We consider driven systems where the driving induces jumps in energy space:

• particles pulsed by a step potential;
• particles in a box with a moving wall;
• particles in a ring driven by an electro-motive-force.

In all these cases the route towards quantum-classical correspondence is highly non-trivial. Some insight is gained by observing that the dynamics in energy space, where n is the level index, is essentially the same as that of Bloch electrons in a tight binding model, where n is the site index. The mean level spacing is like a constant electric field and the driving induces long range hopping 1/(n-m).

In the illustration below the EMF is concentrated at one point along the ring. Whenever a particle cross the EMF region its kinetic energy is boosted. The energy jump is eV. From quantum mechanical point of view this constitutes a non-perturbative effect. It is neither "adiabatic" nor "diabatic" but rather a "semiclassical" transition. In the analagous tight binding model the semicalssical dynamics is regarded as uni-directional Bloch oscillations.


[1] A. Stotland and D. Cohen, J. Phys. A 39, 10703 (2006). [arXiv] [pdf]