We are studying fluctuations in nanoscale systems such as quantum dot fluorescence and faradaic currents in nanoelectrodes in the mass-transport limited regime. These systems display interesting behaviors that can be described by Lévy statistics.

# Nanoelectrodes

We have recently reported on novel effects for nanoelectrodes used in electrochemistry. Non-integrable 1/f^{β} fluctuations are observed in the regime where the faradaic currents are governed by mass transport. We exploit these fluctuations to study the impact of reversible adsorption on the transport of charged species. We find that due to a distribution of binding energies, the faradaic currents display weak ergodicity breaking and aging.

# Quantum dots

Quantum dots show random transitions between dark and bright states upon continuous excitation, where the residence times in these states follows a power law distribution. Due to their power-law temporal statistics, the emission power spectrum scales as S(f) ~ A/f^{β} at low frequencies. This type of spectrum is called 1/f noise and it appears in an extensively large array of physical signals. Intriguingly, this type of noise is not integrable in the low frequency limit.

In our measurements, we observe that as the experimental time increases, the magnitude of the power spectrum is not constant but it decreases. The change of the spectrum with time places a bound on the total power and ensures that the total area under the power spectrum does not blow up. Our work shows that additional critical exponents are needed to fully characterize the dependence of 1/f noise on experimental time.

# Publications

D. Krapf, "Nonergodicity in nanoscale electrodes", Phys. Chem. Chem. Phys. 15, 459 (2013)

S. Sadegh, E. Barkai, and D. Krapf, "1/f noise for intermittent quantum dots exhibits non-stationarity and critical exponents", New J. Phys. 16, 113054 (2014)