Trapped ion density distribution in the presence of He-buffer gas

The spatial density distribution of Ba⁺ ions, confined in a rf quadrupole trap, has been measured by laser scanning across the trap. This allows to determine the ion temperature, assuming thermal equilibrium. Under UHV conditions the average ion energy has been found to be one tenth of the trap potential well depth. Collisions with He at pressures up to 5×10⁻⁶ mbar reduce the ion temperature by a factor of 3.     

An explicit one-soliton solution of the (2+1)-dimensional generalized sine-gordon equations

The (n+1)-dimensional differential geometric generalization of the sine-Gordon equation (SGE) given by Tenenblat and Terng is solved explicitly in the casen=2 to obtain a one-soliton solution. The solution yields the soliton solution of the (1+1)-dimensional SGE in the limit as one of the three independent variables approaches infinity. However, more than one variable plays the role of time in these limits.     

On the quantum Fermi accelerator and its relevance to ‘quantum chaos’

We discuss a quantum version of the Fermi acceleration model, which consists of a particle bouncing between a fixed and oscillating wall. The actual movement of the particle crucially depends on the boundary conditions of the Schrödinger equation. Under Dirichlet boundary conditions, the quantum system displays a regular behaviour, but its classical limit exhibits some unphysical attributes. Only for certain initial conditions does it correspond to the stable motion of a ball bouncing once for an integer number of wall oscillations. In the classical model that situation gives rise to regular islands imbedded in the chaotic sea.     

Multiphoton ionization of nitric oxide in the presence of foreign gases

The addition of foreign gases (e.g. Ar, He, and CH₃Cl) is shown to strongly affect the MPI current resulting from excitation of NO through theC ² Π(v=0) intermediate state. The NO excitation spectrum is not affected by a large excess of Ar. Quantitative and specific determination of NO is demonstrated to 6×10⁻⁶ Torr in a bulk mixture. Foreign gas effects are interpreted as arising from secondary ionization of neutrals by energetic electrons. The linear dependence of the signal on NO pressure and the quadratic dependence on laser power suggest that the technique can be used to determine reaction rates involving selected states of NO. Work supported by the Israel-U.S. Binational Science Foundation.     

Optimization of the optothermal detector for absorption spectroscopy in the low pressure range

To use the sensitivity and the measurement accuracy of the optothermal detector (OT) better for linear absorption detection, a theory of the signal behaviour, worth for the most important range of application, is developed and compared with experimental data. By means of the example of CO₂-laser light absorption by ammonia, containing two different nitrogen isotopes, the possibility of correcting measured values to get more exact information of the absorption behaviour is shown. The limits of error, as well as the reproducibility of the measurments could be kept in a range of about 1%.     

The Green function for the Duffin–Kemmer–Petiau equation

We present a calculation of the Green function for the Duffin–Kemmer–Petiau equation in the case of scalar and vectorial particles interacting with a square barrier potential, and relate it to that of the Klein–Gordon equation. A formal Hamiltonian of the Duffin–Kemmer–Petiau theory is first developed using the Feshbach–Villars analogy and the Sakata and Taketani decomposition. The coefficients of reflection and transmission are deduced.     

Sensitive magnetic rotation spectroscopy of the OH free radical fundamental band with a colour centre laser

The magnetic rotation technique has been optimized and applied for spectroscopy of the OH fundamental band at about 3670 cm^–1 by use of a colour centre laser. The response of the molecules to the modulation field has been studied in detail, resulting in calculation of effectiveg-values, which describe the modulation sensitivity of the transitions and the phase of the signals.     

On the three-body long-range scattering problems

In this Letter, we give results on precise microlocalized time-decay estimates in three-body long-range scattering problems. We prove the asymptotic completeness of wave operators in three-body long-range scattering for a class of long-range interactions of the form V ₁(x)+V ₂(x), where V ₁ is nonnegative and decays like O(|x|^–0), for some ₀ > 1/2 and V ₂ decays like O(|x|^-y) for some > 2(1–₀)/₀.     

On the oscillons in the signum-Gordon model

New periodic solutions of signum-Gordon equation are presented. We first find solutions φ₀(x, t) defined for (x, t) ∈ ? × [0, T ] and satisfying the condition φ₀(x, 0) = φ₀(x, T ) = 0. Then these solutions are extended to the whole spacetime by using (2.4).     

On Darboux transformations for soliton equations in high-dimensional spacetime

The Darboux transformations for a class of completely integrable systems in the spacetimeR ^{n + 1}, which are much more general than the systems inLett. Math. Phys. 26, 199–209 (1989), are considered. The structure of the nonlinear evolution equations with space constraints is elucidated. It is pointed out that the inverse scattering method can be used to solve the Cauchy problem with initial data given on a noncharacteristic line.Supported by National Basic Research Project Nonlinear Science, NNSFC of China, FEYUT-SEDC-CHINA and Fok Ying-Tung Education Foundation of China.     

Compatibility and generalised conditional symmetries

It is shown that the determining equations for generalised conditional symmetries (GCSs) of order n, of an evolution equation of arbitrary order, can be found as a consequence of compatibility with an nth-order invariant surface condition. The compatibility technique is demonstrated on a second-order nonlinear diffusion–convection equation with absorption and used to find new GCSs of a linear diffusion equation with nonlinear source.     

The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA1(1)

The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).     

Blow-up of solution of an initial boundary value problem for a generalized Camassa-Holm equation

In this Letter, we study the following initial boundary value problem for a generalized Camassa-Holm equation

     

Convergence of Logarithmic Quantum Mechanics to the Linear One

We study the nonlinear logarithmic Schrödinger equation in three dimensions. We establish the existence of the solutions of general quasi-linear Schrödinger equations. Finally, we show the convergence of the logarithmic quantum mechanics to the linear regime.     

Measurement of atomic parameters for the3 D 1 state of I–II

The decay rates of the³ D ₁ level of I–II and the 3s ₂ level of neon have been measured by the magnetic-field power dip method. The decay rate at the zero-pressure limit is found to be 7.1 MHz/2π for the³ D ₁ level. The collision cross-section for excited I ions with helium atoms equals 0.19×10⁻¹⁵ cm². This work was supported by project MR-1.5-1.05.     

The general solution of two-dimensional matrix Toda chain equations with fixed ends

It is shown that the two-dimensional matrix Toda chain determines the group of discrete symmetries of the two-dimensional matrix nonlinear Schrödinger equation (the matrix generalization of the Davey-Stewartson system). The general solution of this chain with definite boundary conditions is obtained in explicit form.     

Characterization of the Weyl solutions

For the Weyl solutions(z, x) of the Schrödinger and Dirac equations, asymptotics for |z| are obtained. This gives a possibility of selecting Weyl solutions by their behaviour when |z| . Some applications are given.     

Improved separation of the rare sulfur isotopes by infrared multiphoton dissociation of SF6

The dissociation probabilities of³²SF₆ and some of³⁴SF₆ have been measured at a large number of CO₂ laser lines both at room temperature and at 140 K. The longwavelength wing of this dissociation spectrum is exponential in the wavenumber. Its logarithmic slope is proportional to the inverse temperature. Selectivities are high enough at 140 K, that the photons are consumed only for the rare isotope in the case of³⁴SF₆ and nearly so for³⁶SF₆. For³³SF₆ further improvement of the selectivity would be desirable.     

Left-Symmetric Algebras in Hydrodynamics

Left-Symmetric algebras are shown to appear naturally in integrable hydrodynamical systems. First, to a data a Left-Symmetric algebra and an operator of strong deformation on it is attached an infinite commuting hierarchy of integrable systems of hydrodynamical type in 1+1−d. Second, this picture (without deformation) is embedded into an infinite-component integrable hydrodynamic chain.