Integrable models for vicious and friendly walkers

We consider random walks of two essentially different classes of random walkers, namely, of vicious and friendly ones, on one-dimensional lattices with periodic boundary conditions. The walkers are called vicious since, arriving at a lattice site, they annihilate not only one another but all the remaining walkers as well. On the contrary, an arbitrary number of friendly walkers can share the same lattice sites. It is shown that a natural model describing the behavior of friendly walkers is an integrable model of the boson type. A representation of the generating function for the number of the lattice paths performed by a fixed number of friendly walkers for a certain number of steps is obtained. Bibliography: 22 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 59–74.     

Temporal compression of nanosecond laser pulses using coherent control

We present a study of the temporal compression of nanosecond laser pulses resulting from the coherent control peculiarities of the propagation dynamics in a regime of electromagnetically induced transparency. We describe the general theoretical framework and discuss the crucial conditions required in order to experimentally realize such a temporal compression scheme. A proof-of-concept experimental realization of a scheme of this type in a sample of hot sodium vapors is currently being implemented: we describe in detail the experimental setup designed for this purpose.     

Calculation of the discrepancy of a finite set of points in the unit n-cube

An algorithm for calculating the discrepancy of finitely many points in the unit n-cube [0, 1]ⁿ is suggested. This algorithm is easy to program. For 2 ≤ n ≤ 4, the suggested algorithm is significantly faster than Bundschuh and Zhu’s algorithm. For larger n, whether this algorithm is faster depends on the number of points.     

On the dynamical Casimir effect in a one-dimensional contracting cavity

The dynamical Casimir effect is analyzed in the framework of the S-matrix formulation for a one-dimensional cavity that exhibits contraction at a constant rate over a finite time interval. The exact solution to the problem is presented. It is demonstrated that the efficiency of the creation of pairs nonmonotonically depends on the contraction time. This is due to the fact that the particles are only created at the moments corresponding to the acceleration and stopping of the moving boundary, so that the contributions of these processes on the number of the created particles interfere with each other. The parameters that correspond to the optimal creation of pairs and the stability of a vacuum are presented. The effect of the finiteness of the cavity-boundary acceleration on the results obtained is studied.     

On the effect of magnetic fields on alloys with isothermal kinetics of martensitic transformation

The effect of magnetic treatment on the isothermal martensitic transformation in the Fe-24% Ni-4% Mn alloy has been investigated. The martensitic transformation in a dc magnetic field at liquid-helium temperature has been analyzed.     

Direct observation of charge-carrier capture in an array of self-assembled InAs/GaAs quantum dots

In this work, charge-carrier capture by an array of self-assembled InAs/GaAs quantum dots was directly observed for the first time by capacitance recharge. It is proposed to process the obtained transient-capture data by a similar method to that used for emission, by the box-car method. The capture activation energies are determined and compared with the emission activation energies.     

Specific features of nanosystems based on natural isoferroplatinum

Nanostructuring of natural isoferroplatinum crystals is revealed by atomic-force microscopy for the first time. Typical scales of ～30, 50, and 100 nm are determined and the self-affine character of their relation is established using a wavelet analysis.     

New Heat-Resistant Polyimidates Derived from Bisphenols and Mono- and Dicarboxylic Acid Imidoyl Chlorides

New polyimidates were prepared from bisphenols and mono- and dicarboxylic acid imidoyl chlorides. The structures of the polymers were determined, and their physicochemical, chemical, and thermal properties were studied. The possibility of preparing film and compression materials with good mechanical characteristics from these polymers was examined.