Numerical Study of Periodic Instanton Configurations in Two-dimensional Abelian Higgs Theory

Numerical minimization of the Euclidean action of the two-dimensional Abelian Higgs model is used to construct periodic instantons, the euclidean field configurations with two turning points describing transitions between the vicinities of topologically distinct vacua. Periodic instantons are found at any energy ( up to the sphaleron energy $E_{sph}$ ) and for wide range of parameters of the theory. We obtain the dependence of the action and the energy of periodic instanton on its period; these quantities directly determine the probability of certain multiparticle scattering events.Comment: 8 pages, 6 figures available upon request, LaTeX, ITP-SB-92-7

Directivity patterns of laser-generated sound in solids: Effects of optical and thermal parameters

In the present paper, directivity patterns of laser-generated sound in solids are investigated theoretically. Two main approaches to the calculation of directivity patterns of laser-generated sound are discussed for the most important case of thermo-optical regime of generation. The first approach, which is widely used in practice, is based on the simple modelling of the equivalent thermo-optical source as a mechanical dipole comprising two horizontal forces applied to the surface in opposite directions. The second approach is based on the rigorous theory that takes into account all acoustical, optical and thermal parameters of a solid material and all geometrical and physical parameters of a laser beam. Directivity patterns of laser-generated bulk longitudinal and shear elastic waves, as well as the amplitudes of generated Rayleigh surface waves, are calculated for different values of physical and geometrical parameters and compared with the directivity patterns calculated in case of dipole-source representation. It is demonstrated that the simple approach using a dipole-source representation of laser-generated sound is rather limited, especially for description of generated longitudinal acoustic waves. A practical criterion is established to define the conditions under which the dipole-source representation gives predictions with acceptable errors. It is shown that, for radiation in the normal direction to the surface, the amplitudes of longitudinal waves are especially sensitive to the values of thermal parameters and of the acoustic reflection coefficient from a free solid surface. A discussion is given on the possibility of using such a high sensitivity to the values of the reflection coefficient for investigation of surface properties of real solids.Comment: 14 pages, 7 figure

Quantum Cohomology Rings of Toric Manifolds

We compute the quantum cohomology ring $H^*_{\varphi}({\bf P}, {\bf C})$ of an arbitrary $d$-dimensional smooth projective toric manifold ${\bf P}_{\Sigma}$ associated with a fan $\Sigma$. The multiplicative structure of $H^*_{\varphi}({\bf P}_{\Sigma}, {\bf C})$ depends on the choice of an element $avarphi$ in the ordinary cohomology group $H^2({\bf P}_{\Sigma}, {\bf C})$. There are many properties of the quantum cohomology rings $H^*_{\varphi}({\bf P}_{\Sigma}, {\bf C})$ which are supposed to be valid for quantum cohomology rings of K\"ahler manifoldsComment: 23 pages, Late