The behaviour of a chaotic system and its effect on existing quantum
correlation has been holographically studied in presence of non-conformality.
Keeping in mind the gauge/gravity duality framework, the non-conformality in
the dual field theory has been introduced by considering a Liouville type
dilaton potential for the gravitational theory. The resulting black brane
solution is associated with a parameter $eta$ which represents the deviation
from conformality. The parameters of chaos, namely, the Lyapunov exponent and
butterfly velocity are computed by following the well-known shock wave
analysis. The obtained results reveal that presence of non-conformality leads
to suppression of the chaotic nature of a system. Further, for a particular
value of the nonconformal parameter $eta$, the system achieves Lyapunov
stability resulting from the vanishing of both Lyapunov exponent and butterfly
velocity. Interestingly, this particular value of $eta$ matches with the
previously given upper bound of $eta$. The effects of chaos and
non-conformality on the existing correlation of a thermofield doublet state
have been quantified by holographically computing the two-sided mutual
information in both the presence and absence of the shock wave. Furthermore,
the entanglement velocity is also computed and the effect of non-conformality
on it have been observed. Finally, the obtained results of Lyapunov exponent
and butterfly velocity have also been verified from the pole-skipping analysis.

Future Roadmap: Challenges and Opportunities

Based on the conclusions of the study, there are several potential challenges and opportunities that lie ahead.

1. Exploring the Suppression of Chaos with Non-Conformality

The findings suggest that the presence of non-conformality in a chaotic system leads to its suppression. Further research could focus on understanding the underlying mechanisms behind this phenomenon and investigating its implications in other systems. Challenges in this area may involve developing more precise mathematical models and conducting experimental validations.

2. Investigating Lyapunov Stability in Nonconformal Systems

The study reveals that a particular value of the nonconformal parameter $eta$ can lead to Lyapunov stability, where both the Lyapunov exponent and butterfly velocity vanish. Future research can delve deeper into the characterization and significance of this stability. It would be crucial to determine whether this stability also arises in other nonconformal systems and explore how it relates to existing stability criteria. Challenges in this area may include developing analytical tools for quantifying stability and performing extensive numerical calculations.

3. Quantifying the Effects of Chaos and Non-Conformality on Correlation

The research highlights the importance of studying the effects of chaos and non-conformality on existing correlations within thermofield doublet states. Further investigations could focus on quantifying these effects through advanced computational techniques and theoretical frameworks. Challenges may arise in accurately modeling and capturing the dynamics of correlations in complex systems.

4. Understanding the Role of Non-Conformality in Entanglement Velocity

The study also observes the effect of non-conformality on entanglement velocity. Future research can explore how non-conformality influences entanglement dynamics and its implications for quantum information processing. Challenges in this area may involve the development of new theoretical frameworks that can capture the complexity of entanglement velocity in non-conformal systems.

5. Verifying Results through Pole-Skipping Analysis

The obtained results of the Lyapunov exponent and butterfly velocity can be further validated using pole-skipping analysis. It would be valuable to conduct additional studies to confirm the consistency of these results and investigate their generalizability to other physical systems. Challenges may involve devising innovative techniques for analyzing and interpreting the pole-skipping behavior.

In conclusion, the findings presented in this study open up several avenues for future research in understanding the behavior of chaotic systems in the presence of non-conformality. Addressing the challenges and harnessing the opportunities outlined above will contribute to advancing our knowledge in this field and potentially uncovering new applications for quantum correlation and information processing.

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