Rare Transition Events in Nonequilibrium Systems with State-Dependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices

Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of state-dependent noise. It is applied to a model of electronic transport in semiconductor superlattices to investigate transitions between metastable electric field distributions. When the applied voltage $V$ is varied near a saddle-node bifurcation at $V_th$, the mean life time $$ of the initial metastable state is shown to scale like $log \propto |V_th - V|^{3/2}$ as $V\to V_th$

Scaling properties of noise-induced switching in a bistable tunnel diode circuit

Noise-induced switching between coexisting metastable states occurs in a wide range of far-from-equilibrium systems including micro-mechanical oscillators, epidemiological and climate change models, and nonlinear electronic transport in tunneling structures such as semiconductor superlattices and tunnel diodes. In the case of tunnel diode circuits, noise-induced switching behavior is associated with negative differential resistance in the static current-voltage characteristics and bistability, i.e., the existence of two macroscopic current states for a given applied voltage. Noise effects are particularly strong near the onset and offset of bistable current behavior, corresponding to bifurcation points in the associated dynamical system. In this paper, we show that the tunnel diode system provides an excellent experimental platform for the precision measurement of scaling properties of mean switching times versus applied voltage near bifurcation points. More specifically, experimental data confirm that the mean switching time scales logarithmically as the 3/2 power of voltage difference over an exceptionally wide range of time scales and noise intensities.Comment: 9 pages, 9 figures, accepted manuscript for publication in the European Physical Journal B, Topical Issue: Non-Linear and Complex Dynamics in Semiconductors and Related Material

Experimental metrics for detection of detailed balance violation

We report on the measurement of detailed balance violation in a coupled, noise-driven linear electronic circuit consisting of two nominally identical RC elements that are coupled via a variable capacitance. The state variables are the time-dependent voltages across each of the two primary capacitors, and the system is driven by independent noise sources in series with each of the resistances. From the recorded time histories of these two voltages, we quantify violations of detailed balance by three methods: 1) explicit construction of the probability current density, 2) by constructing the time-dependent stochastic area, and 3) by constructing statistical fluctuation loops. In comparing the three methods, we find that the stochastic area is relatively simple to implement, computationally inexpensive, and provides a highly sensitive means for detecting violations of detailed balance.Comment: 12 pages, 6 figures, this version contains additional material relative to the previous on

Symmetry-breaking transitions in networks of nonlinear circuit elements

We investigate a nonlinear circuit consisting of N tunnel diodes in series, which shows close similarities to a semiconductor superlattice or to a neural network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like system. The tunnel diodes are coupled globally through a load resistor. We find complex bifurcation scenarios with symmetry-breaking transitions that generate multiple fixed points off the synchronization manifold. We show that multiply degenerate zero-eigenvalue bifurcations occur, which lead to multistable current branches, and that these bifurcations are also degenerate with a Hopf bifurcation. These predicted scenarios of multiple branches and degenerate bifurcations are also found experimentally.Comment: 32 pages, 11 figures, 7 movies available as ancillary file

Nonlinear Wave Methods for Charge Transport

The present book introduces and develops mathematical techniques for the treatment of nonlinear waves and singular perturbation methods at a level that is suitable for graduate students, researchers and faculty throughout the natural sciences and engineering. The practice of implementing these techniques and their value are largely realized by showing their application to problems of nonlinear wave phenomena in electronic transport in solid state materials, especially bulk semiconductors and semiconductor superlattices. The authors are recognized leaders in this field, with more than 30 combi