Absorption and emission dynamics in concentrated optical ensembles under laser excitation

A new theoretical model describing the emission and absorption dynamics in an ensemble of molecules under intense coherent pulsed pumping is developed on the basis of the concepts of cooperative light-induced luminescence (CLIL). The CLIL development is described within the framework of formalism of the system density matrix in the space of photon wave functions. It is shown that the fast growth of CLIL relates to the development of coherent states of the quantum field in the area of efficient cooperative interactions of molecules (coherence volume). A system of equations for the calculation of CLIL energy, population of excited states, and optical absorption of the system in dependence on the laser pump energy density is solved. The theoretical results obtained are in good agreement with the experimental data.     

The influence of hyperpolarisability and field-gradient polarisability on field adsorption binding energies for He on W(111)

The effects of imaging-gas hyperpolarisability and field-gradient polarisabuity terms on field-adsorption binding energies have been explored. At best image fields for the noble imaging gases and molecular hydrogen, the correction to long-range binding energy is at most a few percent and may be neglected. At the tungsten evaporation field the correction is significant in the cases of Ar, Kr, H₂, and especially Xe. The system He on W(111) has been used as a paradigm in the investigation of short-range binding energy. The largest correction here is due to one of the field-gradient polarisabuity terms. In the field range of most relevance to the field-ion techniques the total correction is about 15–20%, and should not be neglected in detailed treatments.     

Temperature distribution in the bright spot of the optical discharge in an optical fiber

2D simulation of the optical discharge propagation in an optical fiber is performed. In contrast to the previous works, the temperature dependences of the transfer coefficient are taken into account for the bright-spot plasma. The results are compared with the recently published measurements of the spatial distribution of the bright-spot radiation intensity. Good agreement is obtained for the discharge propagation velocity and the dependence of the bright-spot size on the laser power.     

Characteristic features of carbazole phosphorescence quenching by benzophenone molecules in toluene at 77 K

We have studied the characteristic features of carbazole phosphorescence quenching by benzophenone in toluene at 77 K. We have shown that the decrease in the relative phosphorescence intensity for carbazole (energy donor) by a greater factor than we see for the relative change in its decay time is due to the fact that a change in the phosphorescence decay time occurs only for carbazole molecules participating in triplet-triplet energy transfer, while the substantial decrease in the phosphorescence intensity for carbazole with no change in the phosphorescence decay time is connected with quenching of its singlet states. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 554–556, July–August, 2006.     

Weak infinitesimal Hilbert’s 16th problem

The following weak infinitestimal Hilbert’s 16th problem is solved. Given a real polynomial H in two variables, denote by M(H, m) the maximal number possessing the following property: for any generic set {γ _i } of at most M(H,m) compact connected components of the level lines H = c _i of the polynomial H, there exists a form θ = P dx + Q dy with polynomials P and Q of degrees no greater than m such that the integral ∫ _H=c θ has nonmultiple zeros on the connected components {γ _i }. An upper bound for the number M(H,m) in terms of the degree n of the polynomial H is found; this estimate is sharp for almost every polynomial H of degree n. A multidimensional version of this result is proved. The relation between the weak infinitesimal Hilbert’s 16th problem and the following question is discussed: How many limit cycles can a polynomial vector field of degree n have if it is close to a Hamiltonian vector field?     

Cusp catastrophe in slowly varying equilibriums

Solutions of the equations v _x+v ³?tv+x=0 and v _xx=v ³? tv+x, which describe the nucleation of domain walls occurring in the neighborhood of cusps of slowly varying equilibriums, are analyzed. Examples related to the diffusion in smoothly inhomogeneous media are considered.     

Ionization of Hydrogen and Helium Atoms in Collisions with Relativistic Structural Heavy Ions

Based on the eikonal approximation, cross sections for single and double ionization of hydrogen and helium atoms in collisions with structural multiply charged heavy ions moving with relativistic velocities are calculated. In the present paper, the structural ions are taken to mean the ions with partially filled electronic shells. It is demonstrated that a consideration of the ion charge extension may noticeably change the corresponding cross sections compared to the cross sections for ionization by point ions having the same charges and energies.     

Interaction of charged dust particles in clouds of thermodynamically equilibrium charges

The solution of the Poisson-Boltzmann equation for a cloud of charges surrounding two charged dust particles treated as Debye atoms forming a Debye molecule is investigated numerically using Cassini coordinates. The electric force exerted on a dust particle by the other dust particle was determined by integrating the electrostatic pressure on the surface of the dust particle. It is shown that attractive forces appear when the following two conditions are satisfied. First, the Debye radius (corresponding to the electron density at half the mean distance between the dust particles) must be approximately equal to half the mean distance between the dust particles. Attraction between the dust particles emerges at a distance equal approximately to half the mean distance between the dust particles. Second, attraction takes place when like charges are concentrated predominantly on the dust particles. If the particles carry a small fraction of charge of the same polarity, repulsion between the particles takes place at all distances.