# Emergence and evolution of $k$-gap in spectra of liquid and supercritical states

## TL;DR

This paper uses molecular dynamics simulations to reveal that liquids and supercritical fluids develop a transverse spectral gap, which varies with relaxation time and influences their physical properties.

## Contribution

It provides the first direct evidence of a $k$-gap in the spectra of liquids and supercritical fluids, linking it to relaxation dynamics.

## Key findings

- Liquids develop a transverse spectral gap in reciprocal space.
- The gap size increases as relaxation time decreases.
- Supercritical fluids exhibit similar spectral gap behavior.

## Abstract

Fundamental understanding of strongly-interacting systems necessarily involves collective modes, but their nature and evolution is not generally understood in dynamically disordered and strongly-interacting systems such as liquids and supercritical fluids. We report the results of extensive molecular dynamics simulations and provide direct evidence that liquids develop a gap in solid-like transverse spectrum in the reciprocal space, with no propagating modes between zero and a threshold value. In addition to the liquid state, this result importantly applies to the supercritical state of matter. We show that the emerging gap increases with the inverse of liquid relaxation time and discuss how the gap affects properties of liquid and supercritical states.