Spatial evolution of energy in the Hamiltonian chain

Abstract

The spread of an energy packet in a “Hamiltonian chain” (monatomic, nearest neighbour springs) is considered, which at t = 0 is created via local momentum (ME) or via local displacement (DE) excitation, respectively. In both cases the 2nd moment M 2 displays wavelike behaviour ( M 2∼ t 2) in contrast to a diffusive one ( M 2∼ t). But otherwise quite unexpected features are found. (a) The packet never disintegrates into two wing parts. Its maximum always remains in the central region. (b) For intermediate time regimes the shape of the packet is remarkably different for both initial conditions. (c) The wings of the packets exhibit strong fluctuations which calm down in the central region. (d) In the neighbourhood of the original excitation center the shape of the packet turns independent of the position (quasi-thermalization). (e) The most surprising feature is a difference in the average spread velocities of the energy packet in the 2 prototype cases by a factor of √2. Thus, the spread strongly depends on the nature of the initial excitation even in the long time regime.