Quantization in the neighborhood of classical solutions in theN particle problem and superfluidity

Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 2, pp. 266–288, February, 1994.     

Approximations for strongly singular evolution equations

The problem of specification of self-adjoint operators corresponding to singular bilinear forms is very important for applications, such as quantum field theory and theory of partial differential equations with coefficient functions being distributions. In particular, the formal expression corresponds to a non-trivial self-adjoint operator ? in the space only if d?3. For spaces of larger dimensions (this corresponds to the strongly singular case), the construction of ? is much more complicated: first one should consider the space as a subspace of a wider Pontriagin space, then one implicitly specifies ?. It is shown in this paper that Schrodinger, parabolic and hyperbolic equations containing the operator ? can be approximated by explicitly defined systems of evolution equations of a larger order. The strong convergence of evolution operators taking the initial condition of the Cauchy problem to the solution of the Cauchy problem is proved.     

Kinetics of formation of discrete nanostructures during vacuum condensation from a single-component vapor

The kinetics of cluster formation during the vacuum condensation of thin films from a single-component vapor is investigated by numerically solving the system of kinetic equations. The size distributions of clusters containing from a few atoms to several hundred atoms are obtained. The regions of dominant nucleation on active centers (point defects of the crystal substrate) and random nucleation are determined in the “condensation rate-temperature” coordinates. It is demonstrated that the regions corresponding to the pseudolayer and three-dimensional (rough) growth mechanisms can be separated in the condensation rate-temperature coordinates. The inference is made that the experimentally observed bimodal size distributions of islands can be associated with the difference between the growth rates of clusters at the stage preceding the coalescence.     

Reduced LP-cohomology of warped cylinders

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 10–23, September–October, 1990.     

Effect of ionization of condensing flux and transverse electric field on nucleation of metal films on ionic crystals

Experimental data on the effect of ions in the flux of condensing metal on the orientation of island metal films on alkali halide crystals are given. The effect of ionization of the condensing flux and the transverse electric field is explained on the basis of a previously proposed model of nucleation and oriented growth on point defects on the crystalline substrate.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 35–39, November, 1979.     

Revealing local field structure of focused ultrashort pulses

We utilize the interaction of tightly focused ultrashort pulses with transparent media to imprint their local polarization in the focal region. In particular, we demonstrate that this technique allows for a subwavelength resolution diagnostic of complex polarization states including the presence of the longitudinal component of the electric field. Moreover, we demonstrate the first ever material ablation with the longitudinal electric field of femtosecond pulses.     

Polarization-dependent ablation of silicon using tightly focused femtosecond laser vortex pulses

We demonstrate experimentally that, in a tight focusing geometry, circularly polarized femtosecond laser vortex pulses ablate material differently depending on the handedness of light. This effect offers an additional degree of freedom to control the shape and size of laser-machined structures on a subwavelength scale.