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Public viva-voce Notification Date: Monday, 29 September 2025 Time: 11.00 AM Venue: Seminar Hall (Hybrid mode) Some Investigations into Classical and Quantum Coupled Rotors Ankit Yadav Chennai Mathematical Institute. 29-09-25 Abstract In this talk we discuss the dynamics of coupled rotors in the classical as well as the quantum regime. In the first part of the talk, we study the periodic orbits and some of their features in the classical three-rotor problem. In the second part, we focus on the quantum two-rotor system and its kicked variant as an open quantum system. The three-rotor problem contains a simple family of periodic orbits, which undergoes a doubly infinite cascade of stability transitions. These stability transitions are associated with a certain kind of bifurcations. At these bifurcations, new families of periodic orbits are born. We find these periodic orbits numerically using our search algorithm. Using the perturbation equation, we also solve for these periodic orbits near bifurcations and verify our numerical findings using these analytical results. The energies at which these bifurcations occur form an asymptotic geometric sequence. We calculate the scaling constant associated with it, quantifying the geometric nature. Additionally, the shape of the new orbits born at these bifurcations also has a self-similar structure related to the scaling constants. We also quantify them using two different scaling constants. In the second part, we discuss a quantum mechanical system of two coupled rotors from an open quantum systems point of view. We trace out one rotor and study the density matrix associated with the other one. The reduced density matrix associated with the energy eigenstates of the two-rotor system can be calculated analytically. The von Neumann entropy of the reduced system is related to the Fourier coefficients of the Mathieu functions associated with the two-rotor energy eigenstates. Introducing a kicked potential, we study the time evolution of the von Neumann entropy as the systems interact. Finally, we treat the kicked two-rotor model as a bath-system model and use Markovian approximation to derive the time-local Lindblad type of evolution equation for the system density matrix. All are invited to attend the viva-voce examination
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