Seminars

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For any real irrational number alpha, Dirichlet's theorem guarantees that there are infinitely many rational p/q, such that |alpha - p/q|<1/q^2. Moreover, there are real numbers (with irrationality measure 2) for which this approximation cannot be improved. The same holds true for approximation of real numbers by elements of any fixed totally real field. In this talk, we shall discuss the question of whether it is possible to obtain better approximations of real numbers over infinite totally real extensions. In particular, we prove such a result for totally p-adic real extensions. This is work in progress with Sushant Kala.

In this talk, I will present our recent investigations on the dynamics of entanglement in single and double Jaynes-Cummings models, focusing on the role of structured quantum states such as squeezed coherent thermal states. We explore how thermal and squeezed photons, along with atomic initial conditions like Bell and Werner states, influence the generation, degradation, and revival of entanglement. The effects of additional interactions—such as Ising-type coupling, dipole-dipole interaction, detuning, and Kerr-nonlinearity—are investigated to understand their impact on entanglement of various subsystems. The results reveal rich dynamics, including entanglement sudden death and revival, and provide a deeper understanding of how structured light and atomic correlations can be harnessed to control quantum coherence in realistic cavity-QED systems.

Chennai Combinatorics Colloquium Talk, organized in collaboration with IIT Madras, CMI, ISI Chennai and Krea University.

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