Momentum conservation implies anomalous energy transport in 1d classical lattices

摘要

Under quite general conditions, we prove that for classical many-body latticeHamiltonians in one dimension (1D) total momentum conservation impliesanomalous conductivity in the sense of the divergence of the Kubo expressionfor the coefficient of thermal conductivity, $\kappa$. Our results providerigorous confirmation and explanation of many of the existing ``surprising''numerical studies of anomalous conductivity in 1D classical lattices, includingthe celebrated Fermi-Pasta-Ulam problem.