Schedule Aug 24, 2012
Quantum Parametric Delocalization of Energy in Weakly Anharmonic Lattices
Rafael Hipolito, Vadim Oganesyan, and Anatoli Polkovnikov, ,

Dynamics of coherently excited, high energy states of linear anharmonic lattices is investigated by analytic and numerical means. A natural semiclassical expansion emerges if the thermodynamic limit is taken while holding energy per particle and wavenumber fixed, whereby classical dynamics of %mode energy is effectively localized on countably few quasimodes. This dynamical effect, previously discovered by Fermi, Pasta and Ulam (FPU), is not due to any known special structure of the problem (e.g. integrability); its fate at {it long times} remains controversial.

Here we announce that {it quantum many-body} dynamics leads to rapid destruction of classical FPU orbits as the energy is transfered to a continuum of initially vacant Fourier modes. Remarkably, controlled short-time expansion of many-body dynamics is captured by generalized Richardson-Gaudin models for pseudospins obeying $SU(1,1)$ algebra -- this observation is also borne out in numerical simulations using the so-called "truncated Wigner approximation". We also comment on observed subsequent stages of energy relaxation (including full thermalization) and experimental relevance of our results.

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