Phys. Rev. Lett. 84, 2857–2860 (2000)

Momentum Conservation Implies Anomalous Energy Transport in 1D Classical Lattices

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Tomaž Prosen^* and David K. Campbell^†
CNLS, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

Received 17 August 1999; published in the issue dated 27 March 2000

Under quite general conditions, we prove that for classical many-body lattice Hamiltonians in one dimension (1D) total momentum conservation implies anomalous conductivity in the sense of the divergence of the Kubo expression for the coefficient of thermal conductivity, κ. Our results provide rigorous confirmation and explanation of many of the existing “surprising” numerical studies of anomalous conductivity in 1D classical lattices, including the celebrated Fermi-Pasta-Ulam problem.

URL:

http://link.aps.org/doi/10.1103/PhysRevLett.84.2857

DOI:

10.1103/PhysRevLett.84.2857

PACS:

44.10.+i, 05.45.-a, 05.60.Cd, 05.70.Ln

^*Permanent address: Physics Department, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia.Email address: prosen@fiz.uni-lj.si

^†Permanent address: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801.Email address: dkc@uiuc.edu

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Phys. Rev. Lett. 84, 2857–2860 (2000)

Momentum Conservation Implies Anomalous Energy Transport in 1D Classical Lattices