Dynamical phase transition in vibrational surface modes

TL;DR

This paper investigates a simple vibrational surface mode model, revealing an exact spectrum and discovering a second phase transition where surface mode frequencies become purely imaginary, indicating an overdamped regime, analogous to a damped oscillator.

Contribution

It provides an exact spectrum of vibrational surface modes and identifies a novel phase transition to an overdamped regime, linking surface mode behavior to oscillator damping.

Findings

Exact spectrum of surface excitations obtained

Discovery of a second phase transition to an overdamped regime

Surface mode frequency becomes purely imaginary at transition

Abstract

We consider the dynamical properties of a simple model of vibrational surface modes. We obtain the exact spectrum of surface excitations and discuss their dynamical features. In addition to the usually discussed localized and oscillatory regimes we also find a second phase transition where surface mode frequency becomes purely imaginary and describes an overdamped regime. Noticeably, this transition has an exact correspondence to the oscillatory - overdamped transition of the standard oscillator with a frictional force proportional to velocity.