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Molecular dynamics simulations at a constant electric potential are an essential tool to study electrochemical processes, providing microscopic information on the structural, thermodynamic, and dynamical properties. Despite the numerous…
An exact solution of non-stationary Schrodinger equation is obtained for a one-dimensional movement of electrons in an electromagnetic field with arbitrary intensity and frequency. Using it, the permeability coefficient is calculated for a…
Coulomb coupling between proximal layers in graphene heterostructures results in efficient energy transfer between the layers. We predict that, in the presence of correlated density inhomogeneities in the layers, vertical energy transfer…
Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction…
When floating on a two-dimensional (2D) surface of superfluid $^{4}$He, electrons arrange themselves in 2D crystalline structure known as Wigner crystal. In channels, the boundaries interfere the crystalline order and in case of very narrow…
We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. We show using a one-step multiple scale analysis the strict convexity of the surface tension at high…
High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…
Energies and wave functions of edge states in twodimensional electron gas are evaluated for a finite step potential barrier model. The spectrum, instead of smooth bending of Landau branches in the vicinity of the barrier acquires a steplike…
A first-principle model is proposed to study the electrostatic properties of a double-gated silicon slab of nano scale in the framework of density functional theory. The applied gate voltage is approximated as a variation of the…
It is well understood that various alternatives are available within EM theory for the definitions of energy density, momentum transfer, EM stress-energy tensor, and so forth. Although the various options are all compatible with the basic…
We develop a general approach to calculations of the electron spectrum of metallic multi-wall carbon nanotubes (MWNT) with arbitrary number of coaxial layers. It is based on the model with singular attractive potential of equidistant…
A shallow potential well in a near-perfect quantum wire will bind a single-electron and behave like a quantum dot, giving rise to spin-dependent resonances of propagating electrons due to Coulomb repulsion and Pauli blocking. It is shown…
In this paper we present a novel quasi-exactly solvable model with symmetric inverted potentials which are unbounded from below. The quasi-exactly solvable states are shown to be total transmission (or reflectionless) modes. From these…
The reflectivity of low energy electrons from graphene on copper substrates is studied both experimentally and theoretically. Well-known oscillations in the reflectivity of electrons with energies 0 - 8 eV above the vacuum level are…
The main objective of the present work is the development of an analytically tractable model of screened electron-electron and electron-exciton interactions in layered systems composed of two parallel semiconductor quantum wells separated…
For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean…
Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tight-binding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
Gate-modulated nanopores have emerged as a promising platform for achieving ion selectivity and ionic current rectification (ICR) with the advantage of active field-based control. However, the mechanistic origin of these experimentally…
The exact energy levels and wave functions of an electron free to move on a sphere under the radial magnetic field is found. Wave functions are expressed in terms of Jacobi polynomials which were well-defined and have orthogonality…