Quantum chaos and fractals with atoms in cavities

We study the coupled translational, electronic, and field dynamics of the combined system “a two-level atom + a single-mode quantized field + a standing-wave ideal cavity”. In the semiclassical approximation with a point-like atom, interacting with the classical field, the dynamics is described by the Heisenberg equations for the atomic and field expectation values which are known to produce semiclassical chaos under appropriate conditions. We derive Hamilton–Schrödinger equations for probability amplitudes and averaged position and momentum of a point-like atom interacting with the quantized field in a standing-wave cavity. They constitute, in general, an infinite-dimensional set of equations with an infinite number of integrals of motion which may be reduced to a dynamical system with four degrees of freedom if the quantized field is supposed to be initially prepared in a Fock state. This system is found to produce semiquantum chaos with positive values of the maximal Lyapunov exponent. At exact resonance, the semiquantum dynamics is regular. At large values of detuning |δ|1, the Rabi atomic oscillations are usually shallow, and the dynamics is found to be almost regular. The Doppler–Rabi resonance, deep Rabi oscillations that may occur at any large value of |δ| to be equal to |αp₀|, is found numerically and described analytically (with α to be the normalized recoil frequency and p₀ the initial atomic momentum). Two gedanken experiments are proposed to detect manifestations of semiquantum chaos in real experiments. It is shown that in the chaotic regime values of the population inversion z_out, measured with atoms after transversing a cavity, are so sensitive to small changes in the initial inversion z_in that the probability of detecting any value of z_out in the admissible interval [−1,1] becomes almost unity in a short time. Chaotic wandering of a two-level atom in a quantized Fock field is shown to be fractal. Fractal-like structures, typical with chaotic scattering, are numerically found in the dependence of the time of exit of atoms from the cavity on their initial momenta.     

Dynamic holograms and optical limiting: Asymmetric two-wave interactions

The conditions for obtaining a high efficiency of energy exchange upon two-wave interactions in dynamic holograms are found by analysis and numerical simulation of a system of nonlinear equations. Use of an asymmetric scheme of beam interaction in a medium with two nonlinearities, one of which determines the amplitude and relaxation time of a grating and the other of which provides phase modulation of the interacting beams, is proposed. It is shown that such a scheme in combination with the specific properties of a medium makes it possible to radically reduce the requirements for the nonlinearity of a medium and the intensity of a light flux in limiting systems, as well as to significantly decrease the time of the transition process. As a result, it becomes possible to attain an efficiency of energy transfer higher than 90% and to increase the corresponding attenuation of a high-power beam by almost two orders of magnitude, which is of interest for optical limiting of intense light fluxes.     

Nonequilibrium Ionization by Vibrationally Excited Molecules in Supersonic Flows

The results of experimental investigations on thermal nonequilibrium ionization in CO₂: N₂: He mixtures are presented. Measurements of electron density, n_e, in vibrationally excited nitrogen were made in a supersonic flow with different CO₂ contents as well as in a CO₂: N₂: He = 1 : 5 : 4 mixture laser gas. The mixtures were heated in a shock tube and expanded through a supersonic nozzle. Furthermore, supersonic mixing of N₂ and CO₂ + He was used in some experiments. The measured values of n_e in the plenum chamber and in the supersonic nozzle are reported, and the processes responsible for nonequilibrium ionization in a laser-active medium are discussed.     

Rate constants for the gas‐phase reaction of CF3CF2CF2CF2CF2CHF2 with OH radicals at 250–430 K

The rate constants k₁ for the reaction of CF₃CF₂CF₂CF₂CF₂CHF₂ with OH radicals were determined by using both absolute and relative rate methods. The absolute rate constants were measured at 250–430 K using the flash photolysis–laser‐induced fluorescence (FP‐LIF) technique and the laser photolysis–laser‐induced fluorescence (LP‐LIF) technique to monitor the OH radical concentration. The relative rate constants were measured at 253–328 K in an 11.5‐dm³ reaction chamber with either CHF₂Cl or CH₂FCF₃ as a reference compound. OH radicals were produced by UV photolysis of an O₃–H₂O–He mixture at an initial pressure of 200 Torr. Ozone was continuously introduced into the reaction chamber during the UV irradiation. The k₁ (298 K) values determined by the absolute method were (1.69 ± 0.07) × 10^?15 cm³ molecule^?1 s^?1 (FP‐LIF method) and (1.72 ± 0.07) × 10^?15 cm³ molecule^?1 s^?1 (LP‐LIF method), whereas the K₁ (298 K) values determined by the relative method were (1.87 ± 0.11) × 10^?15 cm³ molecule^?1 s^?1 (CHF₂Cl reference) and (2.12 ± 0.11) × 10^?15 cm³ molecule^?1 s^?1 (CH₂FCF₃ reference). These data are in agreement with each other within the estimated experimental uncertainties. The Arrhenius rate constant determined from the kinetic data was K₁ = (4.71 ± 0.94) × 10^?13 exp[?(1630 ± 80)/T] cm³ molecule^?1 s^?1. Using kinetic data for the reaction of tropospheric CH₃CCl₃ with OH radicals [k₁ (272 K) = 6.0 × 10^?15 cm³ molecule^?1 s^?1, tropospheric lifetime of CH₃CCl₃ = 6.0 years], we estimated the tropospheric lifetime of CF₃CF₂CF₂CF₂CF₂CHF₂ through reaction with OH radicals to be 31 years. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 36: 26–33, 2004     

Naphthyl azomesogens with lateral chloro groups

A homologous series of azomesogens, 2″-[4-(4′-n-alkoxybenzoyloxy)-2-chlorophenylazo] naphthalenes, with lateral chloro groups was synthesised. All the homologues synthesized exhibit enantiotropic nematic mesophase. The mesomorphic properties of the present series are compared with other structurally related series to evaluate the effect of lateral chloro group and its position on mesomorphism This paper was presented at the 10th National Conference on Liquid Crystals held at Bangalore, India during 9–11 October 2003.     

Higher Order Peak Algebras

Using the theory of noncommutative symmetric functions, we introduce the higher order peak algebras (Sym(N))_N≥1, a sequence of graded Hopf algebras which contain the descent algebra and the usual peak algebra as initial cases (N=1 and N=2). We compute their Hilbert series, introduce and study several combinatorial bases, and establish various algebraic identities related to the multisection of formal power series with noncommutative coefficients. Received November 19, 2004     

The effect of traffic noise on sleep of young adults in their homes

The disturbance of sleep by traffic noise is a major problem area in noise pollution. Extensive laboratory tests using multichannel electroencephalograms (EEG) have been carried out by many workers to determine the general response of people when exposed to noise during sleep. An experimental technique for obtaining results in people's homes has been developed using a simplified one-channel EEG. The responses of six people in the age range 19-24 were measured. A significant correlation was found between sleep disturbance and traffic noise when the noise is expressed in EPNdB. In the home experiments the subjects appeared to be approximately 10 dB less sensitive to noises than laboratory subjects for similar noise exposure. There also appeared to be some adaptation to the noise exposure; however, only one subject was tested for a period of 20 days and was insufficient to give definite results on adaptation.