Modelling of Quantum Electromechanical Systems
We discuss methods for numerically solving the generalized Master equation GME which governs the time-evolution of the reduced density matrix ρ of a mechanically movable mesoscopic device in a dissipative environment. As a specific example, we consider the quantum shuttle—a generic quantum nanoelectromechanical system (NEMS). When expressed in the oscillator basis, the stationary limit of the GME becomes a large linear non-sparse matrix problem (characteristic size larger than 104× 104) which however, as we show, can be treated using the Arnoldi iteration scheme. The numerical results are interpreted with the help of Wigner functions, and we compute the current and the noise in a few representative cases.
KeywordsSET Coulomb blockade nanoelectromechanics noise
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- 5.C. Flindt, T. Novotný, and A.P. Jauho, to appear in Phys. Rev. B, 70, 205334 (2004); cond-mat/0405512.Google Scholar
- 6.C. Flindt, T. Novotný, and A.P. Jauho, to appear in Europhys. Lett., 69, 475 (2004); cond-mat/0410322.Google Scholar
- 8.We show in [3–5] that the off-diagonal elements ρ01/10 decouple from ρ00/11, and are not needed in the evaluation of the stationary limit.Google Scholar
- 9.A good introduction to the Arnoldi scheme can be found in Matrix Computations, edited by G.H. Golub and C.F. Loan (The Johns Hopkins University Press, 3rd ed., 1996).Google Scholar
- 10.Prof. T. Eirola, Private communication.Google Scholar
- 11.C. Flindt, Master’s Thesis, MIC, Technical University of Denmark, URL http://www.mic.dtu.dk/Research/TheoreticalNano/10Nanotechnology/Publications/Theses.aspx