Conductance of single-electron devices from imaginary-time path integrals

In this thesis we study two nanoscopic systems -- the metallic <br>single electron transistor and semiconductor quantum dots -- which <br>are important models for research on molecular electronics and <br>quantum computing. Our theoretical description is based on a <br>path-integral expression for the current autocorrelation function <br>which can be related to the conductance using linear response <br>theory. To circumvent the dynamical sign problem in the numerical <br>determination of real-time correlation functions, we calculated <br>the current autocorrelator for imaginary times and employed a <br>scheme for the analytical continuation of the numerical data. <br> <br>For the metallic single electron transistor we used quantum Monte <br>Carlo methods for the evaluation of the path integrals. The <br>numerical data for the imaginary-time correlation function was <br>analytically continued to the real-time spectral function using <br>methods for the solution of inverse problems (SVD, MaxEnt). The <br>comparison of the results with recent experimental studies showed <br>excellent agreement between theory and experiment over the whole <br>range of system parameters. <br> <br>In the description of semiconductor quantum dots we have used a <br>microscopic model to address the shortcomings of the (frequently <br>used) constant interaction model. As in the case of the metallic <br>single electron transistor, the current correlation function could <br>be expressed as a path-integral, although the resulting equations <br>are too complicated for an evaluation by Monte Carlo methods. The <br>application of the stationary phase approximation, on the other <br>hand, leads to a formulation in terms of a selfconsistent solution <br>of the Poisson equation and the Hartree equations for the single <br>particle states which have been applied successfully to the <br>theoretical description of transport in semiconductor quantum <br>dots.

Author dc:creator

• Theis, Christoph

Contributors dc:contributor

• Grabert, Hermann

• Pfadintegral-Monte Carlo
• Coherent State Pfadintegral
• Coulomb Blockade
• SET-Transistor
• Path Integral Monte Carlo
• Inverse Problem
• Quantum Dots

Repository record source_url

https://freidok.uni-freiburg.de/data/1328

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:1328