Noise in nanosystems - Mehay, Timothy Patrick (My University, 2018)
With the increasing interest in nanosystems in various branches of science, the question naturally arises as to whether such systems will have practical applications. At the nano-scale all physical measurements are fundamentally constrained by the Heisenberg uncertainty relations. In addition to these fundamental limitations, ﬂuctuations or noise arising from various physical processes act so as to further obscure the accuracy with which we can perceive the physical world. The goals of this thesis are to investigate the consequences of these ﬂuctuations in physical systems, and to develop methods enabling the study of physical processes associated with these ﬂuctuation phenomena. I begin by developing the necessary framework with which to describe these random ﬂuctuations. After discussing the necessary prerequisites, I develop a probabilistic model of charge-density ﬂuctuations. This model draws on results from kinetic theory and Eulerian perturbation theory. It is found that under certain assumptions regarding the nature of the ﬂuctuations, the equation of motion governing charge-density ﬂuctuationsmaybesolvedanalytically. Ithendevelopamethodenablingthestudy of the statistical correlation of density ﬂuctuations using the ﬂuctuationdissipation theorem. This approach is then applied to the study of density ﬂuctuations in graphene using the electron energy-loss spectrum (EELS) of ideal graphene. It is found that the autocorrelation function (ACF) of density ﬂuctuations contains information related to both plasmonic resonance and to the noise present in the EELS. I conclude this thesis by developing a formalism which allows for the calculation of the dephasing rate of a systemusingonlytheEELS.Thisapproachhasthebeneﬁtofenablingauniformtreatmentofdephasinginbothhigh-temperatureandlow-temperature regimes, and contains both electron-electron and electron-phonon interactions by virtue of the EELS, which are the primary contributions to the dephasing rate in low-dimensional semiconductor systems. The use of this approach is then illustrated using the EELS of ideal graphene. Given the generality of the ﬂuctuation-dissipation theorem, many of the methods discussedinthisworkmaybeextendedtostudyarbitraryﬂuctuationphenomena in a wide variety of systems.
A thesis submitted in fulﬁllment of the requirements for the degree of Doctor of Philosophy in the subject of Physics University of the Witwatersrand Johannesburg, South Africa, October 2018
Keywords: Nanoscience; Nanostructured materials