Department of Physics
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Item Floquet analysis of periodically driven kicked systems(IAS, 2019) Bandyopadhyay, Jayendra N.We employ Floquet theory to study the spectral properties of the Floquet Hamiltonian, also known as the effective static Hamiltonian of periodically driven kicked systems. In general, the Floquet Hamiltonian cannot be determined exactly, and therefore one has to employ some perturbation theory. Here we apply a recently proposed perturbation theory to obtain the Floquet Hamiltonian periodically kicked systems at very high-frequency limit. We studied the spectral properties of two well-known kicked systems: single and double-kicked top. Classical dynamics of these systems is chaotic, but their quantum mechanical spectrum is very different: the first one follows the Bohigas–Giannoni–Schmit conjecture of random matrix theory, but the latter one shows self-similar fractal behavior. Here we show that the fractal spectrum of the double-kicked top system shares some number of theoretical properties with the famous Hoftstadter butterfly.Item Entangling power of quantum chaotic evolutions via operator entanglement(ARXIV, 2005-04) Bandyopadhyay, Jayendra N.We study operator entanglement of the quantum chaotic evolutions. This study shows that properties of the operator entanglement production are qualitatively similar to the properties reported in literature about the pure state entanglement production. This similarity establishes that the operator entanglement quantifies {\it intrinsic} entangling power of an operator. The term `intrinsic' suggests that this measure is independent of any specific choice of initial states.Item Testing Statistical Bounds on Entanglement Using Quantum Chaos(APS, 2002-07) Bandyopadhyay, Jayendra N.Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random matrix theory modeling of composite quantum systems, investigated recently, entails a universal distribution of the eigenvalues of the reduced density matrices. We demonstrate that these distributions are realized in quantized chaotic systems by using a model of two coupled and kicked tops. We derive an explicit statistical universal bound on entanglement, which is also valid for the case of unequal dimensionality of the Hilbert spaces involved, and show that this describes well the bounds observed using composite quantized chaotic systems such as coupled tops.