Towards the Resolution of a Quantized Chaotic Phase-Space: The Interplay of Dynamics with Noise.

We outline formal and physical similarities between the quantum dynamics of open systems and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, which, for suitable timescales, becomes analogous to the Fokker-Planck equation describing classical advection and diffusion. This correspondence allows, in principle, to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol-type oscillators.

Scarring in classical chaotic dynamics with noise.

We report the numerical observation of scarring, which is enhancement of probability density around unstable periodic orbits of a chaotic system, in the eigenfunctions of the classical Perron-Frobenius operator of noisy Anosov ("perturbed cat") maps, as well as in the noisy Bunimovich stadium. A parallel is drawn between classical and quantum scars, based on the unitarity or nonunitarity of the respective propagators. For uniformly hyperbolic systems such as the cat map, we provide a mechanistic explanation for the classical phase-space localization detected, based on the distribution of finite-time Lyapunov exponents, and the interplay of noise with deterministic dynamics. Classical scarring can be measured by studying autocorrelation functions and their power spectra.

Effective Ibuprofen Desensitization in a Patient with Myopericarditis.

To date, aspirin desensitization is employed with patients with nonsteroidal anti-inflammatory drugs (NSAIDs) exacerbated respiratory diseases (NERD) or with aspirin or NSAIDs hypersensitive patients needing a stent procedure for coronary artery disease. On the other hand, few data exist regarding aspirin desensitization in other cardiological features and particularly we haven't data on different NSAIDs desensitization. Only for NERD patients we have data on ketorolac use. We report an efficacious desensitization procedure for ibuprofen in urticaria/angioedema patient with pericarditis and myocarditis associated.

Effective Desensitization to Tocilizumab in Delayed Hypersensitivity Reaction.

We present tocilizumab desensitization of a 47-year-old woman affected by rheumatoid arthritis with full body delayed erythematous urticarial reaction. Skin test for tocilizumab gave cutaneous reaction after 6 h at 20 mg/mL. The schedule of desensitization was then adapted for non-immediate reaction. We prepared a desensitization procedure reaching the cumulative dose of 516 mg in 5 weeks. After 6 months, the repetition of skin tests had a negative result, with demonstration of tolerance induction. Today the patient has good control of the disease.

Counting statistics of chaotic resonances at optical frequencies: Theory and experiments.

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang et al., Phys. Rev. E 93, 040201(R) (2016)2470-004510.1103/PhysRevE.93.040201].

Erratum: Statistics of chaotic resonances in an optical microcavity [Phys. Rev. E 93, 040201(R) (2016)].

This corrects the article DOI: 10.1103/PhysRevE.93.040201.

Statistics of chaotic resonances in an optical microcavity.

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the time scale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.

Localization in chaotic systems with a single-channel opening.

We introduce a single-channel opening in a random Hamiltonian and a quantized chaotic map: localization on the opening occurs as a sensible deviation of the wave-function statistics from the predictions of random matrix theory, even in the semiclassical limit. Increasing the coupling to the open channel in the quantum model, we observe a similar picture to resonance trapping, made of a few fast-decaying states, whose left (right) eigenfunctions are entirely localized on the (preimage of the) opening, and plentiful long-lived states, whose probability density is instead suppressed at the opening. For the latter, we derive and test a linear relation between the wave-function intensities and the decay rates, similar to the Breit-Wigner law. We then analyze the statistics of the eigenfunctions of the corresponding (discretized) classical propagator, finding a similar behavior to the quantum system only in the weak-coupling regime.

Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system.

The finest state-space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation, the stochastic neighborhoods of deterministic periodic orbits can be computed from distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulas for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis.

On-manifold localization in open quantum maps.

A quantized chaotic map exhibiting localization of wave function intensity is opened. We investigate how such patterns as scars in the Husimi distributions are influenced by the losses through a number of numerical experiments. We find the scars to relocate on the stable or unstable manifolds depending on the position of the opening, and provide a classical argument to explain the observations. For asymmetrically introduced openings mode interaction contributes to determine the localization patterns. We finally show examples of similar localization in a simulated dielectric microcavity.

How well can one resolve the state space of a chaotic map?

All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching or contraction and the smearing due to noise. We propose to determine the "finest attainable" partition for a given hyperbolic dynamical system and a given weak additive white noise, by computing the local eigenfunctions of the adjoint Fokker-Planck operator along each periodic point, and using overlaps of their widths as the criterion for an optimal partition. The Fokker-Planck evolution is then represented by a finite transition graph, whose spectral determinant yields time averages of dynamical observables. Numerical tests of such "optimal partition" of a one-dimensional repeller support our hypothesis.