Parth Bhargava, Sayantan Choudhury, Satyaki Chowdhury, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, Gabriel D. Pasquino
SciPost Phys. Core 4, 026 (2021) ·
published 7 October 2021
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$Circuit~ Complexity$, a well known computational technique has recently
become the backbone of the physics community to probe the chaotic behaviour and
random quantum fluctuations of quantum fields. This paper is devoted to the
study of out-of-equilibrium aspects and quantum chaos appearing in the universe
from the paradigm of two well known bouncing cosmological solutions viz.
$Cosine~ hyperbolic$ and $Exponential$ models of scale factors. Besides
$circuit~ complexity$, we use the $Out-of-Time~ Ordered~ correlation~ (OTOC)$
functions for probing the random behaviour of the universe both at early and
the late times. In particular, we use the techniques of well known two-mode
squeezed state formalism in cosmological perturbation theory as a key
ingredient for the purpose of our computation. To give an appropriate
theoretical interpretation that is consistent with the observational
perspective we use the scale factor and the number of e-foldings as a dynamical
variable instead of conformal time for this computation. From this study, we
found that the period of post bounce is the most interesting one. Though it may
not be immediately visible, but an exponential rise can be seen in the
$complexity$ once the post bounce feature is extrapolated to the present time
scales. We also find within the very small acceptable error range a universal
connecting relation between Complexity computed from two different kinds of
cost functionals-$linearly~ weighted$ and $geodesic~ weighted$ with the OTOC.
Furthermore, from the $complexity$ computation obtained from both the
cosmological models and also using the well known MSS bound on quantum Lyapunov
exponent, $\lambda\leq 2\pi/\beta$ for the saturation of chaos, we estimate the
lower bound on the equilibrium temperature of our universe at late time scale.
Finally, we provide a rough estimation of the scrambling time in terms of the
conformal time.
SciPost Phys. Core 4, 006 (2021) ·
published 29 March 2021
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In this paper, our prime objective is to apply the techniques of parameter
estimation theory and the concept of Quantum Metrology in the form of Fisher
Information to investigate the role of certain physical quantities in the open
quantum dynamics of a two entangled qubit system under the Markovian
approximation. There exist various physical parameters which characterize such
system, but can not be treated as any quantum mechanical observable. It becomes
imperative to do a detailed parameter estimation analysis to determine the
physically consistent parameter space of such quantities. We apply both
Classical Fisher Information (CFI) and Quantum Fisher Information (QFI) to
correctly estimate these parameters, which play significant role to describe
the out-of-equilibrium and the long range quantum entanglement phenomena of
open quantum system. Quantum Metrology, compared to classical parameter
estimation theory, plays a two-fold superior role, improving the precision and
accuracy of parameter estimation. Additionally, in this paper we present a new
avenue in terms of Quantum Metrology, which beats the classical parameter
estimation. We also present an interesting result of revival of
out-of-equilibrium feature at the late time scales, arising due to the long
range quantum entanglement at early time scale and provide a physical
interpretation for the same in terms of Bell's Inequality Violation in early
time scale giving rise to non-locality.
Prof. Choudhury: "We have attached the response ..."
in Submissions | report on Circuit Complexity in $\mathcal{Z}_{2}$ ${\cal EEFT}$