13 research outputs found
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 is varied near a
saddle-node bifurcation at , the mean life time of the initial
metastable state is shown to scale like as
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