Noise in nanosystems

Abstract

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.