- Physical Review Journals
All JournalsPhysics Magazine

Physical Review A

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Open quantum systems with particle and bath driven by time-dependent fields

Daniele Gamba1,2,*, Bingyu Cui3, and Alessio Zaccone1,2,†

  • *Contact author: daniele.gamba@theorie.physik.uni-goettingen.de
  • †Contact author: alessio.zaccone@unimi.it
PDF

Phys. Rev. A 112, 012207 – Published 10 July, 2025

DOI: https://doi.org/10.1103/w3vk-wx62

Abstract

We derive a generalized quantum Langevin equation and its fluctuation-dissipation relation describing the quantum dynamics of a tagged particle interacting with a medium (environment), where both the particle and the environment are driven by an external time-dependent (e.g. oscillating) field. We specialize on the case of a charged tagged particle interacting with a bath of charged oscillators, under an external ac electric field, although the results are much more general and can be applied to any type of external time-dependent fields. We derive the corresponding quantum Langevin equation, which obeys a modified fluctuation-dissipation relation (FDR) where the ac field plays an explicit role. The modified FDR is non-Markovian even if the undriven particle-bath system is Markovian without the external field. We provide an illustration of the usefulness of these results and derive a new form of the quantum Nyquist noise for the voltage fluctuations in electrical circuits under ac conditions (finite frequency), which is the most general since it also accounts for the response of the heat bath (e.g. lattice ions) to the applied ac electric field in the GHz–THz region, of relevance for 5G/6G wireless technologies. This generalized quantum fluctuation-dissipation relation for driven systems can also find other applications ranging from quantum noise in quantum optics to quantum computing with trapped ions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University, New York, 2002).
  2. A. A. Tomaz, R. S. Mattos, and M. Barbatti, The quantum measurement problem: A review of recent trends, arXiv:2502.19278.
  3. M. Schlosshauer, Decoherence (Springer-Verlag, Berlin, 2007).
  4. B. Vacchini, Open Quantum Systems (Springer, New York, 2024).
  5. G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986).
  6. G. Ghirardi, Sneaking a Look at God's Cards (Princeton University, Princeton, NJ, 2005).
  7. P. Caldirola, Il Nuovo Cimento (1924-1942) 18, 393 (1941).
  8. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
  9. M. Buchholz, F. Grossmann, and M. Ceotto, J. Chem. Phys. 147, 164110 (2017).
  10. A. Nitzan, Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems (Oxford University, New York, 2006).
  11. G. W. Ford, M. Kac, and P. Mazur, J. Math. Phys. 6, 504 (1965).
  12. G. W. Ford and M. Kac, J. Stat. Phys. 46, 803 (1987).
  13. G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. A 37, 4419 (1988).
  14. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2012).
  15. C. Gardiner and P. Zoller, Quantum Noise (Springer-Verlag, Berlin, 2000).
  16. S. Gupta and M. Bandyopadhyay, Phys. Rev. E 84, 041133 (2011).
  17. E. K. Alpomishev, G. G. Adamian, and N. V. Antonenko, Phys. Rev. B 110, 174308 (2024).
  18. L. Landau, Z. Phys. 64, 629 (1930).
  19. W. Bao, M.-G. Li, R. Xing, and J.-D. Bao, Phys. Rev. Res. 7, 013210 (2025).
  20. J. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, J. Opt. Soc. Am. B 20, 1003 (2003).
  21. J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
  22. K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
  23. Y. V. Nazarov and Y. M. Blanter, Quantum Transport: Introduction to Nanoscience (Cambridge University, New York, 2009).
  24. A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Rev. Mod. Phys. 82, 1155 (2010).
  25. B. Cui and A. Zaccone, Phys. Rev. E 97, 060102(R) (2018).
  26. H. Grabert and M. Thorwart, Phys. Rev. E 98, 012122 (2018).
  27. D. Tiwari, B. Bose, and S. Banerjee, J. Chem. Phys. 162, 114104 (2025).
  28. F. Albarelli, B. Vacchini, and A. Smirne, Quantum Sci. Technol. 10, 015041 (2025).
  29. D. Gamba, B. Cui, and A. Zaccone, Phys. Rev. E 110, 054137 (2024).
  30. H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951).
  31. R. W. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University, New York, 2001).
  32. F. Petruccione and B. Vacchini, Phys. Rev. E 71, 046134 (2005).
  33. P. Hänggi and G.-L. Ingold, Chaos: J. Nonlin. Sci. 15, 026105 (2005).
  34. P. Hänggi, in Stochastic Dynamics, edited by L. Schimansky-Geier and T. Pöschel (Springer-Verlag, Berlin, 1997), pp. 15–22.
  35. V. B. Magalinskii, Sov. Phys. JETP 9, 1382 (1959).
  36. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Butterworth-Heinemann, Oxford, 1981).
  37. J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed. (Cambridge University, New York, 2020).
  38. J. I. Kapusta and C. Gale, Finite-Temperature Field Theory: Principles and Applications, 2nd ed., Cambridge Monographs on Mathematical Physics (Cambridge University, New York, 2023).
  39. A. Kamenev, Field Theory of Non-Equilibrium Systems (Cambridge University, New York, 2011).
  40. P. Gaspard, The Statistical Mechanics of Irreversible Phenomena (Cambridge University, New York, 2022).
  41. J. B. Johnson, Phys. Rev. 32, 97 (1928).
  42. H. Nyquist, Phys. Rev. 32, 110 (1928).
  43. C. Kittel, Elementary Statistical Physics (Wiley, New York, 1958).
  44. J. Lawson and G. Uhlenbeck, Threshold Noise Signals (McGraw-Hill, New York, 1950).
  45. E. Zhitlukhina, M. Belogolovskii, and P. Seidel, J. Low Temp. Phys. 212, 79 (2023).
  46. M. H. Pedersen and M. Büttiker, Phys. Rev. B 58, 12993 (1998).
  47. W. A. Gardner, Introduction to Random Processes with Applications to Signals and Systems (Macmillan, New York, 1985).
  48. T. Yu and J. Eberly, Opt. Commun. 264, 393 (2006).
  49. S. Olivares, A Student's Guide to Quantum Computing (Springer, New York, 2025).
  50. G. Grynberg, A. Aspect, C. Fabre, and C. Cohen-Tannoudji, Introduction to Quantum Optics: From the Semi-Classical Approach to Quantized Light (Cambridge University, New York, 2010).

Outline

Information

Phys. Rev. A 112, 012207– Published 10 July, 2025
  • Received 8 May 2025
  • Accepted 16 June 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation