Search Results (7)

In this paper, we propose an approach for constructing quasiparticle-like asymptotic solutions within the weak diffusion approximation for the generalized population Fisher–Kolmogorov–Petrovskii–Piskunov (Fisher–KPP) equation, which incorporates nonlocal quadratic competitive losses and a fractal time derivative of non-integer order ($\alpha$, where $0<\alpha \le 1$). This approach is based on the semiclassical approximation and the principles of the Maslov method. The fractal time derivative is introduced in the framework of $F^{\alpha }$ calculus. The Fisher–KPP equation is decomposed into a system of nonlinear equations that describe the dynamics of interacting quasiparticles within classes of trajectory-concentrated functions. A key element in constructing approximate quasiparticle solutions is the interplay between the dynamical system of quasiparticle moments and an auxiliary linear system of equations, which is coupled with the nonlinear system. General constructions are illustrated through examples that examine the effect of the fractal parameter ($\alpha$) on quasiparticle behavior. Full article

Mg₃Sb₂-based materials, part of the Zintl compound family, are known for their low thermal conductivity but face challenges in thermoelectric applications due to their low energy conversion efficiency. This study addressed these limitations through first-principles calculations using the CASTEP module in Materials Studio 8.0, aiming to enhance the thermoelectric performance of Mg₃Sb₂ via strategic doping. Density functional theory (DFT) calculations were performed to analyze electronic properties, including band structure and density of states (D.O.S.), providing insights into the influence of various dopants. The semiclassical Boltzmann transport theory, implemented in BoltzTrap (version 1.2.5), was used to evaluate key thermoelectric properties such as the Seebeck coefficient, electrical conductivity, electronic thermal conductivity, and electronic figure of merit (eZT). The results indicate that doping significantly improved the thermoelectric properties of Mg₃Sb₂, facilitating a transition from p-type to n-type behavior. Bi doping reduced the band gap from 0.401 eV to 0.144 eV, increasing carrier concentration and mobility, resulting in an electrical conductivity of 1.66 × 10⁶ S/m and an eZT of 0.757. Ge doping increased the Seebeck coefficient to −392.1 μV/K at 300 K and reduced the band gap to 0.09 eV, achieving an electronic ZT of 0.859 with low thermal conductivity (11 W/mK). Si doping enhanced stability and achieved an electrical conductivity of 1.627 × 10⁶ S/m with an electronic thermal conductivity of 11.3 W/mK, improving thermoelectric performance. These findings established the potential of doped Mg₃Sb₂ as a highly efficient thermoelectric material, paving the way for future research and applications in sustainable energy solutions. Full article

The nonlinear Schrödinger equation (NLSE) with a non-Hermitian term is the model for various phenomena in nonlinear open quantum systems. We deal with the Cauchy problem for the nonlocal generalization of multidimensional NLSE with a non-Hermitian term. Using the ideas of the Maslov method, we propose the method of constructing asymptotic solutions to this equation within the framework of semiclassically concentrated states. The semiclassical nonlinear evolution operator and symmetry operators for the leading term of asymptotics are derived. Our approach is based on the solutions of the auxiliary dynamical system that effectively linearizes the problem under certain algebraic conditions. The formalism proposed is illustrated with the specific example of the NLSE with a non-Hermitian term that is the model of an atom laser. The analytical asymptotic solution to the Cauchy problem is obtained explicitly for this example. Full article

We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach proposed relies on an auxiliary dynamical system of moments of the desired solution to the kinetic equation and the associated linear partial differential equation. The family of asymptotic solutions to the kinetic equation is constructed using the symmetry operators acting on functions concentrated in a neighborhood of a point determined by the dynamical system. Based on these solutions, we introduce the nonlinear superposition principle for the nonlinear kinetic equation. Our formalism based on the Maslov germ method is applied to the Cauchy problem for the specific two-dimensional kinetic equation. The evolution of the ion distribution in the kinetically enhanced metal vapor active medium is obtained as the nonlinear superposition using the numerical–analytical calculations. Full article

We propose the approach to constructing semiclassical spectral series for the generalized multidimensional stationary Gross–Pitaevskii equation with a nonlocal interaction term. The eigenvalues and eigenfunctions semiclassically concentrated on a curve are obtained. The curve is described by the dynamic system of moments of solutions to the nonlocal Gross–Pitaevskii equation. We solve the eigenvalue problem for the nonlocal stationary Gross–Pitaevskii equation basing on the semiclassical asymptotics found for the Cauchy problem of the parametric family of linear equations associated with the time-dependent Gross–Pitaevskii equation in the space of extended dimension. The approach proposed uses symmetries of equations in the space of extended dimension. Full article

We propose an approach to constructing semiclassical solutions for the generalized multidimensional Gross–Pitaevskii equation with a nonlocal interaction term. The key property of the solutions is that they are concentrated on a one-dimensional manifold (curve) that evolves over time. The approach reduces the Cauchy problem for the nonlocal Gross–Pitaevskii equation to a similar problem for the associated linear equation. The geometric properties of the resulting solutions are related to Maslov’s complex germ, and the symmetry operators of the associated linear equation lead to the approximation of the symmetry operators for the nonlocal Gross–Pitaevskii equation. Full article

Here we report the results of the theoretical investigation of the transmission of channeled positrons through various short chiral single walled carbon nanotubes (SWCNT). The main question answered by this study is “What are the manifestations of the rainbow effect in the channeling of quantum particles that happens during the channeling of classical particles?” To answer this question, the corresponding classical and quantum problems were solved in parallel, critically examined, and compared with each other. Positron energies were taken to be 1 MeV when the quantum approach was necessary. The continuum positron-nanotube potential was constructed from the thermally averaged Molière’s positron-carbon potential. In the classical approach, a positron beam is considered as an ensemble of noninteracting particles. In the quantum approach, it is considered as an ensemble of noninteracting wave packages. Distributions of transmitted positrons were constructed from the numerical solutions of Newton’s equation and the time-dependent Schrödinger equation. For the transmission of 1-MeV positrons through 200-nm long SWCNT (14; 4), in addition to the central maximum, the quantum angular distribution has a prominent peak pair (close to the classical rainbows) and two smaller peaks pairs. We have shown that even though the semiclassical approximation is not strictly applicable it is useful for explanation of the observed behavior. In vicinity of the most prominent peak, i.e., the primary rainbow peak, rays interfere constructively. On one of its sides, rays become complex, which explains the exponential decay of the probability density in that region. On the other side, the ray interference alternates between constructive and destructive, thus generating two observed supernumerary rainbow peaks. The developed model was then applied for the explanation of the angular distributions of 1-MeV positrons transmitting through 200 nm long (7, 3), (8, 5), (9, 7), (14, 4), (16, 5) and (17, 7) SWCNTs. It has been shown that this explains most but not all rainbow patterns. Therefore, a new method for the identification and classification of quantum rainbows was developed relying only on the morphological properties of the positron wave function amplitude and the phase function families. This led to a detailed explanation of the way the quantum rainbows are generated. All wave packets wrinkle due to their internal focusing in a mutually coordinated way and are concentrated near the position of the corresponding classical rainbow. This explanation is general and applicable to the investigations of quantum effects occurring in various other atomic collision processes. Full article