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Open System Approach to Transport1

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Quantum Thermodynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 784))

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Abstract

In this section yet another approach to transport is examined. Rather than analyzing spatial energy density dynamics as done in the previous section, we now aim at investigating a stationary non-equilibrium state. This state is induced through the local coupling of reservoirs with different temperatures at either end of the system. The system is a chain of two-level systems coupled according to the Heisenberg model. The baths are modeled according to standard open system theory (see [3–6]). The resulting equations are numerically solved using a stochastic unraveling scheme.

No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it penetrates all bodies and spaces, it influences the processes of the arts, and occurs in all phenomena of the universe.

— J. Fourier [1]

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References

  1. M. Michel, H. Wichterich, J. Gemmer, O. Hess, 77, 104303 (2008)

    Google Scholar 

  2. J. Fourier, The Analytical Theory of Heat (Dover Publ., New York, 1955). Transl. by Alexander Freeman. Original: Théorie analytique de la chaleur (publ. 1822). Unabridged reprinting of the Engl. Transl. anno 1878.

    Google Scholar 

  3. K. Saito, Europhys. Lett. 61, 34 (2003)

    Article  ADS  Google Scholar 

  4. K. Saito, S. Takesue, S. Miyashita, Phys. Rev. E 61, 2397 (2000)

    Article  ADS  Google Scholar 

  5. M. Michel, M. Hartmann, J. Gemmer, G. Mahler, Eur. Phys. J. B 34, 325 (2003)

    Article  ADS  Google Scholar 

  6. M. Michel, Nonequilibrium Aspects of Quantum Thermodynamics. Ph.D. thesis, Universität Stuttgart, Stuttgart (2006). Also available online: http://elib.uni-stuttgart.de/opus/volltexte/2006/2803/

  7. H. Wichterich, M.J. Henrich, H.P. Breuer, J. Gemmer, M. Michel, Phys. Rev. E 76, 031115 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  8. H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)

    MATH  Google Scholar 

  9. E.B. Davies, Commun. Math. Phys. 39, 91 (1974)

    Article  ADS  Google Scholar 

  10. E.B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976)

    MATH  Google Scholar 

  11. R. Dümcke, H. Spohn, Z. Phys. B 34, 419 (1979)

    Article  ADS  Google Scholar 

  12. V. Gorrini, A. Kossakowski, E. Sudarshan, J. Math. Phys. 17, 821 (1976)

    Article  ADS  Google Scholar 

  13. G. Lindblad, Commun. Math. Phys. 48, 119 (1976)

    Article  ADS  Google Scholar 

  14. R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications (Springer, Berlin, 2001)

    MATH  Google Scholar 

  15. V. May, O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems (Wiley-VCH, Berlin, 2003)

    Book  Google Scholar 

  16. M. Michel, J. Gemmer, G. Mahler, Int. J. Mod. Phys. B 20, 4855 (2006)

    Article  ADS  Google Scholar 

  17. K. Mølmer, Y. Castin, Quantum Semiclass. Opt. 8, 49 (1996)

    Article  ADS  Google Scholar 

  18. C. Mejia-Monasterio, H. Wichetrich, EPJST 151, 113 (2007)

    ADS  Google Scholar 

  19. J. Steinbach, B.M. Garraway, P.L. Knight, Phys. Rev. A 51(4), 3302 (1995)

    Article  ADS  Google Scholar 

  20. M. Michel, J. Gemmer, G. Mahler, Eur. Phys. J. B 42, 555 (2004)

    Article  ADS  Google Scholar 

  21. F. Heidrich-Meisner, A. Honecker, W. Brenig, Phys. Rev. B 71(18), 184415 (2005)

    Article  ADS  Google Scholar 

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Gemmer, J., Michel, M., Mahler, G. (2009). Open System Approach to Transport1 . In: Quantum Thermodynamics. Lecture Notes in Physics, vol 784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70510-9_21

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  • DOI: https://doi.org/10.1007/978-3-540-70510-9_21

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