Trajectories in the Context of the Quantum Newton's Law

In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic oscillator. In the classically allowed regions, we show that to each classical trajectory there is a family of quantum trajectories which all pass through some points constituting nodes and belonging to the classical trajectory. We also discuss the generalization to any potential and give a new definition for de Broglie's wavelength in such a way as to link it with the length separating adjacent nodes. In particular, we show how quantum trajectories have as a limit when $\hbar \to 0$ the classical ones. In the classically forbidden regions, the nodal structure of the trajectories is lost and the particle velocity rapidly diverges.Comment: 17 pages, LateX, 6 eps figures, minor modifications, Title changed, to appear in Physica Script

Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position Operator

For Dirac equation, operator-invariants containing explicit time-dependence in parallel to known time-dependent invariants of nonrelativistic Schr\"odinger equation are introduced and discussed. As an example, a free Dirac particle is considered and new invariants are constructed for it. The integral of motion, which is initial Newton-Wigner position operator, is obtained explicitly for a free Dirac particle. For such particle with kick modeled by delta-function of time, the time-depending integral, which has physical meaning of initial momentum, is found.Comment: LATEX,21 pages,submitted to Physica Script

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves

Artistic creativity of martiros saryan as the indicator of national self-identification of the personality in a multicultural space: features of methodology of a retrospective research

In this article, the life and works of the famous Armenian artist, founder of the modern Armenian school of painting Martiros Saryan (1880-1972) are analyzed in the context of the influence of Russian and Armenian culture during the Russian period of his activity. In this retrospective analysis of the life and works of the artist, it is proposed to use the new indicator, which is Russian or the Middle East countries place names being included in the titles of works by the artist. On the basis of the analysis of Russian archival sources and the analytical research of content, it is established that, in Russia, the interest of the artist during the first period of his life and study was mainly on subjects reflecting the life of the Armenian diaspora in the south of Russia. Landscapes were mainly represented against the background in which the artist spent his childhood. During the time which he spent in Moscow, interest in Russian culture was connected with the recognition of the contribution of teachers of the School of Painting, Sculpture and Architecture in the development of the Russian art school and world culture. Saryan has shown the aspiration to seize this particular technic of painting, at the same time he had the original vision of the world. Keywords: methodology, personality, geographical indicators, Martiros Saryan, culture,regional archiv

Nonlinearity Management in Higher Dimensions

In the present short communication, we revisit nonlinearity management of the time-periodic nonlinear Schrodinger equation and the related averaging procedure. We prove that the averaged nonlinear Schrodinger equation does not support the blow-up of solutions in higher dimensions, independently of the strength in the nonlinearity coefficient variance. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management.Comment: 9 pages, 1 figure

Vacuum energy and spectral function sum rules

We reformulate the problem of the cancellation of the ultraviolet divergencies of the vacuum energy, particularly important at the cosmological level, in terms of a saturation of spectral function sum rules which leads to a set of conditions on the spectrum of the fundamental theory. We specialize the approach to both Minkowski and de Sitter space-times and investigate some examples.Comment: 11 pages, revtex4, no figures, version to be published on PR

On the linearization of the generalized Ermakov systems

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included

Resonant enhancement of the jump rate in a double-well potential

We study the overdamped dynamics of a Brownian particle in the double-well potential under the influence of an external periodic (AC) force with zero mean. We obtain a dependence of the jump rate on the frequency of the external force. The dependence shows a maximum at a certain driving frequency. We explain the phenomenon as a switching between different time scales of the system: interwell relaxation time (the mean residence time) and the intrawell relaxation time. Dependence of the resonant peak on the system parameters, namely the amplitude of the driving force A and the noise strength (temperature) D has been explored. We observe that the effect is well pronounced when A/D > 1 and if A/D 1 the enhancement of the jump rate can be of the order of magnitude with respect to the Kramers rate.Comment: Published in J. Phys. A: Math. Gen. 37 (2004) 6043-6051; 6 figure