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Aleksander Stefanov works across mathematical physics, mechanics and optical measurement. A 2022 Sofia University academic statement identifies his education in theoretical and mathematical physics, doctoral work on nonlinear dynamical systems associated with Lie algebras, and work in the Faculty of Mathematics and Informatics. It describes research on integrable models, walking-robot dynamics and educational physical-constant measurements.^[ref]

The same document identifies Korteweg-De Vries equation and nonlinear Schrödinger-type models among his theoretical interests. He also coauthored the 2023 theoretical and experimental comparison of Gouy phase for Bessel-Gaussian beams with Lyubomir Stoyanov, Alexander Dreischuh and Gerhard G. Paulus.^[ref]

An original example illustrates the quantitative idea behind a noise-based constant measurement. For ideal independent charge-transfer events, the one-sided current shot noise spectral density is $S_I=2eI$. With mean current $I=100\mu \mathrm{A}$, elementary charge $e=1.602176634\times 10^{-19}$ C and a rectangular effective noise bandwidth $B=10$ kHz, the predicted root-mean-square fluctuation isThese stipulated numbers are not data from Stefanov's apparatus. They explain why estimating charge from noise requires a calibrated gain, known bandwidth and a model for other fluctuations. Thermal noise and detector noise must be distinguished from the charge-transfer contribution; a measured noise amplitude alone is insufficient.

The attraction of this work is the bridge between mathematical models and observable signals. The academic statement describes physical walking-robot tests as well as electronic measurements; those are different ways to test a theoretical prediction. The available sources identify this Sofia researcher, and do not justify merging him with unrelated researchers who share a surname.

Independent-record averaging and increasing detector bandwidth change a measurement in different ways. Let $Y_1,\dots ,Y_N$ be independent measurements of zero-mean noise, made with the same fixed filter, and suppose each has finite variance ${\sigma }_B^2$. Their average satisfiesThe vanishing mean is an ensemble statement; the finite-record noise fluctuations only decrease as the number of independent records grows. For correlated records the variance is instead $N^{-2}{\sum }_{i,j}\mathrm{Cov}(Y_i,Y_j)$, so merely increasing the number of samples need not give the same reduction.

Bandwidth controls which fluctuations enter a record. With two-sided angular-frequency power spectral density $S(\omega )$ and an ideal low-pass filter retaining $|\omega |\le \Omega$, the filtered variance isFor flat noise spectrum $S(\omega )=S_0>0$ in that range, this is $S_0\Omega /\pi$, and averaging $N$ independent records gives $S_0\Omega /(\pi N)$. Increasing bandwidth exposes more of the physical fluctuations; independent averaging reduces their variance. Sampling faster from one correlated trajectory is not automatically equivalent to obtaining independent records.