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Estimating the Lieb-Robinson Velocity for Classical Anharmonic Lattice Systems

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Abstract

We estimate the Lieb-Robsinon velocity, also known as the group velocity, for a system of harmonic oscillators and a variety of anharmonic perturbations with mainly short-range interactions. Such bounds demonstrate a quasi-locality of the dynamics in the sense that the support of the time evolution of a local observable remains essentially local. Our anharmonic estimates are applicable to a special class of observables, the Weyl functions, and the bounds which follow are not only independent of the volume but also the initial condition.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Davis, Davis, CA, 95616, USA

    Hillel Raz

  2. School of Mathematics, Cardiff University, Senghennydd Road, Cardiff, Wales, UK, CF24 4AG

    Hillel Raz

  3. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    Robert Sims

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  1. Hillel Raz
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  2. Robert Sims
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Correspondence to Hillel Raz.

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Raz, H., Sims, R. Estimating the Lieb-Robinson Velocity for Classical Anharmonic Lattice Systems. J Stat Phys 137, 79–108 (2009). https://doi.org/10.1007/s10955-009-9839-5

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  • DOI: https://doi.org/10.1007/s10955-009-9839-5

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