Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula

Details Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula

2007-08-02

arxiv.org/abs/0708.0303v4

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

20 pages, submitted

Scientific paper

10.1063/1.2992839

Consider a three dimensional system which looks like a cross-connected pipe system, i.e. a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we adiabatically turn on an electrical bias between leads. The main technical tool is the use of a finite volume regularization, which allows us to define the current coming out of a lead as the time derivative of its charge. We finally prove that in virtually all physically interesting situations, the conductivity tensor is given by a Landauer-B{\"u}ttiker type formula.

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