Prof. M.Baggioli: Gapped momentum states in physics. A derivation from symmetries

Abstract. The vibrational, thermodynamically and mechanical properties of solids are well-understood since Debye's work in 1912. On the contrary, the same understanding for amorphous systems (liquids and glasses) has remained elusive for more than a century and it is still a mystery. In these lectures, we will consider three distinctive properties of liquids which are drastically different from their solid counterpart and which remain largely unexplained: (I) the dynamics of (k-gapped) shear waves and their dispersion relation, (II) the low frequency scaling of the vibrational density of states and (III) the temperature dependence of the heat capacity. After reviewing these three problems, we will tackle them from a theoretical point of view using symmetries, effective field theory and hydrodynamics.
The lectures are mainly based on:
- "Gapped momentum states", Physics Reports 2020 [arXiv:1904.01419]
- "Field Theory of Dissipative Systems with Gapped Momentum States", PRD 2020 [arXiv:2004.13613]
- "Universal law for the vibrational density of states of liquids", PNAS 2021 [arXiv:2101.01380]
- "Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory" [arXiv:2101.05015]
- "Explaining the specific heat of liquids based on instantaneous normal modes", PRE 2021 [arXiv:2101.07585 ]

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