Time-dependent current through a quantum dot in the presence of a voltage probe

Sat, 05 Mar 2016 00:00:00 +0000

This is the thesis for my Diploma (Master’s and Bachelor’s combined) in Mathematical Physics at the University of Ljubljana. It was advised by dr. Tomaž Rejec from the Department of Theoretical Physics, Jožef Stefan Institute.

The work is an original examination of the effects that a coupled voltage probe has on the current flowing through a quantum dot, specifically its temporal properties. This was done by numerically simulating the problem from first principles (i.e. from a version of Schrödinger’s equation). The main challenge was to ensure that the voltage on the probe was set just so there was no current flowing in or out of it, while the system was being integrated - i.e. without knowing what the actual currents at that step were.

By varying the coupling to the voltage probe, one can control the incoherent contribution to transport and trace the transition from coherent quantum transport toward classical conductance behavior. The simulations reproduce the stationary current predicted by the Landauer–Büttiker formalism and show that stronger probe-induced decoherence substantially shortens the time required to reach the stationary state. The observed relaxation rate is approximately proportional to the system’s total resonance width.

The thesis document gives a compressed account of the underlying theoretical framework; for a fuller treatment, see, for example, Kurth et al.

Thesis | Andrej Leban

Time-dependent current through a quantum dot in the presence of a voltage probe