• Arul Lakshminarayan

      Articles written in Pramana – Journal of Physics

    • Accuracy of trace formulas

      Arul Lakshminarayan

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      Using quantum maps, we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical accuracy in some systems is demonstrated quantitatively. However, our study of the standard map cautions that this may not be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one trace even in the presence of fixed points on singularities the trace formula may be exact, and in any case has no logarithmic divergences observed for the quantum bakers map. As a byproduct we introduce fantastic periodic curves akin to curlicues.

    • Local identities involving Jacobi elliptic functions

      Avinash Khare Arul Lakshminarayan Uday Sukhatme

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      We derive a number of local identities involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with an extension to several new cyclic identities. Second, we obtain a generalization to cyclic identities in which successive terms have a multiplicative phase factor exp(2iπ/s), wheres is any integer. Third, we systematize the local identities by deriving four local ‘master identities’ analogous to the master identities for the cyclic sums discussed by us previously. Fourth, we point out that many of the local identities can be thought of as exact discretizations of standard non-linear differential equations satisfied by the Jacobi elliptic functions. Finally, we obtain explicit answers for a number of definite integrals and simpler forms for several indefinite integrals involving Jacobi elliptic functions.

    • Entanglement production in quantized chaotic systems

      Jayendra N Bandyopadhyay Arul Lakshminarayan

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      Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, chaos in the system produces more entanglement. However, coupling strength between two subsystems is also a very important parameter for entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed-state entanglement production are qualitatively similar to the pure state entanglement production. We however still lack an analytical understanding of the mixed-state entanglement production in chaotic systems.

    • Preface

      Neelima Gupte Arul Lakshminarayan Ram Ramaswamy

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