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Physica A Statistical Mechanics and its Applications

Long time limit of correlation functions between massless modes interacting with a quantum oscillator

Salvador V. Godoy, Ernest Braun

Published Jun 1, 1978• 1 citation
Publisher
DOI
10.1016/0378-4371(78)90032-8

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Abstract We present a numerical study of dynamical correlations (structure factors) of the long-range generalization of the Fermi–Pasta–Ulam oscillator chain, where the strength of the interaction between two lattice sites decays as a power of the inverse of their distance. The structure factors at finite energy density display distinct peaks, corresponding to long-wavelength propagating modes, whose dispersion relation is compatible with the predictions of the linear theory. We demonstrate that dynamical scaling holds, with a dynamical exponent z that depends weakly on in the range . The lineshapes have a non-trivial functional form and appear somehow independent of . Within the accessible time and size ranges, we also find that the short-range limit is hardly attained even for relatively large values of .
We study the quantum quench in two coupled Tomonaga-Luttinger Liquids (TLLs), from the off-critical to the critical regime, relying on the conformal field theory approach and the known solutions for single TLLs. We consider a squeezed form of the initial state, whose low energy limit is fixed in a way to describe a massive and a massless mode, and we encode the non-equilibrium dynamics in a proper rescaling of the time. In this way, we compute several correlation functions, which at leading order factorize into multipoint functions evaluated at different times for the two modes. Depending on the observable, the contribution from the massive or from the massless mode can be the dominant one, giving rise to exponential or power-law decay in time, respectively. Our results find a direct application in all the quench problems where, in the scaling limit, there are two independent massless fields: these include the Hubbard model, the Gaudin-Yang gas, and tunnel-coupled tubes in cold atoms experiments.