Quantum signatures of chaos or quantum chaos?

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.     

C.w. optical parametric oscillators: single mode or multimode?

This paper details the conditions for which a c.w. OPO pumped by a single mode field is working in a single or multimode regime. It shows that c.w. OPOs are intrinsically single mode systems in the steady state regime, both for the longitudinal and transverse modes, unless special conditions of mode degeneracy or mode coupling are met. Complex optical patterns may appear in such cicumstances, that we have recently observed. Furthermore, if one adds a linear coupling between the signal and idler modes, these two modes can phase-lock on each other: one then obtains a perfect degenerate single mode operation for the c.w. OPO.     

Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?

Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of SOAEs.     

Deterministic and stochastic components of nonlinear Markov models with an application to decision making during the bailout votes 2008 (USA)

We apply a nonlinear Markov chain model to examine decision making in the US house of representatives during the period between the bailout votes of September 29 and October 3, 2008. We show how to determine deterministic and stochastic properties of the nonlinear model and, in doing so, estimate the strength of the attractors and the amplitudes of fluctuating forces that putatively influenced representatives’ decision making.     

Oscillons: an encounter with dynamical chaos in 1953?

We discuss the works of one of electronic art pioneers, Ben F. Laposky (1914-2000), and argue that he might have been the first to create a family of essentially nonlinear analog circuits that allowed him to observe chaotic attractors.     

Nanosciences: Evolution or revolution?

In miniaturized objects fabricated by modern technology the smallest linear size may be of a few nanometers. In the field of microelectronics, the advantages of such a miniaturization are huge (increased complexity and reliability, reduced costs). The technology is now approaching the limits where further size reduction will be impossible, except for very novel techniques such as molecular electronics. Miniaturization research has also led to the discovery of nanometric objects such as carbon nanotubes, which turn out to be particularly appropriate for inventing new materials. Miniaturization techniques have been progressively applied in other fields, with the hope of obtaining improvements similar to those encountered in microelectronics. Examples are biochips, which concentrate on a few cm² the recognition of ADN sequences, or ‘lab-on-a-chip’ devices, each of which constitutes a whole laboratory of chemical analysis, or MEMs (Micro Electro Mechanical Systems). New therapies will use miniaturized objects with multiple functions: For instance a nanoparticle can both recognize the target organ thanks to an appropriate protein, and deliver the therapeutic molecule to this target. These results have only been possible through new observation instruments, able to observe and manipulate nano objects. Is the observed evolution really a revolution of science and techniques? This is a point discussed in the conclusion, which also deals with risks associated to nanotechnologies, while the need for a social regulation is stressed.     

Some observations on the question: Is ventricular fibrillation “chaos”?

Ventricular fibrillation has been modeled as cardiac chaos occuring after a series of subharmonic bifurcations. However, previous experimental studies have suggested that fibrillatory oscillations have a relatively narrow-band frequency spectrum inconsistent with a turbulent process. Similarly, during the first minute of canine fibrillation we observed only a few localized frequency peaks from the epicardial and body surface electrocardiogram rather than a broadband type of spectrum as would be predicted for chaotic dynamics. Further narrowing of the frequency spectrum occured during the second minute of fibrillation. The frequency spectrum of ventricular fibrillation contrasts with scaled, broadband spectra observed in normal cardiac function. We suggest that ventricular fibrillation may serve as a general model for transitions from broadband stability to certain types of pathological periodicities in other physiological perturbations.     

Nucleon Strangeness: Intrinsic or Extrinsic?

A review of experimental results for the measurement of the strange quark distributions in the nucleon, is given. Contributions of the strange quarks to the nucleon mass, electromagnetic form factors and spin, are discussed.     

Can potentially useful dynamics to solve complex problems emerge from constrained chaos and/or chaotic itinerancy?

Complex dynamics including chaos in systems with large but finite degrees of freedom are considered from the viewpoint that they would play important roles in complex functioning and controlling of biological systems including the brain, also in complex structure formations in nature. As an example of them, the computer experiments of complex dynamics occurring in a recurrent neural network model are shown. Instabilities, itinerancies, or localization in state space are investigated by means of numerical analysis, for instance by calculating correlation functions between neurons, basin visiting measures of chaotic dynamics, etc. As an example of functional experiments with use of such complex dynamics, we show the results of executing a memory search task which is set in a typical ill-posed context. We call such useful dynamics "constrained chaos," which might be called "chaotic itinerancy" as well. These results indicate that constrained chaos could be potentially useful in complex functioning and controlling for systems with large but finite degrees of freedom typically observed in biological systems and may be such that working in a delicate balance between converging dynamics and diverging dynamics in high dimensional state space depending on given situation, environment and context to be controlled or to be processed.     

Forward masking: adaptation or integration?

The aim of this study was to attempt to distinguish between neural adaptation and persistence (or temporal integration) as possible explanations of forward masking. Thresholds were measured for a sinusoidal signal as a function of signal duration for conditions where the delay between the masker offset and the signal offset (the offset-offset interval) was fixed. The masker was a 200-ms broadband noise, presented at a spectrum level of 40 dB (re: 20 microPa), and the signal was a 4-kHz sinusoid, gated with 2-ms ramps. The offset-offset interval was fixed at various durations between 4 and 102 ms and signal thresholds were measured for a range of signal durations at each interval. A substantial decrease in thresholds was observed with increasing duration for signal durations up to about 20 ms. At short offset-offset intervals, the amount of temporal integration exceeded that normally found in quiet. The results were simulated using models of temporal integration (the temporal-window model) and adaptation. For both models, the inclusion of a peripheral nonlinearity, similar to that observed physiologically in studies of the basilar membrane, was essential in producing a good fit to the data. Both models were about equally successful in accounting for the present data. However, the temporal-window model provided a somewhat better account of similar data from a simultaneous-masking experiment, using the same parameters. This suggests that the linear, time-invariant properties of the temporal-window approach are appropriate for modeling forward masking. Overall the results confirm that forward masking can be described in terms of peripheral nonlinearity followed by linear temporal integration at higher levels in the auditory system. However, the difference in predictions between the adaptation and integration models is relatively small, meaning that influence of adaptation cannot be ruled out.     

Vortex collisions: crossing or recombination?

We investigate the collision of two vortex lines moving with viscous dynamics and driven towards each other by an applied current. Using London theory in the approach phase we observe a nontrivial vortex conformation producing antiparallel segments; their attractive interaction triggers a violent collision. The collision region is analyzed using the time-dependent Ginzburg-Landau equation. While we find that vortices will always recombine through the exchange of segments, a crossing channel appears naturally through a double collision process.     

Quantization: Deformation and/or Functor?

After a short presentation of the difference in motivation between the Berezin and deformation quantization approaches, we start with a reminder of Berezin’s view of quantization as a functor followed by a brief overview of deformation quantization in contrast with the latter. We end by a short survey of two main avatars of deformation quantization, quantum groups and quantum spaces (especially noncommutative geometry) presented in that perspective.     

Quantum information paradox: Real or fictitious?

One of the outstanding puzzles of theoretical physics is whether quantum information indeed gets lost in the case of black hole (BH) evaporation or accretion. Let us recall that quantum mechanics (QM) demands an upper limit on the acceleration of a test particle. On the other hand, it is pointed out here that, if a Schwarzschild BH exists, the acceleration of the test particle would blow up at the event horizon in violation of QM. Thus the concept of an exact BH is in contradiction with QM and quantum gravity (QG). It is also reminded that the mass of a BH actually appears as an integration constant of Einstein equations. And it has been shown that the value of this integration constant is actually zero! Thus even classically, there cannot be finite mass BHs though zero mass BH is allowed. It has been further shown that during continued gravitational collapse, radiation emanating from the contracting object gets trapped within it by the runaway gravitational field. As a consequence, the contracting body attains a quasi-static state where outward trapped radiation pressure gets balanced by inward gravitational pull and the ideal classical BH state is never formed in a finite proper time. In other words, continued gravitational collapse results in an ‘eternally collapsing object’ which is a ball of hot plasma and which is asymptotically approaching the true BH state with M = 0 after radiating away its entire mass energy. And if we include QM, this contraction must halt at a radius suggested by the highest QM acceleration. In any case no event horizon (EH) is ever formed and in reality, there is no quantum information paradox.     

Black Hole Entropy: Inside or Out?

A trialogue. Ted, Don, and Carlo consider the nature of black hole entropy. Ted and Carlo support the idea that this entropy measures in some sense “the number of black hole microstates that can communicate with the outside world.” Don is critical of this approach, and discussion ensues, focusing on the question of whether the first law of black hole thermodynamics can be understood from a statistical mechanics point of view.