Alladi Ramakrishnan Hall

Out of Time Ordered Quantum Dissipation

Bidisha Chakrabarty

ICTS-TIFR, Bangalore

Recently the connection of Out of Time Ordered Correlators
(OTOCs) to scrambling, quantum chaos, thermalisation etc has been realised.
With the increasing interest in OTOCs, it will be useful to develop a
systematic prescription to compute them. In this talk I will discuss
techniques of effective theory to compute OTOCs in open quantum systems. In
particular, I will focus on the problem of a quantum Brownian particle
interacting with a dissipative bath composed of two sets of harmonic
oscillators. Besides the linear coupling between the particle and each set
of oscillators, we add a small 3-body interaction, between the particle and
the oscillators. This cubic coupling induces non-linear dissipation and
noise terms in the effective theory of the particle. For appropriate choice
of distributions of bath oscillators, all the bath correlators decay
exponentially fast at late times. Hence after the decay of the bath
correlators has set in, one can write down a suitable 1-PI effective action
of the particle which is local in time. The correlators computed from the
microscopic theory evolve the same way as the correlators computed from
this 1-PI effective action. If the bath has microscopic time-reversal
invariance and thermality, it imposes constraints on the 1-PI effective
action. These constraint relations between the effective couplings of 1-PI
action are OTO generalisations of the well-known Onsager-Casimir reciprocal
relations and fluctuation-dissipation relations. Combining these relations,
the non-Gaussianity of the thermal noise gets related to the thermal jitter
in the damping constant of the Brownian particle.

Reference: arxiv.org/pdf/1811.01513.pdf