19 research outputs found
The effect of additive noise on dynamical hysteresis
We investigate the properties of hysteresis cycles produced by a
one-dimensional, periodically forced Langevin equation. We show that depending
on amplitude and frequency of the forcing and on noise intensity, there are
three qualitatively different types of hysteresis cycles. Below a critical
noise intensity, the random area enclosed by hysteresis cycles is concentrated
near the deterministic area, which is different for small and large driving
amplitude. Above this threshold, the area of typical hysteresis cycles depends,
to leading order, only on the noise intensity. In all three regimes, we derive
mathematically rigorous estimates for expectation, variance, and the
probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure
Dynamical suppression of decoherence in two-state quantum systems
The dynamics of a decohering two-level system driven by a suitable control
Hamiltonian is studied. The control procedure is implemented as a sequence of
radiofrequency pulses that repetitively flip the state of the system, a
technique that can be termed quantum "bang-bang" control after its classical
analog. Decoherence introduced by the system's interaction with a quantum
environment is shown to be washed out completely in the limit of continuous
flipping and greatly suppressed provided the interval between the pulses is
made comparable to the correlation time of the environment. The model suggests
a strategy to fight against decoherence that complements existing quantum
error-correction techniques.Comment: 15 pages, RevTeX style, 3 figures. Submitted to Phys. Rev.
Sub-Riemannian Methods in Shape Analysis
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