Bruno Huepper | Searcharxiv

arXiv2000

Conductance of the Single Electron Transistor for Arbitrary Tunneling Strength

We study the temperature and gate voltage dependence of the conductance of the single electron transistor focusing on highly conducting devices. Electron tunneling is treated nonperturbatively by means of path integral Monte Carlo techniques and the conductance is determined from the Kubo formula. A regularized singular value decomposition scheme is employed to calculate the conductance from imaginary time simulation data. Our findings are shown to bridge between available analytical results in the semiclassical and perturbative limits and are found to explain recent experimental results in a regime not accessible by earlier methods.

cond-mat.mes-hall↗

arXiv1998

A new method for numerical inversion of the Laplace transform

A formula of Doetsch ({\em Math. Zeitschr.} {\bf 42}, 263 (1937)) is generalized and used to numerically invert the one-sided Laplace transform ${\hat C}(β)$. The necessary input is only the values of ${\hat C}(β)$ on the positive real axis. The method is applicable provided that the functions $\hat{C}(β)$ belong to the function space $L^2_α$ defined by the condition that $ G(x) = e^{xα}\hat{C}(e^x),~ α> 0$ has to be square integrable. This space includes sums of exponential decays ${\hat C}(β)=\sum_n^{\infty}a_n e^{-βE_n}$, e.g. partition functions with $a_n = 1$. In practice, the inversion algorithm consists of two subsequent fast Fourier transforms. High accuracy inverted data can be obtained, provided that the signal is also highly accurate. The method is demonstrated for a harmonic partition function and resonant transmission through a barrier. We find accurately inverted functions even in the presence of noise.

physics.data-an↗