| In this thesis, we examine three problems motivated by self-sustained oscillators, such as lasers, electronic oscillators, and biological oscillators, which are broadly encountered in science and technology.;In modern computation and communication systems, self-sustained oscillators are provide clock signals for system synchronization and frequency references for signal up/down-conversion. Their timing accuracy and frequency stability are characterized by phase noise, which is among the most important and interesting aspects of oscillator's dynamics and quality. Although it has been extensively studied since 1960s, two fundamental aspects of phase noise had yet to be understood, which we solve by applying the stochastic calculus methods of non-equilibrium statistical physics.;First, we develop an explicit, physically-intuitive analysis for phase noise in distributed oscillators, whose large or even infinite degrees of freedom make the problem particularly difficult. In addition to providing a calculation method and useful design strategies, we also demonstrate how the phase noise varies with different oscillation waveforms, and how this can be reconciled in thermodynamic terms.;Second, the phase noise process is governed by an inherent nonlinear stochastic equation, which has been treated using a linear approximation, without knowing the physical effects of the nonlinearity. We solve this long-standing problem by an appropriate perturbation method borrowed from quantum mechanics, and find a surprising spectral shift that formally corresponds to the Lamb shift in quantum electrodynamics.;Besides the two phase noise problems, our third study is motivated by reducing the size of self-sustained oscillators, by utilizing plasmonic resonance phenomena (instead of electromagnetic resonance) in one-dimensional (1D) nanodevices, such as carbon nanotubes and GaAs quantum wires. While it typically occurs at optical frequencies with bulk conductors, GHz∼THz plasmonic phenomena have been predicted to exist in 1D nanodevices, featuring attractive properties such as extremely large kinetic inductance and short plasmonic wavelength. We initiated a research aiming to first observe 1D plasmonics, whose current development is presented in this thesis. The long-term goal is to utilize their unique properties in circuit applications, including self-sustained oscillators and THz detectors, which are advantageous in terms of size and operating frequency over circuits using conventional electromagnetic components. |
