No abstract

Understanding the spatiotemporal structure of most probable fluctuation pathways to rarely occurring states is a central problem in the study of noise-driven, nonequilibrium dynamical systems. When the underlying system does not possess detailed balance, the optimal fluctuation pathway to a particular state and relaxation pathway from that state may combine to form a looplike structure in the system phase space called a fluctuation loop. Here, fluctuation loops are studied in a linear circuit model consisting of coupled RC elements, where each element is driven by its own independent noise source. Using a stochastic Hamiltonian approach, we determine the optimal fluctuation pathways, and analytically construct corresponding fluctuation loops. To quantitatively characterize fluctuation loops, we study the time-dependent area tensor that is swept out by individual stochastic trajectories in the system phase space. At long times, the area tensor scales linearly with time, with a coefficient that precisely vanishes when the system satisfies detailed balance.

Static domain formation in doped semiconductor superlattices results in several current branches separated by abrupt discontinuities that exhibit hysteresis. The transition from one branch to its adjacent one is studied by time-resolved switching experiments. The mean value of the relocation time increases by more than one order of magnitude, when the final voltage on the adjacent branch is reduced to a value approaching the discontinuity. At the same time, the distribution function of the relocation time changes from a simple Gaussian to a first-passage time form.

Physical mechanisms responsible for nonlinear phenomena and anomalous transient response of cooled extrinsic far-infrared photoconductors are discussed. A simple model describing carrier generation, trapping, and impact ionization is presented, which describes the transient response on fast time scales 10−3 to 10−4 sec, neglecting changes in space charge. Carrier heating by a dc electric field produces relatively fast, damped oscillatory response to external excitation. A small-signal analysis of these equations is a test of stability. An analysis of the role of ideal electrical contacts and space charge is also presented. The very slow (∼1 sec) overshoot and transient response commonly observed in cooled extrinsic photoconductors is explained by the dynamics of trapped space charge near the injecting electrical contact. A small-signal analysis determines the characteristic time constants for these processes, which are typically ∼1 sec. Calculated examples of the recombination and ionization coefficients, dc I-V curves, differential equation flow diagrams, and transient response are presented for parameters typical of  p-type Ge photoconductors doped with shallow acceptor levels, and suggestions for the design of more stable photoconductors are presented.

Self-generated nonlinear oscillations and chaos are found in the conductance of liquidHe-cooled far-infrared photoconductors made from ultrapure Ge. Complex behavior includes a period-doubling cascade to chaotic oscillation with increasing applied electric field, quasiperiodic oscillation, frequency locking, and intermittent switching between modes of oscillation. A rate-equation model is presented which includes impurity impact ionization and space-charge injection.PACS numbers: 72.70.+ m, 05.40.+j, 05.70.Ln