We revisit the mechanism of Poole-Frenkel non-ohmic conduction in materials of non-volatile memory. Percolation theory is shown to explain both the Poole and Frenkel dependencies corresponding to the cases of respectively small and large samples compared to the correlation radii of their percolation clusters. The applied bias modifies a limited number of microscopic resistances forming the percolation pathways. That understanding opens a pathway to multi-valued non-volatile memory and related neural network applications. arXiv:1906.07677v2 [cond-mat.dis-nn]

We develop a theory of percolation with plasticity media (PWPs) rendering properties of interest for neuromorphic computing. Unlike the standard percolation, they have multiple (N ≫ 1) interfaces and exponentially large number (N!) of conductive pathways between them. These pathways consist of non-ohmic random resistors that can undergo bias induced nonvolatile modifications (plasticity). The neuromorphic properties of PWPs include: multi-valued memory, high dimensionality and nonlinearity capable of transforming input data into spatiotemporal patterns, tunably fading memory ensuring outputs that depend more on recent inputs, and no need for massive interconnects. A few conceptual examples of functionality here are random number generation, matrix-vector multiplication, and associative memory. Understanding PWP topology, statistics, and operations opens a field of its own calling upon further theoretical and experimental insights.

The traditional pedagogical paradigm in physics is based on a deductive approach. However, with the recent advances in information technology, we are facing a dramatic increase in the amount of readily available information; hence, the ability to memorize the material and provide rigorous derivations lacks significance. Our success in navigating the current "sea" of information depends increasingly on our skills in pattern recognition and prompt qualitative analysis. Inductive learning (using examples and intuition-based) is most suitable for the development of such skills. This needed change in our pedagogical paradigm remains yet to be addressed in physics curricula. We propose that incorporating inductive elements in teaching -by infusing qualitative methods -will better prepare us to deal with the new information landscape. These methods bring the learning experience closer to the realities of active research. As an example, we are presenting a compendium for teaching qualitative methods in quantum mechanics, a traditionally non-intuitive subject. arXiv:1907.08154v2 [physics.ed-ph]

We present a numerical model that simulates the current–voltage (I–V) characteristics of materials exhibiting percolation conduction. The model consists of a two dimensional grid of exponentially different resistors in the presence of an external electric field. We obtained exponentially nonohmic I–V characteristics validating earlier analytical predictions and consistent with multiple experimental observations of the Poole–Frenkel laws in noncrystalline materials. The exponents are linear in voltage for samples smaller than the correlation length of percolation cluster L and square root in voltage for samples larger than L.

We develop a theory of pulse conduction in percolation type of materials such as noncrystalline semiconductors and nano-metal compounds. For short voltage pulses, the corresponding electric currents are inversely proportional to the pulse length and exhibit significant nonohmicity due to strong local fields in resistive regions of the percolation bonds. These fields can trigger local switching events incrementally changing bond resistances in response to pulse trains. Our prediction opens a venue to a class of multi-value nonvolatile memory implementable with a variety of materials.