Title: Quantum correspondence for Painleve VI
Abstract: The wave vector of the scalar Lax pair of Fuchs for PVI obeys a generalized heat equation whose coefficients are independent of the PVI field (Suleimanov 1994). Its identification to a time-dependent Schrödinger equation of quantum mechanics however required an ad hoc ordering of the products of position and impulsion operators.We remove this ambiguity by showing that thequantum Hamiltonian is the natural quantization of the logaritmic derivative of the tau-function of Painleve (1906), not of the tau-function of Chazy (1911), because the latter breaks the parity invariance in one of the four $theta_j$’s.
About the speaker:: After graduating from Ecole polytechnique, Robert Conte obtained a degree in solid state physics from Orsay then his PhD in theoretical fluid mechanics from Paris VI. His current interests are exact solutions of nonlinear ordinary differential, partial differential or discreteequations using the theories of Painleve.
Date: May 16,
Time: 4:30 --
628, Administrative Building, SZU
Host: Dr. Chengfa Wu