Defects Induced Criticality and Gapped Momentum States in Condensed Matter

Abstract

There are two conventionally discussed dispersion relations (DR) in condensed matter: the gapless phonon-like DR and the DR with the energy or frequency gap. The third type of DR has been emerging in different areas of condensed matter physics: the gapped momentum states (GMS) when the DR with the gap in momentum, or k-space. Increasing interest for the gapped momentum states are related to important implications for dynamical and thermodynamic properties of the system (hydrodynamic turbulence, plasticity, failure). Traditionally GMS emerge in the Maxwell-Frenkel approach to liquid or solid viscoelasticity, relate the k-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space. Generalized hydrodynamics seeks to start with hydrodynamic equations for liquid properties and subsequently add non-hydrodynamic effects. GMS can also be obtained starting from solid-like elastic equations and generalizing them by adding hydrodynamic flow effects. Original interpretation of GMS and dispersion properties in condensed matter is developed considering the defects induced criticality (structural-scaling transition) in shocked liquid and solid. The nature of the viscosity limit is discussed analyzing the scenario of GMS in the presence of dynamics of collective modes of defects.