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Monte Carlo Least-Squares Fitting Of Experimental Signal Waveforms, Xianming Han, Vladimir Pozdina, C. Haridas, Prabhakar Misra
Monte Carlo Least-Squares Fitting Of Experimental Signal Waveforms, Xianming Han, Vladimir Pozdina, C. Haridas, Prabhakar Misra
Scholarship and Professional Work - LAS
This paper focuses on why the regular least{squares ¯tting technique is unstable when used to ¯t exponential functions to signal waveforms, since such functions are highly correlated. It talks about alternative approaches, such as the search method, which has a slow convergence rate of 1=N1=M, for M parameters, where N is the number of computations performed. We have used the Monte Carlo method, utilizing both search and random walk, to devise a stable least{squares ¯tting algorithm that converges rapidly at a rate 1=N1=2, regardless of the number of parameters used in ¯tting the waveforms. The Monte Carlo approach has been …
Bound States In The Continuum In Quantum-Dot Pairs, Gonzalo Ordonez, Kyungsun Na, Sungyun Kim
Bound States In The Continuum In Quantum-Dot Pairs, Gonzalo Ordonez, Kyungsun Na, Sungyun Kim
Scholarship and Professional Work - LAS
It is shown that for two open quantum dots connected by a wire, “bound states in the continuum” of a single electron are formed at nearly periodic distances between the dots. This is due to Fabry-Pérot interference between quasibound states in each dot. The bound states are nonlocal, describing the electron trapped in both dots at the same time. Theoretical and numerical results show that trapped states exist even if the wire connecting the dots is relatively long.