K\"ahler geometry and SUSY mechanics

We present two examples of SUSY mechanics related with K\"ahler geometry. The first system is the N=4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N=2 SUSY mechanics whose phase space is the external algebra of an arbitrary K\"ahler manifold. The relation of these models with antisymplectic geometry is discussed.Comment: 6 pages, one reference added,to be published in Nuclear Physics B Conference Supplements (D.V.Volkov Memorial Conference, July 25-29, 2000, Kharkov

A note on N=4 supersymmetric mechanics on K\"ahler manifolds

The geometric models of N=4 supersymmetric mechanics with (2d.2d)_{\DC}-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N=2 supersymmetric sigma-models by Alvarez-Gaum\'e and Freedman. The related construction of supersymmetric mechanics whose phase space is a K\"ahler supermanifold is considered. Also, its relation with antisymplectic geometry is discussed.Comment: 4 pages, revte

Intertwining technique for the one-dimensional stationary Dirac equation

The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and scalar potentials. The method is widely illustrated by numerous examples

Negative Kaons in Dense Baryonic Matter

Kaon polarization operator in dense baryonic matter of arbitrary isotopic composition is calculated including s- and p-wave kaon-baryon interactions. The regular part of the polarization operator is extracted from the realistic kaon-nucleon interaction based on the chiral and 1/N_c expansion. Contributions of the Lambda(1116), Sigma(1195), Sigma*(1385) resonances are taken explicitly into account in the pole and regular terms with inclusion of mean-field potentials. The baryon-baryon correlations are incorporated and fluctuation contributions are estimated. Results are applied for K- in neutron star matter. Within our model a second-order phase transition to the s-wave K- condensate state occurs at rho_c \gsim 4 \rho_0 once the baryon-baryon correlations are included. We show that the second-order phase transition to the p-wave $K^-$ condensate state may occur at densities $\rho_c \sim 3\div 5 \rho_0$ in dependence on the parameter choice. We demonstrate that a first-order phase transition to a proton-enriched (approximately isospin-symmetric) nucleon matter with a p-wave K- condensate can occur at smaller densities, \rho\lsim 2 \rho_0. The transition is accompanied by the suppression of hyperon concentrations.Comment: 41 pages, 24 figures, revtex4 styl

Stochastic resonance in a periodically modulated dissipative nuclear dynamics

A fission decay of highly excited periodically driven compound nuclei is considered in the framework of Langevin approach. The authors have used residual-time distribution (RTD) as the tool for studying of dynamic features in a presence of periodic perturbation. The structure of RTD essentially depends on the relation between Kramers decay rate and the frequency {omega} of the periodic perturbation. In particular, intensity of the first peak in RTD has a sharp maximum at certain nuclear temperature depending on {omega}. This maximum should be considered as first-hand manifestation of stochastic resonance in nuclear dynamics

Theoretical study of cut of plant tops sugar beet with copying-rotor separator

На основании построенной математической модели движения очистительного элемента нового отделителя ботвы по головке корнеплода сахарной свёклы и решения полученных выражений на ПЭВМ получены аналитические зависимости усилий в указанной точке контакта. Построены графические зависимости изменения составляющих нормальной реакции в точке кон такта рабочего элемента с головкой корнеплода. Значения составляющих нормальной реакции были использованы в дальнейшем для силового анализа указанного взаимодействия.On basis of constructed mathematical model of motion of new separator cleaning element topper on head of sugar beet and solutions derived forms on PC based analytical dependence of efforts in indicated point of contact. Constructed graphic dependence changes of components of normal reaction at point of contact of working element with the head root. Values of components of normal reaction was used in future for power analysis of this interaction