9 research outputs found
Pathways of activated escape in periodically modulated systems
We investigate dynamics of activated escape in periodically modulated
systems. The trajectories followed in escape form diffusion broadened tubes,
which are periodically repeated in time. We show that these tubes can be
directly observed and find their shape. Quantitatively, the tubes are
characterized by the distribution of trajectories that, after escape, pass
through a given point in phase space for a given modulation phase. This
distribution may display several peaks separated by the modulation period.
Analytical results agree with the results of simulations of a model Brownian
particle in a modulated potential
Activated escape of periodically modulated systems
The rate of noise-induced escape from a metastable state of a periodically
modulated overdamped system is found for an arbitrary modulation amplitude .
The instantaneous escape rate displays peaks that vary with the modulation from
Gaussian to strongly asymmetric. The prefactor in the period-averaged
escape rate depends on nonmonotonically. Near the bifurcation amplitude
it scales as . We identify three scaling
regimes, with , and 1/2
Universality in escape from a modulated potential well
We show that the rate of activated escape from a periodically modulated
potential displays scaling behavior versus modulation amplitude . For
adiabatic modulation of an optically trapped Brownian particle, measurements
yield with . The theory gives
in the adiabatic limit and predicts a crossover to scaling as
approaches the bifurcation point where the metastable state disappears.Comment: 4 pages, 3 figure
Resonant symmetry lifting in a parametrically modulated oscillator
We study a parametrically modulated oscillator that has two stable states of
vibrations at half the modulation frequency . Fluctuations of the
oscillator lead to interstate switching. A comparatively weak additional field
can strongly affect the switching rates, because it changes the switching
activation energies. The change is linear in the field amplitude. When the
additional field frequency is , the field makes the
populations of the vibrational states different thus lifting the states
symmetry. If differs from , the field modulates the
state populations at the difference frequency, leading to fluctuation-mediated
wave mixing. For an underdamped oscillator, the change of the activation energy
displays characteristic resonant peaks as a function of frequency
Scaling and crossovers in activated escape near a bifurcation point
Near a bifurcation point a system experiences critical slowing down. This
leads to scaling behavior of fluctuations. We find that a periodically driven
system may display three scaling regimes and scaling crossovers near a
saddle-node bifurcation where a metastable state disappears. The rate of
activated escape scales with the driving field amplitude as , where is the bifurcational value of . With
increasing field frequency the critical exponent changes from
for stationary systems to a dynamical value and then again to
. The analytical results are in agreement with the results of
asymptotic calculations in the scaling region. Numerical calculations and
simulations for a model system support the theory.Comment: 18 page