 284 (1940)

    Article  ADS  MathSciNet  Google Scholar 

  4. F L Barboza, A J Costa, N F Ribeiro and E D Filho, Rev. Bras. de Ensino de Fis. 29, 543 (2007)

    Article  Google Scholar 

  5. W C DeMarcus, Am. J. Phys. 46, 733 (1978)

    Article  ADS  Google Scholar 

  6. N B Slater, Nature 180, 1352 (1957)

    Article  ADS  Google Scholar 

  7. M Peyrard, Nonlinearity 17(2), R1 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  8. D Reguera and G Birnbaum, J. Chem. Phys. 125, 184304 (2006)

    Article  ADS  Google Scholar 

  9. P Hänggi, P Talkner and M Borkovec, Rev. Mod. Phys. 62, 251 (1990)

  10. B Dybiec, E Gudowska-Nowak and P Hänggi, Phys. Rev. E 75, 021109 (2007)

    Article  ADS  Google Scholar 

  11. C Gardiner, Handbook of stochastic methods (Springer, Berlin, 1985)

    Google Scholar 

  12. N E Henriksen and Y Flemmiing, Theories of molecular reaction dynamics: The microscopic foundation of chemical kinetics (Oxford University Press, Oxford, 2018)

    Book  Google Scholar 

  13. A D McNaught and A Wilkinson, Compendium of chemical terminology (Blackwell Science, Oxford, 1997) Vol. 1669

  14. C Rossant and I Python, Interactive computing and visualization cookbook (Packt Publishing Ltd., Birmingham, 2018)

    Google Scholar 

  15. K Capala et al, Chaos 30, 123103 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  16. R Toral and P Colet, Stochastic numerical methods: An introduction to students and scientists (John Wiley & Sons, 2014)

  17. R Larson and E J Lightfoot, Physica A 149, 296 (1988)

    Article  ADS  Google Scholar 

  18. A Kenfack and J M Rost, J. Chem. Phys. 123, 204 (2005)

    Article  Google Scholar 

  19. R Metzler and J Klafter, Chem. Phys. Lett. 321, 238 (2000)

    Article  ADS  Google Scholar 

  20. O G Berg, Chem. Phys. 31, 47 (1978)

    Article  ADS  Google Scholar 

  21. G Srinivas, Y Arun and B Bagchi, The J. Chem. Phys. 114, 20 (2001)

    Google Scholar 

  22. B Shizgal, Spectral methods in chemistry and physics (Springer, Netherlands, 2015)

  23. C M Bender and S A Orszag, Advanced mathematical methods for scientists and engineers I: Asymptotic methods and perturbation theory (Springer, USA, 2013)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, National Institute of Technology, Tiruchirappalli, 620 015, India

    P Vipin & R Sankaranarayanan

Authors
  1. P Vipin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R Sankaranarayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P Vipin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vipin, P., Sankaranarayanan, R. Exit dynamics from Morse potential under thermal fluctuations. Pramana - J Phys 97, 43 (2023). https://doi.org/10.1007/s12043-023-02527-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-023-02527-y

Keywords

PACS Nos

Search

Navigation