Correlations in the adiabatic response of chaotic systems

Adiabatic variation of the parameters of a chaotic system results in a fluctuating reaction force. The quantum analog of a classical dissipative force, proportional to the time integral of the force-force correlation function, vanishes. We study this quantum-classical crossover for random matrix models. For the Gaussian unitary ensemble the crossover is found to take place on the Heisenberg time scale and the finite time integral practically vanishes for longer times. For the Gaussian orthogonal case, there is no such time scale and the integral falls off inversely proportional to time.     

Complex tone processing in primary auditory cortex of the awake monkey. I. Neural ensemble correlates of roughness

Previous physiological studies [e.g., Bieser and Muller-Preuss, Exp. Brain Res. 108, 273-284 (1996); Schulze and Langner, J. Comp. Physiol. A 181, 651-663 (1997); Steinschneider et al., J. Acoust. Soc. Am. 104, 2935-2955 (1998)] have suggested that neural activity in primary auditory cortex (A1) phase-locked to the waveform envelope of complex sounds with low (<300 Hz) periodicities may represent a neural correlate of roughness perception. However, a correspondence between these temporal response patterns and human psychophysical boundaries of roughness has not yet been demonstrated. The present study examined whether the degree of synchronized phase-locked activity of neuronal ensembles in A1 of the awake monkey evoked by complex tones parallels human psychoacoustic data defining the existence region and frequency dependence of roughness. Stimuli consisted of three consecutive harmonics of fundamental frequencies (f(0)s) ranging from 25 to 4000 Hz. The center frequency of the complex tones was fixed at the best frequency (BF) of the cortical sites, which ranged from 0.3 to 10 kHz. Neural ensemble activity in the thalamorecipient zone (lower lamina III) and supragranular cortical laminae (upper lamina III and lamina II) was measured using multiunit activity and current source density techniques and the degree of phase-locking to the f0 was quantified by spectral analysis. In the thalamorecipient zone, the stimulus f0 at which phase-locking was maximal increased with BF and reached an upper limit between 75 and 150 Hz for BFs greater than about 3 kHz. Estimates of limiting phase-locking rates also increased with BF and approximated psychoacoustic values for the disappearance of roughness. These physiological relationships parallel human perceptual data and therefore support the relevance of phase-locked activity of neuronal ensembles in A1 for the physiological representation of roughness.     

Complex tone processing in primary auditory cortex of the awake monkey. II. Pitch versus critical band representation

Noninvasive neurophysiological studies in humans support the existence of an orthogonal spatial representation of pure tone frequency and complex tone pitch in auditory cortex [Langner et al., J. Comp. Physiol. A 181, 665-676 (1997)]. However, since this topographic organization is based on neuromagnetic responses evoked by wideband harmonic complexes (HCs) of variable fundamental frequency (f0), and thus interharmonic frequency separation (deltaF), critical band filtering effects due to differential resolvability of harmonics may have contributed to shaping these responses. To test this hypothesis, the present study examined responses evoked by three-component HCs of variable f0 in primary auditory cortex (A1) of the awake monkey. The center frequency of the HCs was fixed at the best frequency (BF) of the cortical site. Auditory evoked potential (AEP), multiunit activity, and current source density techniques were used to evaluate A1 responses as a function of f0 (=deltaF). Generally, amplitudes of nearly all response components increased with f0, such that maximal responses were evoked by HCs comprised of low-order resolved harmonics. Statistically significant increases in response amplitude typically occurred at deltaFs between 10% and 20% of center frequency, suggestive of critical bandlike behavior. Complex tone response amplitudes also reflected nonlinear summation in that they could not be predicted by the pure tone frequency sensitivity curves of the cortical sites. A mechanism accounting for the observed results is proposed which involves mutual lateral inhibitory interactions between responses evoked by stimulus components lying within the same critical band. As intracortical AEP components likely to be propagated to the scalp were also strongly modulated by deltaF, these findings indicate that noninvasive recordings of responses to complex sounds may require a consideration of critical band effects in their interpretation.     

Critical petermann K factor for intensity noise squeezing

We investigate the impact of the Petermann-excess-noise factor K>/=1 on the possibility of intensity noise squeezing of laser light below the standard quantum limit. Using an N-mode model, we show that squeezing is limited to a floor level of 2(K-1) times the shot noise limit. Thus, even a modest Petermann factor significantly impedes squeezing, which becomes impossible when K>/=1.5. This appears as a serious limitation for obtaining sub-shot-noise light from practical semiconductor lasers. We present experimental evidence for our theory.     

Counting subsets of contingency tables

We describe multistage Markov chain Monte Carlo (MSMCMC) procedures which, in addition to estimating the total number of contingency tables with given positive row and column sums, estimate the number, $Q$ , and the proportion, $P$ , of those tables that satisfy an additional, possibly, nonlinear constraint. Three Options, A, B, and C, are studied. Options A and B exploit locally optimal statistical properties whereas judicious assignment of a particular parameter of Option C allows estimation with approximately minimal standard error. Ten examples of varying dimensions and total entries illustrate and compare the procedures, where $Q$ and $P$ denote the number and proportion of chi-squared statistics less than a given value. For both small and large dimensional tables, the comparisons favor Options A and B for moderate $P$ and Option C for small $P$ . Additional comparison with sequential importance sampling estimates favors the latter for small dimensional tables and moderate $P$ but favors Option C for large dimensional tables for both small and moderate $P$ . The proposed options extend an earlier MSMCMC technique for estimating total count and, in principle, can be further extended to incorporate additional constraints.     

Probing the statistics of transport in the Hénon Map

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant “boundary circles.” We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.     

Spectral Statistics of the Rectangular Billiard with a Flux Line

The density of states of a rectangular billiard with an Aharonov–Bohm flux line in its center was calculated in the semiclassical approximation and was used for the calculation of the form factor in the diagonal approximation. The distribution of nearest level spacings and the form factor were calculated also numerically. For some values of the flux these were found to be close to the ones of the semi-Poisson statistics. The difference between the numerical results and the semiclassical ones were found to be much larger than for chaotic and for integrable systems within similar approximations. Possible reasons for these discrepancies are discussed.