The scattering of Dirac fermions in the background fields of topological solitons of the ( 2 + 1 )-dimensional nonlinear O ( 3 ) σ -model is studied using both analytical and numerical methods. ...General formulas describing fermion scattering are obtained and the symmetry properties of the partial scattering amplitudes and elements of the S -matrix are determined. Within the framework of the Born approximation, the scattering amplitudes, differential cross sections, and total cross sections of fermion-soliton scattering are obtained in analytical forms, and their symmetry properties and asymptotic behavior are investigated. The dependences of the first several partial elements of the S -matrix on the momentum of the fermion are obtained using numerical methods, and some properties of these dependences are ascertained and discussed.
Radially excited U(1) gauged Q-balls are studied using both analytical and numerical methods. Unlike the nongauged case, there exists only a finite number of radially excited gauged Q-balls at given ...values of the model's parameters. Similarly to the unexcited gauged Q-ball, the radially excited one cannot possess the Noether charge exceeding some limiting value. This limiting Noether charge decreases with an increase in the radial excitation of the gauged Q-ball. For n th radial excitation, there is a maximum allowable value of the gauge coupling constant, and the existence of the n th radially excited gauged Q-ball becomes impossible if the gauge coupling constant exceeds this limiting value. Similarly to the limiting Noether charge, the limiting gauge coupling constant decreases with an increase in the radial excitation. At a fixed Noether charge, the energy of the gauged Q-ball increases with an increase in the radial excitation, and thus the radially excited gauged Q-ball is unstable against transit into a less excited or unexcited one.
The ( 1 + 1 )-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is ...shown that the model has nontopological soliton solutions describing soliton systems consisting of two Q -ball components possessing opposite electric charges. The two Q -ball components interact with each other through the Abelian gauge field and the quartic scalar interaction. The interplay between the attractive electromagnetic interaction and the repulsive quartic interaction leads to the existence of symmetric and nonsymmetric soliton systems. Properties of these systems are investigated by analytical and numerical methods. The symmetric soliton system exists in the whole allowable interval of the phase frequency, whereas the nonsymmetric soliton system exists only in some interior subinterval. Despite the fact that these soliton systems are electrically neutral, they nevertheless possess nonzero electric fields in their interiors. It is found that the nonsymmetric soliton system is more preferable from the viewpoint of energy than the symmetric one. Both symmetric and nonsymmetric soliton systems are stable against decay into massive scalar bosons.
The scattering of Dirac fermions on the sine-Gordon kink is studied both analytically and numerically. To achieve invariance with respect to a discrete symmetry, the sine-Gordon model is treated as a ...nonlinear
σ
-model with a circular target space that interacts with fermionic isodublets through the Yukawa interaction. It is shown that the diagonal and antidiagonal parts of the fermionic wave function interact independently with the external field of the sine-Gordon kink. The wave functions of the fermionic scattering states are expressed in terms of the Heun functions. General expressions for the transmission and reflection coefficients are derived, and their dependences on the fermion momentum and mass are studied numerically. The existence condition is found for two fermionic zero modes, and their analytical expressions are obtained. It is shown that the zero modes do not lead to fragmentation of the fermionic charge, but can lead to polarization of the fermionic vacuum. The scattering of the diagonal and antidiagonal fermionic states is found to be significantly different; this difference is shown to be due to the different dependences of the energy levels of these bound states on the fermion mass, and is in accordance with Levinson’s theorem.
(2 + 1)-dimensional Abelian gauged CP(2) model with a self-interaction potential is considered. It is shown that there are topological solitons in this model. The magnetic flux of these solitons can ...be either quantized or nonquantized. Properties of the topological soliton with quantized magnetic flux are investigated as well as properties of the topological soliton with nonquantized magnetic flux. A comparative analysis of the properties is performed for the topological solitons of both types. Solutions of the model field equations are obtained numerically for the topological solitons of both types. The dependencies on the model parameters are presented for the energy and magnetic flux of the solitons. The stability of the topological solitons of both types to the decay into solitons with smaller topological charges is studied numerically. Possible generalizations of the investigated topological solitons are discussed.
The decays of excited bosonic and excited fermionic modes in the external field of the domain wall are studied. The wave functions of the excited fermionic modes are found analytically in the ...external field approximation. Some properties of the fermionic modes are investigated. The reflection and transmission coefficients are calculated for fermion scattering from the domain wall. Properties of the reflection and transmission coefficients are studied. The decays of the first excited fermionic mode are investigated to the first order in the Yukawa coupling constant. The amplitudes, angular distributions, and widths of these decays are found by analytical and numerical methods. Decays of the excited bosonic mode are also investigated to the first order in the Yukawa and self-interaction coupling constants. The amplitudes, angular distributions, and widths of these decays are obtained analytically and by numerical methods.
Scanning tunneling microscopy and atomic force microscopy were used to study the topography of epitaxial Mo films of small thicknesses grown on the
R
-plane of sapphire. The domain of parameters of ...the Kardar–Parisi–Zhang model for the evolution of film surface profile in which it corresponds to the experimental results is found.
In the present paper, we continue to study the two-dimensional soliton system that is composed of vortex and Q-ball components interacting with each other through an Abelian gauge field. This ...vortex-Q-ball system is electrically neutral as a whole, nevertheless it possesses a nonzero electric field. Moreover, the vortex-Q-ball system has a quantized magnetic flux and a nonzero angular momentum, and combines properties of topological and nontopological solitons. We investigate radially and azimuthally excited states of the vortex-Q-ball system along with the unexcited vortex-Q-ball system at different values of gauge coupling constants. We also ascertain the behaviour of the vortex-Q-ball system in several extreme regimes, including thin-wall and thick-wall regimes.
The electrophysical parameters and surface morphology of
n
/
n
–
GaAs structures with Schottky contacts before and after exposure to neutrons with an average energy of ~1 MeV are studied. Changes in ...the electron concentration and mobility profiles in the structures are determined by capacitance–voltage measurements. Using atomic force microscopy, radiation-induced defect clusters are revealed; a comprehensive approach to determining their parameters is proposed.
A novel rhodium-catalyzed tandem C–H annulation of commercially available benzaldehydes and aminobenzoic acids with 2 equiv of alkyne is reported for the construction of isocoumarin-conjugated ...isoquinolinium salts that demonstrate diverse outstanding photoactivity. Depending on the substituents in the isoquinolinium moiety, they display either highly efficient fluorescence (up to 99% of quantum yield) or strong fluorescence quenching, which is provided by the transfer of the HOMO from the isoquinolinium to the isocoumarin moiety. Importantly, the functional groups in the benzaldehyde coupling partner also strongly affect the reaction selectivity, shifting the pathway to the formation of the photoinactive isocoumarin-substituted indenone imines and indenyl amines. Selective formation of the latter can be achieved by using a reduced amount of the oxidizing additive.
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