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.     

Analysis of tunable diode-laser spectra of Q(J,0) lines in CH3F near 1475 cm using a multispectrum fitting technique

We have analyzed the methyl fluoride ^RQ(J,0)Q branch lines located near 1475 cm⁻¹ using a simultaneous multi-spectrum fitting technique. In this analysis we have used previously recorded diode-laser data in which we collected many data points covering only one or two Q branch lines in a particular run. The analysis consists of simultaneously fitting 57 spectra collected with numerous pressure and path length conditions for all absorption lines. The data are concatenated to create one continuous spectrum of the Q branch. We have determined the intensity and self-broadened widths at 296 K for 23 ^RQ(J,0) lines.     

Quantum effects in a one-dimensional magnetic gravitational trap for ultracold neutrons

JETP Letters - The problem of storing ultracold neutrons over a plane magnetic mirror in the presence of gravity is considered. For neutrons with a definite polarization, the sum of the magnetic...     

Liquid flows and vibration characteristics of straight-tube cylindrical shells

The influence of a moving fluid confined by a solid circular cylindrical shell on the propagation of acoustic waves generated by sources located on the circular cylindrical shell is examined. An expression for the acoustic pressure in a moving fluid is derived including azimuthal asymmetry effects in the general case, where the fluid velocity points along the cylindrical shell axis and can be written as an infinite power series expansion in the radial co-ordinate. Secondly, continuity of pressure and normal velocity at the liquid-shell interface is imposed to (a) derive a set of coupled differential equations governing the possible vibrational modes of the shell and (b) determine dispersion relations, i.e., mode propagation constants β as a function of frequency as well as changes in β values accomodated by flow. In the remaining part of the paper, phase speed changes with flow and transit-time differentials of circular cylindrical shell vibrations are discussed with special emphasis to flow measurement properties.     

Destruction of a solid film under the action of ultrashort laser pulse

Molecular-dynamics (MD) simulation of the destruction of a crystal film heated by a femtosecond laser pulse was carried out. Heating is assumed to be instantaneous, because there is no time for the material to be displaced during the pulse. Film destruction is caused by the interaction of unloading waves. It can be considered as a model of a more complex process of splitting out of a thin surface layer from a massive target in the case where the layer remains solid after heating. It was found that the crystal order is broken due to the stretching strains and to the strong anisotropy of residual stress, resulting in a bipartition of the layer separating from the target. The lattice stretching and the formation of anisotropic stresses are due to the expansion of a heated lattice.     

To the Jubilee of Vsevolod Alekseevich Solonnikov

Bibliography: 42 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 7–15.     

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

Ferromagnetism at 300 K in spin-coated films of Co doped anatase and rutile-TiO2

Thin films of Ti_1−xCo_xO₂ (x=0 and 0.03) have been prepared on sapphire substrates by spin-on technique starting from metalorganic precursors. When heat treated in air at 550 and 700 °C, respectively, these films present pure anatase and rutile structures as shown both by X-ray diffraction and Raman spectroscopy. Optical absorption indicate a high degree of transparency in the visible region. Such films show a very small magnetic moment at 300 K. However, when the anatase and the rutile films are annealed in a vacuum of 1×10⁻⁵ Torr at 500 and 600 °C, respectively, the magnetic moment, at 300 K, is strongly enhanced reaching 0.36μ_B/Co for the anatase sample and 0.68μ_B/Co for the rutile one. The ferromagnetic Curie temperature of these samples is above 350 K.