Influence of Rashba and Dresselhaus spin-orbit interactions of equal strengths on electron states in a circular quantum ring in the presence of a magnetic field

Solutions of the Schr\"odinger equation are obtained for an electron in a two-dimensional circular semiconductor quantum ring in the presence of both external uniform constant magnetic field and the Rashba and Dresselhaus spin-orbit interactions of equal strengths. Confinement is simulated by a realistic potential well of a finite depth. The dependence of the energy levels on a magnetic field strength, strength of spin-orbit interaction and a relative ring width is presented.Comment: 6 pages, 2 figures, 1 tabl

Rashba spin-orbit interaction in a circular quantum ring in the presence of a magnetic field

Exact wave functions and energy levels are obtained for an electron in a two-dimensional semiconductor circular quantum ring with a confining potential of finite depth in the presence of both an external magnetic field and the Rashba spin-orbit interaction.Comment: 7 pages, 4 figures, 2 table

Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations

Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational, periodic, elliptic) are found for a wide class of autonomous nonlinear ordinary differential equations

Explicit summation of the constituent WKB series and new approximate wave functions

The independent solutions of the one-dimensional Schr\"odinger equation are approximated by means of the explicit summation of the leading constituent WKB series. The continuous matching of the particular solutions gives the uniformly valid analytical approximation to the wave functions. A detailed numerical verification of the proposed approximation is performed for some exactly solvable problems arising from different kinds of potentials.Comment: 8 pages, LaTeX, minor changes and stylistic improvements, final versio

Hydrodynamic role of fish squamosal integument as an analog of the surfaces directly formed by the turbulent flow. Report 2: Hydrodynamic function of squamosal integument

The stream flowing round the slowly swimming squama free fish can be laminized with the aid of the external slime coat alone. The slime of the fish with well developed squamae can laminize the stream together with the squamatic integument. Adjustments preventing a loss of the slime during laminization are better developed in the fastest squama free fishes

Meromorphic exact solutions of the generalized Bretherton equation

The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given