  In the study of 1D nonlinear Hamiltonian lattices, the conserved quantities
play an important role in determining the actual behavior of heat conduction.
Besides the total energy, total momentum and total stretch could also be
conserved quantities. In microcanonical Hamiltonian dynamics, the total energy
is always conserved. It was recently argued by Das and Dhar that whenever
stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and
energy fields exhibit normal diffusion. In this work, we will systematically
investigate the stretch diffusions for typical 1D nonlinear lattices. No clear
connection between the conserved quantities and heat conduction can be
established. The actual situation is more complicated than what Das and Dhar
claimed.
