The next talk at our seminar by Alexander Gorsky (IITP Moscow) "Phase-locking in dynamical systems and quantum mechanics" will be this coming Thursday, November 27, 2025 at 12PM EDT  (which currently is 6pm in Europe, 5pm in the UK, 12noon in Toronto, 9am in California).

Abstract: We will discuss the Prüfer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schr?dinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the band-gap structure of the Hill equation. For the parametric oscillator, we provide the relation between the non-adiabatic Hannay angle and the Poincaré rotation number of the corresponding dynamical system. In terms of quantum mechanics, the integer rotation number is connected to the quantization number via the Milne quantization approach and exact WKB. Using recent results concerning the exact WKB approach in quantum mechanics, we discuss the possible non-perturbative effects in the dynamical systems on the torus and for the parametric oscillator. The semiclassical WKB is interpreted in the framework of a slow-fast dynamical system. The link between the classification of the coadjoint Virasoro orbits and the Hill equation yields a classification of the phase-locking domains in the parameter space in terms of the classification of Virasoro orbits. Our picture is supported by numerical simulations for the model of the Josephson junction and Mathieu equation.

We'll keep the Zoom coordinates the same:
Zoom at   99576627828
Passcode: 448487
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FROM 202.120.11.*