Shakerpoor, Alireza, authorSzamel, Grzegorz, advisorVan Orden, Alan, committee memberKim, Seonah, committee memberGelfand, Martin, committee member2022-05-302022-05-302022https://hdl.handle.net/10217/235276This dissertation focuses on stationary and dynamical properties of non-equilibrium systems of disordered matter. In particular, we discuss the correlation between the stability of ultra-stable to moderately stable amorphous solids and the structural fluctuations of the elastic field at low frequencies. We report a strong correlation between the stability and the structural homogeneity which we demonstrate numerically through the calculation of local elastic moduli of the solid. Notably, we do not identify any significant length scale associated with elastic correlations which bears specific implications for the wave attenuation in amorphous solids. In the second part of the dissertation, we shift our focus to the disordered systems of active matter. We derive a formal expression for the stationary probability density function of a tagged active particle in an interacting system of active Ornstein-Uhlenbeck particles. We further identify an effective temperature in the probability density function which allows for the subsequent numerical validation of our theoretical results beyond the linear response regime. We show that the effective temperature defined through the violation of the Einstein relation (or equivalently the fluctuation-dissipation theorem), can predict the tagged active particle's density distribution. Lastly, we derive theoretical expressions for the stationary probability density distribution and the current of a non-interacting active Ornstein-Uhlenbeck particle in a tilted periodic potential. We demonstrate the quantitative agreement of these expressions with our numerical results for small to moderate correlation times of the colored-noise. We further explore the dependence of the diffusive motion on the strength of tilting force. We observe a giant enhancement in the diffusion of the particle which becomes more pronounced with increasing the persistence time.born digitaldoctoral dissertationsengcondensed matter physicsglass physicsstochastic processesdisordered systemsactive particlesnonequilibrium statistical physicsTextThe material is open access and distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 United States License (https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode).