CHAOS IN WAVE MECHANICS WITH A LOGARITHMIC NONLINEARITY

In order to extract chaotic features from the nonlinear extension of wave mechanics proposed by Bialynicki-Birula and Mycielski [Ann. Phys. 100 (1976) 621 we examine - within an ad hoc model involving the one-band tight binding Hamiltonian - the time evolution of a periodic wave function of period s in a periodic potential of period 2-pi/alpha. For alpha=2-pi-r/s the quantum dynamics reduces to a finite number of dimensions and can be expressed in terms of a classical Hamilton system with 2s-dimensional phase space. Standard methods of investigation show that the nonlinearity may produce ergodicity and positive Lyapunov exponents.