There are certain classes of resistors, capacitors, and inductors that, when subject to a periodic input of appropriate frequency, develop hysteresis loops in their characteristic response. Here we show that the hysteresis of such memory elements can also be induced by white noise of appropriate intensity even at very low frequencies of the external driving field. We illustrate this phenomenon using a physical model of memory resistor realized by TiO(2) thin films sandwiched between metallic electrodes and discuss under which conditions this effect can be observed experimentally. We also discuss its implications on existing memory systems described in the literature and the role of colored noise.

The calculation of the heating rate of cold atoms in vibrating traps requires a theory that goes beyond the Kubo linear response formulation. If a strong "quantum chaos" assumption does not hold, the analysis of transitions shows similarities with a percolation problem in energy space. We show how the texture and the sparsity of the perturbation matrix, as determined by the geometry of the system, dictate the result. An improved sparse random matrix model is introduced: it captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture.

The calculation of the conductance of disordered rings requires a theory that goes beyond the Kubo-Drude formulation. Assuming "mesoscopic" circumstances the analysis of the electro-driven transitions show similarities with a percolation problem in energy space. We argue that the texture and the sparsity of the perturbation matrix dictate the value of the conductance, and study its dependence on the disorder strength, ranging from the ballistic to the Anderson localization regime. An improved sparse random matrix model is introduced to captures the essential ingredients of the problem, and leads to a generalized variable range hopping picture. ‡ Hence there is no issue of quantum recurrences which would arise for a strictly linear or periodic driving. From here on we use units such that = 1. § The terminology of this paper, and in particular our notion of "conductance" are the same as in the theoretical review [4] and in the experimental work [5].

Semilinear response theory determines the absorption coefficient of a driven system using a resistor network calculation: each unperturbed energy level of a particle in a vibrating trap, or of an electron in a mesoscopic ring, is regarded as a node ͑n͒ of the network; the transition rates ͑w mn ͒ between the nodes are regarded as the elements of a random matrix that describes the network. If the size distribution of the connecting elements is wide ͑e.g., log-normal-like rather than Gaussian type͒ the result for the absorption coefficient differs enormously from the conventional Kubo prediction of linear response theory. We use a generalized variable range hopping scheme for the analysis. In particular, we apply this approach to obtain practical approximations for the conductance of mesoscopic rings. In this context Mott's picture of diffusion and localization is revisited.

We consider driven systems where the driving induces jumps in energy space:(1) particles pulsed by a step potential; (2) particles in a box with a moving wall; (3) 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) .