Ultrasmall double junction in terms of orthogonal polynomials
Heinz-Olaf M\"uller (1), Andreas H\"adicke (2), Ulrik Hanke (1), K., A. Chao (1) ((1) Norwegian University of Science, Technology, (2), Universit\"at Jena/F. R. Germany)
TL;DR
This paper presents a method using orthogonal polynomials to solve the master equation for double junctions, enabling analysis of time-dependent behavior and current noise, especially when stationary solutions are simple.
Contribution
It introduces a novel approach employing orthogonal polynomials to solve the master equation for double junctions, facilitating analysis of dynamic solutions and noise characteristics.
Findings
Time-dependent solutions can be constructed from stationary solutions using orthogonal polynomials.
The method simplifies analysis when stationary solutions are straightforward.
Current noise can be calculated explicitly in the considered cases.
Abstract
The ``orthodox theory'' of a single electron double junction is dealt with. It is shown that the stationary solution of the underlying master equation allows the construction of any time-dependent solution in terms of orthogonal polynomials. The approach pays off if the stationary solution becomes simple. Two special cases are considered. We use the time-dependent solution to calculate the current noise in these cases.
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Taxonomy
TopicsAdvanced Electrical Measurement Techniques · Mechanical and Optical Resonators · Photoacoustic and Ultrasonic Imaging