Progress of silicon based technology is nearing its physical limit, as minimum feature size of components is reaching a mere 5 nm. The resistive switching behavior of transition metal oxides and the associated memristor device is emerging as a competitive technology for next generation electronics. Significant progress has already been made in the past decade and devices are beginning to hit the market; however, it has been mainly the result of empirical trial and error. Hence, gaining theoretical insight is of essence. In the present work we report a new connection between the resistive switching and shock wave formation, a classic topic of non-linear dynamics. We argue that the profile of oxygen ions that migrate during the commutation in insulating binary oxides may form a <i>shock wave</i>, which propagates through a poorly conductive region of the device. We validate the scenario by means of model simulations.
In itinerant magnetic systems with disorder, the quantum Griffiths phase at T = 0 is unstable to formation of a
cluster glass (CG) of frozen droplet degrees of freedom. In the absence of the fluctuations associated with these
degrees of freedom, the transition from the paramagnetic Fermi liquid (PMFL) to the ordered phase proceeds
via a conventional second-order quantum phase transition. However, when the Griffiths anomalies due to the
broad distribution of local energy scales are included, the transition is driven first-order via a novel mechanism
for a fluctuation induced first-order transition. At higher temperatures, thermal effects restore the transition to
second-order. Implications of the enhanced non-Ohmic dissipation in the CG phase are briefly discussed.
Glassy behavior is a generic feature of electrons close to disorder-driven metal-insulator transitions. Deep in the insulating phase, electrons are tightly bound to impurities, and thus classical models for electron glasses have long been used. As the metallic phase is approached, quantum fluctuations become more important, as they control the electronic mobility. In this paper we review recent work that used extended dynamical mean-field approaches to discuss the influence of such quantum fluctuations on the glassy behavior of electrons, and examine how the stability of the glassy phase is affected by the Anderson and the Mott mechanisms of localization.