08-147 Philippe A. Jacquet

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs (560K, pdf) Aug 6, 08

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Abstract. We introduce a model for charge and heat transport based on the Landauer-B\"uttiker 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, \ie we fix the boundary values $(T_\L,\mu_\L)$ and $(T_\R,\mu_\R)$, and adjust the parameters $(T_i,\mu_i)$, for $i = 1,\dots,N$, so that the net electric and heat currents through all the intermediate reservoirs vanish. This 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 electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that the statistical average currents are governed by Ohm and Fourier laws.

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