Quantization of a two-dimensional map with a strange attractor

M. Terraneo, Bertrand Georgeot, Dima L. Shepelyansky

Ervin Goldfain

T. D. Palev

R. Graham

The quantum-mechanical master equation of a homogeneously broadened single-mode laser is solved in the regime of the Lorenz strange attractor. The quantum Wigner distribution is obtained, replacing the classical invariant measure on the attractor, and reducing to it in the classical limit.

Alexei D. Chepelianskii, Dima L. Shepelyansky

The quantum dissipative time evolution of a fluxonium under a pulsed field (kicks) is studied numerically and analytically. In the classical limit the system dynamics is converged to a strange chaotic attractor. The quantum properties of this system are studied for the density matrix in the frame of Lindblad equation. In the case of dissipative quantum evolution the steady-state density matrix is converged to a quantum strange attractor being similar to the classical one. It is shown that depending on the dissipation strength there is a regime when the eigenstates of density matrix are localized at a strong or moderate dissipation. At a weak dissipation the eigenstates are argued to be delocalized being linked to the Ehrenfest explosion of quantum wave packet. This phenomenon is related with the Lyapunov exponent and Ehrenfest time for the quantum strange attractor. Possible experimental realisations of this quantum strange attractor with fluxonium are discussed.

Xue Xinfeng, Zhang Yuesheng, Yao Duanzheng

The resonance interaction of two-state atoms with single mode field is described theoretically by using the semi-classical theory and Jaynes-Cummings model. The nonlinear characteristics of this system are calculated by using FFT and Runge-Kutta methods. The chaotic strange attractors in this system are obtained from the numerical results.