Department of Physics

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    Entanglement production in quantized chaotic systems
    (Springer, 2005-04) Bandyopadhyay, Jayendra N.
    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.
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    European Physical Society logo. Italian Physical Society logo. EDP Sciences logo. The Institute of Physics logo. Quantum chaotic system as a model of decohering environment
    (IOP, 2009-03) Bandyopadhyay, Jayendra N.
    As a model of decohering environment, we show that a quantum chaotic system behaves equivalently as a many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic environment is derived. This theoretical formulation is substantiated by the numerical study of the decoherence of two qubits interacting with a quantum chaotic environment modeled by a chaotic kicked top. Like the many-body model of environment, the quantum chaotic system is an efficient decoherer, and it can generate entanglement between the two qubits which have no direct interaction.
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    Entanglement production in coupled chaotic systems: Case of the kicked tops
    (APS, 2004-01) Bandyopadhyay, Jayendra N.
    Entanglement production in coupled chaotic systems is studied with the help of kicked tops. Deriving the correct classical map, we have used the reduced Husimi function, the Husimi function of the reduced density matrix, to visualize the possible behaviors of a wave packet. We have studied a phase-space based measure of the complexity of a state and used random matrix theory (RMT) to model the strongly chaotic cases. Extensive numerical studies have been done for the entanglement production in coupled kicked tops corresponding to different underlying classical dynamics and different coupling strengths. An approximate formula, based on RMT, is derived for the entanglement production in coupled strongly chaotic systems. This formula, applicable for arbitrary coupling strengths and also valid for long time, complements and extends significantly recent perturbation theories for strongly chaotic weakly coupled systems.