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Discrete mathematical modelling seminar
Seminar information archive ～06/10｜Next seminar｜Future seminars 06/11～
| Organizer(s) | Tetsuji Tokihiro, Ralph Willox |
|---|
2025/06/11
17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Andy Hone (University of Kent)
Quantum minimal surfaces and discrete Painlevé equations (English)
Andy Hone (University of Kent)
Quantum minimal surfaces and discrete Painlevé equations (English)
[ Abstract ]
We consider the quantum version of the Poisson bracket equations for a Riemann surface immersed as a minimal surface in 4D Euclidean space. For the case of the quantum parabola, we show that the equation for normalisation of states corresponds to a discrete Painlevé I equation (dP1). The condition that the norms should be positive yields a unique positive solution of the dP1, and by constructing the space of initial conditions we find that it corresponds to a sequence of classical solutions of Painlevé V, which we present explicitly in terms of ratios of modified Bessel functions and their Wronskians.
We consider the quantum version of the Poisson bracket equations for a Riemann surface immersed as a minimal surface in 4D Euclidean space. For the case of the quantum parabola, we show that the equation for normalisation of states corresponds to a discrete Painlevé I equation (dP1). The condition that the norms should be positive yields a unique positive solution of the dP1, and by constructing the space of initial conditions we find that it corresponds to a sequence of classical solutions of Painlevé V, which we present explicitly in terms of ratios of modified Bessel functions and their Wronskians.
