Dynamical phase transition in vibrational surface modes

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 the 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.

Revisiting the Fermi Golden Rule: Quantum dynamical phase transition as a paradigm shift

“…However, the inclusion of Γ can be justified, within statistical mechanics, by including the action of a Brownian bath [41]. Recently, we obtained a simpler demonstration [42] using as environment a chain of oscillators whose N degrees of freedom are considered by taking the thermodynamic limit of N → ∞ precisely in the same way as described above in the context of the FGR. It is interesting to note that while 2ω o /Γ ≫ 1 corresponds to the standard oscillation.…”

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