Quantum calculus of classical vortex images, integrable models and quantum states

International Conference on Quantum Science and Applications 2016

Pashaev, Oktay K.^1

Department of Mathematics, Izmir Institute of Technology, Gulbahce Campus, Urla-Izmir

35430, Turkey^1

关键词: Analytic functions;    Integrable models;    Non-linear oscillators;    Periodic function;    Quantum calculus;    Streamfunctions;    Vortex polygons;    Vortex problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/766/1/012015/pdf
DOI  :  10.1088/1742-6596/766/1/012015

来源: IOP

【 摘 要 】

From two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.