On the Scaling of Type-1 Intermittency in a Semiconductor Experiment

Abstract

Spontaneous oscillations developing during low-temperature impact ionization breakdown in extrinsic germanium are looked at with respect to characteristic features of type-I intermittency

Time-Averaged Quantity of a Low-Temperature Semiconductor Experiment Reflects Scaling Behavior of Saddle-Node Bifurcation to Chaos

“…In contrast, the mean burst length i c remains constant in the vicinity of B0, be cause it is the stability of the limit cycle, but not the structure and the stability of the embedding chaotic attractor, which is affected under the transition. In agreement with the stability of the chaotic attractor, we found previously [10] that the distribution of re injections does not depend on the bifurcation param eter. The statements above are in accordance with the observation that unstable periodic orbits representing the skeleton of a chaotic attractor are robust against bifurcations [11].…”

“…2(c), a series of almost periodic oscillations (so-called laminar phase of length tl ) is interrupted by chaotic bursts of duration tc . During a chaotic burst, the sample in the time average conducts a slightly higher current I c, whereas during a laminar phase only the lower current I L remains which is equivalent to the current at the bifurcation In previous experiments [10], we have already proved that for the prevailing transition the mean laminar phase length i L obeys the well-known scaling law of type-I intermittency [5],…”

“…of the kink starting at about B = 1.65 mT, a stronger devia tion between fit and data can be recognized. However, as shown by previous measurements [10], it is caused by the distance from the bifurcation point where chaotic dynamics becomes more and more important. In the following, we demonstrate that the twofold square-root law of (1) is characteristic for the time average of an oscillatory quantity undergoing a type-I intermittent transition to chaos.…”

“…They are fast, but still well accessible in the time do main (oscillations in the kHz frequency regime) such that both time-averaged and time-resolved measure ments are possible [8], In a previous work, we have investigated various types of intermittency, consider-ing especially the distribution and scaling behavior of the laminar phase lengths counted from the time trace [9,10]. In the following, we demonstrate that under generic conditions the scaling behavior of type-I inter mittency also appears in the control parameter depen dence of a time-averaged quantity.…”