Quantify the effect of velocity projection on transport

Quantify the effect of periodically projecting out the center-of-mass velocity on heat transport in the Langevin-thermostatted long-wave continuum discretization of the symmetric beta-Fermi–Pasta–Ulam–Tsingou chain.

Background

The numerical protocol periodically subtracts the center-of-mass velocity from all nodal velocities to control drift of the translational zero mode. Although this operation preserves instantaneous relative velocities and therefore leaves the strain-dependent internal motion unchanged at the moment of projection, it removes the kinetic energy associated with collective translation and modifies the subsequent dynamics because the Langevin reservoirs act on the nodal velocities.

The paper explicitly notes that the transport consequences of this projection have not been quantitatively separated from the reported conductivity and scaling results. Determining whether the projection affects the anomalous conductivity exponent, conductivity amplitude, or finite-size crossover is therefore an unresolved methodological problem within the presented simulation framework.

References

This preservation of the instantaneous internal motion does not establish invariance of the subsequent thermostatted dynamics, because the Langevin forces act on the nodal velocities. The effect of the projection on transport has not been isolated quantitatively.

— Heat Transport of the $β$-Fermi--Pasta--Ulam--Tsingou chain in the long-wave limit  (2610.09405 - Lima et al., 7 Oct 2026) in Section 2, subsection “Reduced units and numerical parameters”