99 research outputs found
Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem
A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the small diffusion parameter. No mesh aspect ratio assumption is made. Numerical results are presented that support our theoretical estimat
Ultimate photo-induced Kerr rotation achieved in semiconductor microcavities
Photoinduced Kerr rotation by more than radians is demonstrated in
planar quantum well microcavity in the strong coupling regime. This result is
close to the predicted theoretical maximum of . It is achieved by
engineering microcavity parameters such that the optical impedance matching
condition is reached at the smallest negative detuning between exciton
resonance and the cavity mode. This ensures the optimum combination of the
exciton induced optical non-linearity and the enhancement of the Kerr angle by
the cavity. Comprehensive analysis of the polarization state of the light in
this regime shows that both renormalization of the exciton energy and the
saturation of the excitonic resonance contribute to the observed optical
nonlinearities.Comment: Shortened version prepared to submit in Phys. Rev. Letter
Continuous time crystal in an electron-nuclear spin system: stability and melting of periodic auto-oscillations
Crystals spontaneously break the continuous translation symmetry in space,
despite the invariance of the underlying energy function. This has triggered
suggestions of time crystals analogously lifting translational invariance in
time. Originally suggested for closed thermodynamic systems in equilibrium,
no-go theorems prevent the existence of time crystals. Proposals for open
systems out of equilibrium led to the observation of discrete time crystals
subject to external periodic driving to which they respond with a sub-harmonic
response. A continuous time crystal is an autonomous system that develops
periodic auto-oscillations when exposed to a continuous, time-independent
driving, as recently demonstrated for the density in an atomic Bose-Einstein
condensate with a crystal lifetime of a few ms. Here we demonstrate an
ultra-robust continuous time crystal in the nonlinear electron-nuclear spin
system of a tailored semiconductor with a coherence time exceeding hours.
Varying the experimental parameters reveals huge stability ranges of this time
crystal, but allows one also to enter chaotic regimes, where aperiodic behavior
appears corresponding to melting of the crystal. This novel phase of matter
opens the possibility to study systems with nonlinear interactions in an
unprecedented way.Comment: 12 figures, 17 page
Computation of saddle type slow manifolds using iterative methods
This paper presents an alternative approach for the computation of trajectory
segments on slow manifolds of saddle type. This approach is based on iterative
methods rather than collocation-type methods. Compared to collocation methods,
that require mesh refinements to ensure uniform convergence with respect to
, appropriate estimates are directly attainable using the method of
this paper. The method is applied to several examples including: A model for a
pair of neurons coupled by reciprocal inhibition with two slow and two fast
variables and to the computation of homoclinic connections in the
FitzHugh-Nagumo system.Comment: To appear in SIAM Journal of Applied Dynamical System
Optics of spin-noise-induced gyrotropy of asymmetric microcavity
The optical gyrotropy noise of a high-finesse semiconductor Bragg microcavity
with an embedded quantum well (QW) is studied at different detunings of the
photon mode and the QW exciton resonances. A strong suppression of the noise
magnitude for the photon mode frequencies lying above exciton resonances is
found. We show that such a critical behavior of the observed optical noise
power is specific of asymmetric Fabry-Perot resonators. As follows from our
analysis, at a certain level of intracavity loss, the reflectivity of the
asymmetric resonator vanishes, while the polarimetric sensitivity to the
gyrotropy changes dramatically when moving across the critical point. The
results of model calculations are in a good agreement with our experimental
data on the spin noise in a single-quantum-well microcavity and are confirmed
also by the spectra of the photo-induced Kerr rotation in the pump-probe
experiments.Comment: 6 pages, 5 figure
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