1,445 research outputs found
Quantum versus classical phase-locking transition in a driven-chirped oscillator
Classical and quantum-mechanical phase locking transition in a nonlinear
oscillator driven by a chirped frequency perturbation is discussed. Different
limits are analyzed in terms of the dimensionless parameters and
( and being the driving amplitude,
the frequency chirp rate, the nonlinearity parameter and the linear frequency
of the oscillator). It is shown that for , the passage
through the linear resonance for above a threshold yields classical
autoresonance (AR) in the system, even when starting in a quantum ground state.
In contrast, for , the transition involves
quantum-mechanical energy ladder climbing (LC). The threshold for the
phase-locking transition and its width in in both AR and LC limits are
calculated. The theoretical results are tested by solving the Schrodinger
equation in the energy basis and illustrated via the Wigner function in phase
space
Quantum Fluctuations in the Chirped Pendulum
An anharmonic oscillator when driven with a fast, frequency chirped voltage
pulse can oscillate with either small or large amplitude depending on whether
the drive voltage is below or above a critical value-a well studied classical
phenomenon known as autoresonance. Using a 6 GHz superconducting resonator
embedded with a Josephson tunnel junction, we have studied for the first time
the role of noise in this non-equilibrium system and find that the width of the
threshold for capture into autoresonance decreases as the square root of T, and
saturates below 150 mK due to zero point motion of the oscillator. This unique
scaling results from the non-equilibrium excitation where fluctuations, both
quantum and classical, only determine the initial oscillator motion and not its
subsequent dynamics. We have investigated this paradigm in an electrical
circuit but our findings are applicable to all out of equilibrium nonlinear
oscillators.Comment: 5 pages, 4 figure
Kinetic simulations of ladder climbing by electron plasma waves
The energy of plasma waves can be moved up and down the spectrum using
chirped modulations of plasma parameters, which can be driven by external
fields. Depending on whether the wave spectrum is discrete (bounded plasma) or
continuous (boundless plasma), this phenomenon is called ladder climbing (LC)
or autoresonant acceleration of plasmons. It was first proposed by Barth
\textit{et al.} [PRL \textbf{115}, 075001 (2015)] based on a linear fluid
model. In this paper, LC of electron plasma waves is investigated using fully
nonlinear Vlasov-Poisson simulations of collisionless bounded plasma. It is
shown that, in agreement with the basic theory, plasmons survive substantial
transformations of the spectrum and are destroyed only when their wave numbers
become large enough to trigger Landau damping. Since nonlinear effects decrease
the damping rate, LC is even more efficient when practiced on structures like
quasiperiodic Bernstein-Greene-Kruskal (BGK) waves rather than on Langmuir
waves \textit{per~se}
- …