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Transmission from reverse reaction coordinate mappings

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Abstract

We point out that the transport properties of non-interacting fermionic chains tunnel-coupled to two reservoirs at their ends can be mapped to those of a single quantum dot that is tunnel-coupled to two transformed reservoirs. The parameters of the chain are mapped to additional structure in the spectral densities of the transformed reservoirs. For example, this enables the calculation of the transmission of quantum dot chains by evaluating the known transmission of a single quantum dot together with structured spectral densities. We exemplify this analytically for short chains, which allows to optimize the transmission. In addition, we also demonstrate that the mapping can be performed numerically by computing the transmission of a Su-Schrieffer-Heeger chain.

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References

  1. C. Flindt, C. Fricke, F. Hohls, T. Novotny, K. Netocny, T. Brandes, R.J. Haug, PNAS 106, 10116 (2009)

    Article  ADS  Google Scholar 

  2. G. Schaller, G. Kießlich, T. Brandes, Phys. Rev. B 80, 245107 (2009)

    Article  ADS  Google Scholar 

  3. L.S. Levitov, G.B. Lesovik, JETP Lett. 58, 230 (1993)

    ADS  Google Scholar 

  4. I. Klich, in NATO Science Series, edited by Y.V. Nazarov (Springer, Dordrecht, 2003), Vol. 97

  5. K. Schönhammer, Phys. Rev. B 75, 205329 (2007)

    Article  ADS  Google Scholar 

  6. H. Haug, A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer, 2008)

  7. E.N. Economou, Green’s functions in quantum physics (Springer, Berlin, Heidelberg, 2006)

  8. G.E. Topp, T. Brandes, G. Schaller, Europhys. Lett. 110, 67003 (2015)

    Article  ADS  Google Scholar 

  9. P. Zedler, G. Schaller, G. Kießlich, C. Emary, T. Brandes, Phys. Rev. B 80, 045309 (2009)

    Article  ADS  Google Scholar 

  10. R. Martinazzo, B. Vacchini, K.H. Hughes, I. Burghardt, J. Chem. Phys. 134, 011101 (2011)

    Article  ADS  Google Scholar 

  11. M.P. Woods, R. Groux, A.W. Chin, S.F. Huelga, M.B. Plenio, J. Math. Phys. 55, 032101 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  12. P. Strasberg, G. Schaller, N. Lambert, T. Brandes, New J. Phys. 18, 073007 (2016)

    Article  ADS  Google Scholar 

  13. G. Schaller, J. Cerrillo, G. Engelhardt, P. Strasberg, Phys. Rev. B 97, 195104 (2018)

    Article  ADS  Google Scholar 

  14. P. Strasberg, G. Schaller, T.L. Schmidt, M. Esposito, Phys. Rev. B 97, 205405 (2018)

    Article  ADS  Google Scholar 

  15. A. Nazir, G. Schaller, in Thermodynamics in the quantum regime – Recent progress and outlook, edited by F. Binder, L.A. Correa, C. Gogolin, J. Anders, G. Adesso (Springer, 2018)

  16. L.S. Levitov, H. Lee, J. Math. Phys. 37, 4845 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  17. R. Landauer, IBM J. Res. Dev. 1, 223 (1957)

    Article  MathSciNet  Google Scholar 

  18. S. Böhling, G. Engelhardt, G. Platero, G. Schaller, Phys. Rev. B 98, 035132 (2018)

    Article  ADS  Google Scholar 

  19. B.K. Agarwalla, D. Segal, Phys. Rev. B 98, 155438 (2018)

    Article  ADS  Google Scholar 

  20. A.C. Barato, U. Seifert, Phys. Rev. Lett. 114, 158101 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  21. P. Pietzonka, A.C. Barato, U. Seifert, Phys. Rev. E 93, 052145 (2016)

    Article  ADS  Google Scholar 

  22. T.R. Gingrich, J.M. Horowitz, N. Perunov, J.L. England, Phys. Rev. Lett. 116, 120601 (2016)

    Article  ADS  Google Scholar 

  23. J.M. Horowitz, T.R. Gingrich, Phys. Rev. E 96, 020103 (2017)

    Article  ADS  Google Scholar 

  24. P. Pietzonka, U. Seifert, Phys. Rev. Lett. 120, 190602 (2018)

    Article  ADS  Google Scholar 

  25. G. Bulnes Cuetara, M. Esposito, G. Schaller, P. Gaspard, Phys. Rev. B 88, 115134 (2013)

    Article  ADS  Google Scholar 

  26. R.S. Burkey, C.D. Cantrell, J. Opt. Soc. Am. B 1, 169 (1984)

    Article  ADS  Google Scholar 

  27. A. Garg, J.N. Onuchic, V. Ambegaokar, J. Chem. Phys. 83, 4491 (1985)

    Article  ADS  Google Scholar 

  28. U. Kleinekathöfer, J. Chem. Phys. 121, 2505 (2004)

    Article  ADS  Google Scholar 

  29. W.P. Su, J.R. Schrieffer, A.J. Heeger, Phys. Rev. Lett. 42, 1698 (1979)

    Article  ADS  Google Scholar 

  30. J.K. Asbóth, L. Oroszlány, A. Pályi, in Lecture Notes in Physics (Springer, Berlin, 2016), Vol. 919

  31. C.H. Lewenkopf, E.R. Mucciolo, J. Comput. Electr. 12, 203 (2013)

    Article  Google Scholar 

  32. P. Bonardi, S. Achilli, G.F. Tantardini, R. Martinazzo, Phys. Chem. Chem. Phys. 17, 18413 (2015)

    Article  Google Scholar 

  33. G. Schaller, P. Zedler, T. Brandes, Phys. Rev. A 79, 032110 (2009)

    Article  ADS  Google Scholar 

  34. Y. Meir, N.S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Institut für Theoretische Physik, Hardenbergstr. 36, Technische Universität Berlin, 10623, Berlin, Germany

    Niklas Martensen & Gernot Schaller

Authors
  1. Niklas Martensen
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  2. Gernot Schaller
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Correspondence to Gernot Schaller.

Additional information

Contribution to the Topical Issue “Non-Linear and Complex Dynamics in Semiconductors and Related Materials”, edited by Kathy Lüdge.

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Martensen, N., Schaller, G. Transmission from reverse reaction coordinate mappings. Eur. Phys. J. B 92, 30 (2019). https://doi.org/10.1140/epjb/e2019-90585-0

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  • DOI: https://doi.org/10.1140/epjb/e2019-90585-0

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