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.     

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.     

Post deposition purification of PTCDA thin films

The decomposition of perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) molecules during evaporation of unpurified raw material in ultra high vacuum was studied. The fragments were identified by mass spectrometry and the influence of these fragments and further contaminations of the raw material on the electronic structure of PTCDA thin films was measured by photoemission spectroscopy. Annealing of contaminated PTCDA films was tested as cheap and easy to perform method for (partial) post deposition purification of the contaminated films.     

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.     

A rigid subspace of the real line whose square is a homogeneous subspace of the plane

Working in ZFC, we give an example as indicated in the title.