#### 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

Done