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Recent ideas of many-body chaos in classical Hamiltonian systems --- namely decorrelators
or the classical analogues of OTOCs --- have opened an interesting window to revisit problems
in non-linear, out of equilibrium flows. In this talk we will introduce this idea through a classical
spin chain model and then motivate how the same can be applied to nonlinear, Hamiltonian, thermalised fluids
to show how the Lyapunov exponent scales with temperature in a classical many-body system. We then take two further
examples from non-Hamiltonian, out-of-equilibrium systems --- namely fully developed high Reynolds number classical turbulence
and low Reynolds active turbulence of bacterial suspensions --- to further exploit such decorrelators in order
to see how the Lyaponov exponent $\lambda$ scales with the Reynolds number Re in the first and activity in the second case.
In particular, for the high Reynolds number fully developed turbulence problem, we show
$\lambda\propto{\rm Re}^\alpha$ and investigate the interplay of the competing
effects of viscous dissipation and nonlinearity. We obtain a precise value of
$\alpha = 0.59 \pm 0.04$ and show that the departure from the Kolmogorov mean field
result $\lambda \propto \sqrt{{\rm Re}}$ is a consequence of the intermittent
fluctuations in the velocity-gradient tensor. The robustness of our results are
further confirmed in a local, dynamical systems model for turbulence.
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For reference, this talk will build on work reported in the following papers:
1. Light-cone spreading of perturbations and the butterfly effect in a classical spin chain,
A. Das, S. Chakrabarty, A. Dhar, A. Kundu, D. A. Huse, R. Moessner, Samriddhi Sankar Ray, and S. Bhattacharjee.
Physical Review Letters 121, 024101 (2018).
2. Many-body Chaos in Thermalised Fluids,
S. D. Murugan, D. Kumar, S. Bhattacharjee, and Samriddhi Sankar Ray.
Physical Review Letters 127, 124501 (2021)
3. Intermittency, fluctuations and maximal chaos in an emergent universal state of active turbulence,
S. Mukherjee, R. K. Singh, M. James and Samriddhi Sankar Ray.
Nature Physics 19, 891 (2023)
4. Many-body Chaos in Fully Developed Turbulence,
A. Banerjee, R. Mukherjee, S. D. Murugan, S. Bhattacharjee, and Samriddhi Sankar Ray. |