Delocalization-Localization Transition due to Anharmonicity

TL;DR

This paper investigates the transition between energy delocalization and localization in a nonlinear chain, revealing a sharp transition at a critical amplitude with diverging time scales and the coexistence of localized breathers and ballistic transport.

Contribution

It provides analytical and numerical evidence for a delocalization-localization transition in a reduced Fermi-Pasta-Ulam chain, highlighting the role of anharmonicity and critical amplitude effects.

Findings

Existence of a sharp delocalization-localization transition at a critical amplitude

Diverging time scales near the critical point from both sides

Localized energy packets form discrete breathers above the critical amplitude

Abstract

Analytical and numerical calculations for a reduced Fermi-Pasta-Ulam chain demonstrate that energy localization does not require more than one conserved quantity. Clear evidence for the existence of a sharp delocalization-localization transition at a critical amplitude is given. Approaching the critical amplitude from above and below, diverging time scales occur. Above the critical amplitude, the energy packet converges towards a discrete breather. Nevertheless, ballistic energy transportation is present, demonstrating that its existence does not necessarily imply delocalization.