- Arul Lakshminarayan

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# Arul Lakshminarayan

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Arul Lakshminarayan

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Arul Lakshminarayan

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Lakshminarayan, A.

Lakshminarayan, Arul

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- PublicationOut-of-time-ordered correlators and the Loschmidt echo in the quantum kicked top: How low can we go?(01-07-2021)
;Pg, Sreeram; Show more The out-of-time-ordered correlators (OTOCs) and the Loschmidt echo are two measures that are now widely being explored to characterize sensitivity to perturbations and information scrambling in complex quantum systems. Studying few qubits systems collectively modeled as a kicked top, we solve exactly the three- and four-qubit cases, giving analytical results for the OTOC and the Loschmidt echo. While we may not expect such few-body systems to display semiclassical features, we find that there are clear signatures of the exponential growth of OTOC even in systems with as low as four qubits in appropriate regimes, paving way for possible experimental measurements. We explain qualitatively how classical phase space structures like fixed points and periodic orbits have an influence on these quantities and how our results compare to the large-spin kicked top model. Finally we point to a peculiar case at the border of quantum-classical correspondence which is solvable for any number of qubits and yet has signatures of exponential sensitivity in a rudimentary form.Show more - PublicationOrdered level spacing probability densities(11-01-2019)
;Srivastava, Shashi C.L.; ;Tomsovic, StevenBÃ¤cker, ArndShow more Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest neighbour and farther neighbour spacings from a given level are introduced. Analytical predictions are derived using a 3 × 3 matrix model. The closest neighbour density is generalized to the kth closest neighbour spacing density, which allows for investigating long-range correlations. For larger k the probability density of kth closest neighbour spacings is well described by a Gaussian. Using these kth closest neighbour spacings we propose the ratio of the closest neighbour to the second closest neighbour as an alternative to the ratio of successive spacings. For a Poissonian spectrum the density of the ratio is flat, whereas for the three Gaussian ensembles repulsion at small values is found. The ordered spacing statistics and their ratio are numerically studied for the integrable circle billiard, the chaotic cardioid billiard, the standard map and the zeroes of the Riemann zeta function. Very good agreement with the predictions is found.Show more