We consider time-dependent Schrödinger equations in one dimension with doublewell potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues, then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solu...

We consider the Γ−limit of a family of functionals which model the interaction of a material that undergoes phase transition with a rapidly oscillating conservative vector field. These functionals consist of a gradient term, a double-well potential and a vector field. The scaling is such that all three terms scale in the same way and the frequency of the vector field is equal to the interface t...

We present evidence for a close analogy between the nonlinear behavior of a pulsed microwave-driven Josephson junction at low temperature and the experimentally observed behavior of Josephson systems operated below the quantum transition temperature under similar conditions. We specifically address observations of Ramsey-type fringe oscillations, which can be understood in classical nonlinear d...

We discuss the Γ-convergence, under the appropriate scaling, of the energy functional ‖u‖Hs(Ω) + ∫ Ω W (u) dx, with s ∈ (0, 1), where ‖u‖Hs(Ω) denotes the total contribution from Ω in the Hs norm of u, and W is a double-well potential. When s ∈ [1/2, 1), we show that the energy Γ-converges to the classical minimal surface functional – while, when s ∈ (0, 1/2), it is easy to see that the functio...

The effects on the exchange coupling in magnetic trilayers due to the presence of a spin-independent potential well are investigated. It is shown that within the RKKY theory no bias nor extra periods of oscillation associated with the depth of the well are found, contrary to what has been claimed in recent works. The range of validity of the RKKY theory is also discussed. PACS numbers 75.70.Fr,...

Additive white noise may significantly increase the response of bistable systems to a periodic driving signal. We consider two classes of double-well potentials, symmetric and asymmetric, modulated periodically in time with period 1/ε, where ε is a moderately (not exponentially) small parameter. We show that the response of the system changes drastically when the noise intensity σ crosses a thr...