Characterization of Landau-Zener transitions in systems with complex spectra

Abstract

This paper is concerned with the study of one-body dissipation effects in idealized models resembling a nucleus. In particular, we study the quantum mechanics of a free particle that collides elastically with the slowly moving walls of a Bunimovich stadium billiard. Our results are twofold. First, we develop a method to solve in a simple way the quantum mechanical evolution of planar billiards with moving walls. The formalism is based on the scaling method [1] which enables the resolution of the problem in terms of quantities defined over the boundary of the billiard.The second result is related to the quantum aspects of dissipation in systems

Time-optimal control fields for quantum systems with multiple avoided crossings

“…This can be seen as follows: if the system is initially preparred in some state |n and the control parameter λ does not deviate much from the position of the corresponding AC (i.e. |λ − λ n | ∆ n [50]), then the dynamics of the system is effectively confined to a two-dimensional subspace, as the remaining N − 2 levels can be adiabatically eliminated [47]. This is the key characteristic of our model, and we will expand on its consequences later on.…”

Controlling open quantum systems using fast transitions

“…Consider the LZ system prepared initially in the state |ψ(0) = |0 . We now consider λ(t) to be a piecewise constant function with initial value λ(0) = −λ 0 , with λ 0 ∆/|α| [13]. In this way, the initial state is approximately an instantaneous eigenstate of the Hamiltonian H LZ (0).…”

“…The method is based on the knowledge of the spectrum of the closed system as a function of a suitable external parameter and requires that the system behaves locally -near avoided crossings-as the Landau-Zener (LZ) two level model [11,12]. Although this characteristic may seem rather restrictive, it is, in fact, a general prop-erty of systems with interaction between its energy levels [13,14], at least in the low energy region. We apply a well-defined series of fast (diabatic) and sudden (steplike) variations of the control parameter, which allows us to travel through the state space of the system and reach the desired target state.…”

Localized structures embedded in the eigenfunctions of chaotic Hamiltonian systems

“…In ref. [19] an efficient way of determining a.c was described in terms of the coefficients C µν (ℓ) ≡< ϕ µ |∂ϕ ν /∂ℓ > which define a driven evolution of the system. Using equation (2) and perturbation theory we obtain C µν (ℓ) = H ′ µν /(k 2 µ − k 2 ν ) , where µ and ν are associated to eigenstates of H(ℓ) (the adiabatic basis).…”

“…We have studied the desymmetrized stadium billiard with radius r and straight line of length a [19]. The boundary only depends on the shape parameter ℓ = a/r (the area is fixed to the value 1+π/4).…”