The Landau-Zener effect explains the promotion mechanism from one adiabatic intrinsic energy level to another one when the generalized coordinates vary. The two levels have the same spin. In the case of single-particle models without including residual interactions, it is possible to quantify the Landau-Zener effect by mean of a time dependent system of coupled channel equations. At this conference, a generalization of the Landau-Zener equations for seniority one superfluid nuclear systems is presented. A new set of time dependent coupled channel equations are derived in detail. The particular cases of these equations are the classical time dependent Landau-Zener equations and the time dependent Hartree-Fock-Bogoliubov equations for even systems.
In this work, we investigate the influence of colored noise originating from a heat bath on nonlinear Landau-Zener (LZ) tunneling. The nonlinearity might arise intrinsically from many-body mean-field atomic self-interactions or Kerr nonlinearities in optical systems. Contrary to the well-established picture of thermally enhanced quantum tunneling within the linear LZ paradigm, ensemble statistics of our numerical simulations demonstrate that nonlinearity can give rise to thermally suppressed LZ tunneling: the tunneling probability of the nonlinear LZ system decreases as the amplitude of the colored noise increases beyond a critical value. Analytically, the Wiener-Hermite expansion facilitates elucidation of the intrinsic mechanism accounting for the nonmonotonic dependence of tunneling probability on noise amplitude. We compare these behaviors with stochastic resonance responses and clarify that the two phenomena stem from distinct physical mechanisms. In addition, we obtain approximate solutions in the weak- and strong-noise limits and discuss the implications of our theory.