Journal of Statistical Physics

, Volume 134, Issue 4, pp 709–748 | Cite as

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs



We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T L,μ L) and (T R,μ R), and adjust the parameters (T i ,μ i ), for i=1,…,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.


Quantum transport Quantum dots Landauer-Büttiker scattering approach Onsager relations Entropy production Random matrix theory Ohm and Fourier laws 


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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Département de Physique ThéoriqueUniversité de GenèveGenève 4Switzerland

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