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Microscopic Theory of Linear Response in Amorphous Materials 10.17863/CAM.58558 Cui, Bingyu 0000000236538115 Terentjev, Eugene Zaccone, Alessio This thesis provides an analytical and systematic framework from first-principles to study dielectric and mechanical properties of disordered materials, as well as non-centrosymmetric crystals. The Caldeira-Leggett Hamiltonian opens a route to the (both Markovian and nonMarkovian) fluctuation-dissipation theorem (FDT) and gives rise to the generalised Langevin equation (GLE) in classical dynamics. In the first place, I extend the GLE and the corresponding FDT for more general cases where both the tagged particle and bath oscillators respond to an external oscillatory field. This is the example of a charged or polarisable particle immersed in a bath of other particles that are also charged or polarisable, under an external AC electric field. Being linked to the vibrational density of states (VDOS), the dielectric function calculated based on the GLE is compared with experimental data for the paradigmatic case of molecular glasses: glycerol and Freons 112 & 113, around and above the glass transition temperature, Tg. Moving to the mechanical aspect, the theory of nonaffine lattice dynamics is able to describe the various relaxation processes in the linear viscoelastic response of metallic glasses. In particular, to understand universal properties of relaxation, the VDOS obtained in simulations, or in experiments, is substituted into the model. The nonaffine contribution to elasticity is also important for the pre-stressed/stretched harmonic networks. In order to give an insight on nonaffinity, I compute static elastic constants of α-quartz, taking into account the long-range Coulomb interaction. The nonaffine (softening) correction is found very large, such that the overall elastic constants are at least 3-4 times smaller than the affine Born-Huang estimate. Finally, I formulate the analytical expression of the dynamical structure factor by averaging over all quenched disorder along the acoustic branch, which stores the information of phonon transport in disordered materials. The Rayleigh scattering may be enhanced by a logarithmic factor in an intermediate range of wavenumber. I present a tensorial replica field-theoretic derivation based on heterogeneous or fluctuating elasticity, which suggests that long-range spatial correlations (in power-law decay) of elastic constants (or stress tensors) might be responsible for the logarithmic enhancement to Rayleigh scattering of phonons in amorphous solids. University of Cambridge 2020-06-29 Thesis Doctoral eng CSC-Cambridge scholarship https://www.repository.cam.ac.uk/handle/1810/311466 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/53aaaac5-efc2-4238-a0c5-88a41a987491/download a037c50a7603d971f06bfdb97fa23802 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/1e70fec9-1da4-4972-ac79-3e51742e93b0/download 353adac0d1ebdfd65ab16480263c3c87 https://www.rioxx.net/licenses/all-rights-reserved/ linear response amorphous glasses nonaffine damping