Skip to main content
SpringerLink
Log in

Dissipative electronic nonadiabatic dynamics within the framework of the Schrödinger–Langevin equation

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

A two-state version of the Schrödinger–Langevin equation is developed to describe dissipative effects on electronic nonadiabatic dynamics. This equation is obtained by including the dissipative potential on each potential surface into the coupled time-dependent Schrödinger equations for a two-state system in the diabatic representation. The hydrodynamic equations of motion for dissipative Bohmian trajectories evolving on each potential surface are derived using the quantum trajectory formulation. Several important properties associated with the two-state Schrödinger–Langevin equation are derived as well. The frictional effects on nonadiabatic transitions are studied for two model systems. Computational results are presented and analyzed, including the evolution of the probability densities, the dynamics of quantum trajectories, and the evolution of population transfer between two surfaces. This study demonstrates that the two-state Schrödinger–Langevin equation provides a phenomenological description for dissipative electronic nonadiabatic dynamics.

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
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. M. Razavy, Classical and Quantum Dissipative Systems (Imperial College Press, London, 2006)

    Book  Google Scholar 

  2. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2012)

    Book  Google Scholar 

  3. A.O. Caldeira, An Introduction to Macroscopic Quantum Phenomena and Quantum Dissipation (Cambridge University Press, New York, 2014)

    Book  Google Scholar 

  4. H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2007)

    Book  Google Scholar 

  5. H. Dekker, Phys. Rep. 80, 1 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  6. D. Schuch, Int. J. Quantum Chem. 72, 537 (1999)

    Article  Google Scholar 

  7. M.D. Kostin, J. Chem. Phys. 57, 3589 (1972)

    Article  ADS  Google Scholar 

  8. M.D. Kostin, J. Stat. Phys. 12, 145 (1975)

    Article  ADS  Google Scholar 

  9. A.B. Nassar, Ann. Phys. (N.Y.) 331, 317 (2013)

  10. A.B. Nassar, S. Miret-Artés, Phys. Rev. Lett. 111, 150401 (2013)

  11. P. Bargueño, S. Miret-Artés, Ann. Phys. (N.Y.) 346, 59 (2014)

  12. A.B. Nassar, S. Miret-Artés, Bohmian Mechanics, Open Quantum Systems and Continuous Measurements (Springer, New York, 2017)

    Book  Google Scholar 

  13. A.F. Vargas, N. Morales-Durán, P. Bargueño, Ann. Phys . (N.Y.) 356, 498 (2015)

  14. R. Katz, P.B. Gossiaux, Ann. Phys. (N.Y.) 368, 267 (2016)

  15. C.-C. Chou, Ann. Phys. (N.Y.) 373, 325 (2016)

  16. C.-C. Chou, Ann. Phys. (N.Y.) 362, 57 (2015)

  17. C.-C. Chou, Chem. Phys. Lett. 633, 195 (2015)

    Article  ADS  Google Scholar 

  18. B. Gu, R.J. Hinde, V.A. Rassolov, S. Garashchuk, J. Chem. Theory Comput. 11, 2891 (2015)

    Article  Google Scholar 

  19. C.-C. Chou, Chem. Phys. Lett. 669, 181 (2017)

    Article  ADS  Google Scholar 

  20. C.-C. Chou, Phys. Lett. A 381, 3384 (2017)

    Article  ADS  Google Scholar 

  21. C.-C. Chou, Ann. Phys. (N.Y.) 377, 22 (2017)

  22. C.D. Richardson, P. Schlagheck, J. Martin, N. Vandewalle, T. Bastin, Phys. Rev. A 89, 032118 (2014)

  23. C.-C. Chou, Ann. Phys. (N.Y.) 371, 437 (2016)

  24. C.-C. Chou, Int. J. Quantum Chem. 116, 1752 (2016)

    Article  Google Scholar 

  25. C.-C. Chou, Ann. Phys. (N.Y.) 393, 167 (2018)

  26. S.V. Mousavi, S. Miret-Artés, J. Phys. Commun. 2, 035029 (2018)

  27. S.V. Mousavi, S. Miret-Artés, Ann. Phys. (N.Y.) 393, 76 (2018)

  28. C.-C. Chou, Int. J. Quantum Chem. 119, e25812 (2019)

  29. S.V. Mousavi, S. Miret-Artés, Eur. Phys. J. Plus 134, 311 (2019)

    Article  Google Scholar 

  30. S.V. Mousavi, S. Miret-Artés, Eur. Phys. J. Plus 134, 431 (2019)

    Article  Google Scholar 

  31. S.V. Mousavi, S. Miret-Artés, Eur. Phys. J. Plus 135, 83 (2020)

    Article  Google Scholar 

  32. J.C. Tully, J. Chem. Phys. 93, 1061 (1990)

    Article  ADS  Google Scholar 

  33. J.C. Burant, J.C. Tully, J. Chem. Phys. 112, 6097 (2000)

    Article  ADS  Google Scholar 

  34. R.E. Wyatt, C.L. Lopreore, G. Parlant, J. Chem. Phys. 114, 5113 (2001)

    Article  ADS  Google Scholar 

  35. C.L. Lopreore, R.E. Wyatt, J. Chem. Phys. 116, 1228 (2002)

    Article  ADS  Google Scholar 

  36. V.A. Rassolov, S. Garashchuk, Phys. Rev. A 71, 032511 (2005)

  37. S. Garashchuk, V.A. Rassolov, G.C. Schatz, J. Chem. Phys. 123, 174108 (2005)

  38. S. Garashchuk, V.A. Rassolov, G.C. Schatz, J. Chem. Phys. 124, 244307 (2006)

  39. B. Poirier, G. Parlant, J. Phys. Chem. A 111, 10400 (2007)

    Article  Google Scholar 

  40. N. Zamstein, D.J. Tannor, J. Chem. Phys. 137, 22A517 (2012)

    Article  Google Scholar 

  41. N. Zamstein, D.J. Tannor, J. Chem. Phys. 137, 22A518 (2012)

    Article  Google Scholar 

  42. Y. Wang, C.-C. Chou, Chem. Phys. Lett. 699, 125 (2018)

    Article  ADS  Google Scholar 

  43. D. Bohm, Phys. Rev. 85, 166 (1952)

    Article  ADS  MathSciNet  Google Scholar 

  44. D. Bohm, Phys. Rev. 85, 180 (1952)

    Article  ADS  MathSciNet  Google Scholar 

  45. P.R. Holland, The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics (Cambridge University Press, New York, 1993)

    Book  Google Scholar 

  46. R.E. Wyatt, Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics (Springer, New York, 2005)

    MATH  Google Scholar 

  47. A. S. Sanz, S. Miret-Artés, A Trajectory Description of Quantum Processes. I. Fundamentals (Springer, New York, 2012)

  48. A.S. Sanz, S. Miret-Artés, A Trajectory Description of Quantum Processes. II, Applications (Springer, New York, 2014)

    Book  Google Scholar 

  49. M. Barbatti, WIREs Comput. Mol. Sci. 1, 620 (2011)

    Article  Google Scholar 

  50. L.M. Ibele, B.F.E. Curchod, Phys. Chem. Chem. Phys. 22, 15183 (2020)

    Article  Google Scholar 

  51. B.G. Levine, T.J. Martínez, Annu. Rev. Phys. Chem. 58, 613 (2007)

    Article  ADS  Google Scholar 

  52. M. Barbatti, A.J.A. Aquino, H. Lischka, Mol. Phys. 104, 1053 (2006)

    Article  ADS  Google Scholar 

  53. L. Shen, D. Tang, B. Xie, W.-H. Fang, J. Phys. Chem. A 123, 7337 (2019)

    Article  Google Scholar 

  54. D.A. McQuarrie, Statistical Mechanics (University Science Books, Sausalito, 2008)

    MATH  Google Scholar 

  55. D.J. Tannor, Introduction to Quantum Mechanics: A Time-Dependent Perspective (University Science Books, Sausalito, 2007)

    Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge Ministry of Science and Technology, Taiwan (Grant No. MOST 109-2113-M-007-004) for its financial support of this research.

Author information

Authors and Affiliations

  1. Department of Chemistry, National Tsing Hua University, Hsinchu, 30013, Taiwan

    Ching-Hwa Ho & Chia-Chun Chou

Authors
  1. Ching-Hwa Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chia-Chun Chou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chia-Chun Chou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ho, CH., Chou, CC. Dissipative electronic nonadiabatic dynamics within the framework of the Schrödinger–Langevin equation. Eur. Phys. J. Plus 136, 973 (2021). https://doi.org/10.1140/epjp/s13360-021-01963-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01963-2

Search

Navigation