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Out of time ordered effective dynamics of a quartic oscillator

par Chakrabarty, Bidisha;Chaudhuri, Soumyadeep
Référence SciPost Physics, 7, 1, 013
Publication Publié, 2019-07-29

Article révisé par les pairs

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Résumé :

We study the dynamics of a quantum Brownian particle weakly coupledto a thermal bath. Working in the Schwinger-Keldysh formalism, wedevelop an effective action of the particle up to quartic terms. Wedemonstrate that this quartic effective theory is dual to a stochasticdynamics governed by a non-linear Langevin equation. TheSchwinger-Keldysh effective theory, or the equivalent non-linearLangevin dynamics, is insufficient to determine the out of time ordercorrelators (OTOCs) of the particle. To overcome this limitation, weconstruct an extended effective action in a generalisedSchwinger-Keldysh framework. We determine the additional quarticcouplings in this OTO effective action and show their dependence on thebath’s 4-point OTOCs. We analyse the constraints imposed on the OTOeffective theory by microscopic reversibility and thermality of thebath. We show that these constraints lead to a generalisedfluctuation-dissipation relation between the non-Gaussianity in thedistribution of the thermal noise experienced by the particle and thethermal jitter in its damping coefficient. The quartic effective theorydeveloped in this work provides extension of several results previouslyobtained for the cubic OTO dynamics of a Brownian particle.