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The Reaction Coordinate Mapping in Quantum Thermodynamics

  • Ahsan NazirEmail author
  • Gernot Schaller
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 195)

Abstract

We present an overview of the reaction coordinate approach to handling strong system-reservoir interactions in quantum thermodynamics. This technique is based on incorporating a collective degree of freedom of the reservoir (the reaction coordinate) into an enlarged system Hamiltonian (the supersystem), which is then treated explicitly. The remaining residual reservoir degrees of freedom are traced out in the usual perturbative manner. The resulting description accurately accounts for strong system-reservoir coupling and/or non-Markovian effects over a wide range of parameters, including regimes in which there is a substantial generation of system-reservoir correlations. We discuss applications to both discrete stroke and continuously operating heat engines, as well as perspectives for additional developments. In particular, we find narrow regimes where strong coupling is not detrimental to the performance of continuously operating heat engines.

Notes

Acknowledgements

G.S. gratefully acknowledges discussions with J. Cerrillo, N. Martensen, S. Restrepo, and P. Strasberg and financial support by the DFG (GRK 1558, SFB 910, SCHA 1646/3-1, BR 1528/9-1).

A.N. would like to thank D. Newman, F. Mintert, J. Iles-Smith, N. Lambert, Z. Blunden-Codd and V. Jouffrey for discussions. A.N. is supported by the Engineering and Physical Sciences Research Council, grant no. EP/N008154/1.

References

  1. 1.
    Y. Liu, Y. Zheng, W. Gong, W. Gao, T. Lü, Phys. Lett. A 365, 495 (2007).  https://doi.org/10.1016/j.physleta.2007.02.005ADSCrossRefGoogle Scholar
  2. 2.
    F. Nesi, E. Paladino, M. Thorwart, M. Grifoni, Europhys. Lett. 80, 40005 (2007).  https://doi.org/10.1209/0295-5075/80/40005ADSCrossRefGoogle Scholar
  3. 3.
    C. Hörhammer, H. Büttner, J. Stat. Phys. 133, 1161 (2008).  https://doi.org/10.1007/s10955-008-9640-xADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. Campisi, P. Talkner, P. Hänggi, Phys. Rev. Lett. 102, 210401 (2009).  https://doi.org/10.1103/PhysRevLett.102.210401ADSCrossRefGoogle Scholar
  5. 5.
    L. Nicolin, D. Segal, Phys. Rev. B 84, 161414 (2011).  https://doi.org/10.1103/PhysRevB.84.161414ADSCrossRefGoogle Scholar
  6. 6.
    S. Deffner, E. Lutz, Phys. Rev. Lett. 107, 140404 (2011).  https://doi.org/10.1103/PhysRevLett.107.140404ADSCrossRefGoogle Scholar
  7. 7.
    J. Hausinger, M. Grifoni, Phys. Rev. A 83, 030301 (2011).  https://doi.org/10.1103/PhysRevA.83.030301ADSCrossRefGoogle Scholar
  8. 8.
    L. Pucci, M. Esposito, L. Peliti, J. Stat. Mech. Theory Exp. 2013, P04005 (2013).  https://doi.org/10.1088/1742-5468/2013/04/P04005
  9. 9.
    G. Schaller, T. Krause, T. Brandes, M. Esposito, New J. Phys. 15, 033032 (2013).  https://doi.org/10.1088/1367-2630/15/3/033032ADSCrossRefGoogle Scholar
  10. 10.
    J. Ankerhold, J.P. Pekola, Phys. Rev. B 90, 075421 (2014).  https://doi.org/10.1103/PhysRevB.90.075421ADSCrossRefGoogle Scholar
  11. 11.
    J. Iles-Smith, N. Lambert, A. Nazir, Phys. Rev. A 90, 032114 (2014).  https://doi.org/10.1103/PhysRevA.90.032114ADSCrossRefGoogle Scholar
  12. 12.
    R. Gallego, A. Riera, J. Eisert, New J. Phys. 16, 125009 (2014).  https://doi.org/10.1088/1367-2630/16/12/125009
  13. 13.
    C. Wang, J. Ren, J. Cao, Sci. Rep. 5, 11787 (2015).  https://doi.org/10.1038/srep11787ADSCrossRefGoogle Scholar
  14. 14.
    M. Esposito, M.A. Ochoa, M. Galperin, Phys. Rev. Lett. 114, 080602 (2015a).  https://doi.org/10.1103/PhysRevLett.114.080602ADSCrossRefGoogle Scholar
  15. 15.
    M. Esposito, M.A. Ochoa, M. Galperin, Phys. Rev. B 92, 235440 (2015b).  https://doi.org/10.1103/PhysRevB.92.235440ADSCrossRefGoogle Scholar
  16. 16.
    D. Gelbwaser-Klimovsky, A. Aspuru-Guzik, J. Phys. Chem. Lett. 6, 3477 (2015).  https://doi.org/10.1021/acs.jpclett.5b01404CrossRefGoogle Scholar
  17. 17.
    M. Carrega, P. Solinas, A. Braggio, M. Sassetti, U. Weiss, New J. Phys. 17, 045030 (2015).  https://doi.org/10.1088/1367-2630/17/4/045030
  18. 18.
    P. Strasberg, G. Schaller, N. Lambert, T. Brandes, New J. Phys. 18, 073007 (2016).  https://doi.org/10.1088/1367-2630/18/7/073007ADSCrossRefGoogle Scholar
  19. 19.
    G. Katz, R. Kosloff, Entropy 18, 186 (2016).  https://doi.org/10.3390/e18050186ADSCrossRefGoogle Scholar
  20. 20.
    J. Cerrillo, M. Buser, T. Brandes, Phys. Rev. B 94, 214308 (2016).  https://doi.org/10.1103/PhysRevB.94.214308ADSCrossRefGoogle Scholar
  21. 21.
    U. Seifert, Phys. Rev. Lett. 116, 020601 (2016).  https://doi.org/10.1103/PhysRevLett.116.020601ADSCrossRefGoogle Scholar
  22. 22.
    D. Newman, F. Mintert, A. Nazir, Phys. Rev. E 95, 032139 (2017).  https://doi.org/10.1103/PhysRevE.95.032139ADSCrossRefGoogle Scholar
  23. 23.
    P. Strasberg, M. Esposito, Phys. Rev. E 95, 062101 (2017).  https://doi.org/10.1103/PhysRevE.95.062101ADSCrossRefGoogle Scholar
  24. 24.
    H.J.D. Miller, J. Anders, Phys. Rev. E 95, 062123 (2017).  https://doi.org/10.1103/PhysRevE.95.062123ADSCrossRefGoogle Scholar
  25. 25.
    A. Mu, B.K. Agarwalla, G. Schaller, D. Segal, New J. Phys. 19, 123034 (2017).  https://doi.org/10.1088/1367-2630/aa9b75ADSCrossRefGoogle Scholar
  26. 26.
    C. Jarzynski, Phys. Rev. X 7, 011008 (2017).  https://doi.org/10.1103/PhysRevX.7.011008CrossRefGoogle Scholar
  27. 27.
    N. Freitas, J.P. Paz, Phys. Rev. E 95, 012146 (2017).  https://doi.org/10.1103/PhysRevE.95.012146ADSCrossRefGoogle Scholar
  28. 28.
    M. Perarnau-Llobet, H. Wilming, A. Riera, R. Gallego, J. Eisert, Phys. Rev. Lett. 120, 120602 (2018).  https://doi.org/10.1103/PhysRevLett.120.120602ADSCrossRefGoogle Scholar
  29. 29.
    R.S. Burkey, C.D. Cantrell, J. Opt. Soc. Am. B 1, 169 (1984).  https://doi.org/10.1364/JOSAB.1.000169ADSCrossRefGoogle Scholar
  30. 30.
    A. Garg, J.N. Onuchic, V. Ambegaokar, J. Chem. Phys. 83, 4491 (1985).  https://doi.org/10.1063/1.449017ADSCrossRefGoogle Scholar
  31. 31.
    R. Martinazzo, B. Vacchini, K.H. Hughes, I. Burghardt, J. Chem. Phys. 134, 011101 (2011).  https://doi.org/10.1063/1.3532408ADSCrossRefGoogle Scholar
  32. 32.
    M.P. Woods, R. Groux, A.W. Chin, S.F. Huelga, M.B. Plenio, J. Math. Phys. 55, 032101 (2014).  https://doi.org/10.1063/1.4866769ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    G. Schaller, J. Cerrillo, G. Engelhardt, P. Strasberg, Phys. Rev. B 97, 195104 (2018).  https://doi.org/10.1103/PhysRevB.97.195104ADSCrossRefGoogle Scholar
  34. 34.
    P. Strasberg, G. Schaller, T.L. Schmidt, M. Esposito, Phys. Rev. B 97, 205405 (2018).  https://doi.org/10.1103/PhysRevB.97.205405ADSCrossRefGoogle Scholar
  35. 35.
    S. Restrepo, J. Cerrillo, P. Strasberg, G. Schaller, New J. Phys. (2018).  https://doi.org/10.1088/1367-2630/aac583CrossRefGoogle Scholar
  36. 36.
    J. Iles-Smith, A.G. Dijkstra, N. Lambert, A. Nazir, J. Chem. Phys. 144, 044110 (2016).  https://doi.org/10.1063/1.4940218ADSCrossRefGoogle Scholar
  37. 37.
    J. Huh, S. Mostame, T. Fujita, M.-H. Yung, A. Aspuru-Guzik, New J. Phys. 16, 123008 (2014).  https://doi.org/10.1088/1367-2630/16/12/123008ADSCrossRefGoogle Scholar
  38. 38.
    M.P. Woods, M. Cramer, M.B. Plenio, Phys. Rev. Lett. 115, 130401 (2015).  https://doi.org/10.1103/PhysRevLett.115.130401ADSCrossRefGoogle Scholar
  39. 39.
    M.P. Woods, M.B. Plenio, J. Math. Phys. 57, 022105 (2016).  https://doi.org/10.1063/1.4940436ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    C. Gogolin, J. Eisert, Rep. Prog. Phys. 79, 056001 (2016).  https://doi.org/10.1088/0034-4885/79/5/056001ADSCrossRefGoogle Scholar
  41. 41.
    R. Dümcke, H. Spohn, Z. Phys. B 34, 419 (1979).  https://doi.org/10.1007/BF01325208
  42. 42.
    H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).  https://doi.org/10.1093/acprof:oso/9780199213900.001.0001
  43. 43.
    K. Le Hur, Phys. Rev. B 85, 140506 (2012).  https://doi.org/10.1103/PhysRevB.85.140506CrossRefGoogle Scholar
  44. 44.
    M. Goldstein, M.H. Devoret, M. Houzet, L.I. Glazman, Phys. Rev. Lett. 110, 017002 (2013).  https://doi.org/10.1103/PhysRevLett.110.017002ADSCrossRefGoogle Scholar
  45. 45.
    B. Peropadre, D. Zueco, D. Porras, J.J. García-Ripoll, Phys. Rev. Lett. 111, 243602 (2013).  https://doi.org/10.1103/PhysRevLett.111.243602ADSCrossRefGoogle Scholar
  46. 46.
    A. Nazir, D.P.S. McCutcheon, J. Phys. Condens. Matter 28, 103002 (2016).  https://doi.org/10.1088/0953-8984/28/10/103002
  47. 47.
    R. Kosloff, A. Levy, Annu. Rev. Phys. Chem. 65, 365 (2014).  https://doi.org/10.1146/annurev-physchem-040513-103724ADSCrossRefGoogle Scholar
  48. 48.
    M. Esposito, K. Lindenberg, C.V. den Broeck, Europhys. Lett. 85, 60010 (2009).  https://doi.org/10.1209/0295-5075/85/60010ADSCrossRefGoogle Scholar
  49. 49.
    H. Haug, A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, Berlin, 2008).  https://doi.org/10.1007/978-3-540-73564-9
  50. 50.
    G.E. Topp, T. Brandes, G. Schaller, Europhys. Lett. 110, 67003 (2015).  https://doi.org/10.1209/0295-5075/110/67003ADSCrossRefGoogle Scholar
  51. 51.
    A. Bruch, M. Thomas, S. Viola Kusminskiy, F. von Oppen, A. Nitzan, Phys. Rev. B 93, 115318 (2016).  https://doi.org/10.1103/PhysRevB.93.115318ADSCrossRefGoogle Scholar
  52. 52.
    D.Y. Baines, T. Meunier, D. Mailly, A.D. Wieck, C. Bäuerle, L. Saminadayar, P.S. Cornaglia, G. Usaj, C.A. Balseiro, D. Feinberg, Phys. Rev. B 85, 195117 (2012).  https://doi.org/10.1103/PhysRevB.85.195117ADSCrossRefGoogle Scholar
  53. 53.
    T. Hensgens, T. Fujita, L. Janssen, X. Li, C.J.V. Diepen, C. Reichl, W. Wegscheider, S.D. Sarma, L.M.K. Vandersypen, Nature 548, 70 (2017).  https://doi.org/10.1038/nature23022ADSCrossRefGoogle Scholar
  54. 54.
    J.C. Bayer, T. Wagner, E.P. Rugeramigabo, R.J. Haug, Phys. Rev. B 96, 235305 (2017).  https://doi.org/10.1103/PhysRevB.96.235305ADSCrossRefGoogle Scholar
  55. 55.
    C.V. den Broeck, Phys. Rev. Lett. 95, 190602 (2005).  https://doi.org/10.1103/PhysRevLett.95.190602CrossRefGoogle Scholar
  56. 56.
    A. Gomez-Marin, J.M. Sancho, Phys. Rev. E 74, 062102 (2006).  https://doi.org/10.1103/PhysRevE.74.062102ADSCrossRefGoogle Scholar
  57. 57.
    S. Sheng, Z.C. Tu, J. Phys. Math. Theor. 46, 402001 (2013).  https://doi.org/10.1088/1751-8113/46/40/402001CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Physics and AstronomyThe University of ManchesterManchesterUK
  2. 2.Institut für Theoretische PhysikTechnische Universität BerlinBerlinGermany

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