Related papers: An explicit formula for the number of tunnels in d…

In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are…

The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…

Digital topology has its own working conditions and sometimes differs from the normal topology. In the area of topological robotics, we have important counterexamples in this study to emphasize this red line between a digital image and a…

The tunneling of Gaussian wave packets has been investigated by numerically solving the one-dimensional Schr\"odinger equation. The shape of wave packets interacting with a square barrier has been monitored for various values of the barrier…

We calculate a tunneling time distribution by means of Nelson's quantum mechanics and investigate its statistical properties. The relationship between the average and deviation of tunneling time suggests the exsistence of ``wave-particle…

The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function…

A standard approach to analyzing tunneling processes in various physical contexts is to use instanton or imaginary time path techniques. For systems in which the tunneling takes place in a time dependent setting, the standard methods are…

Tube formulas (by which we mean an explicit formula for the volume of an $\epsilon$-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of…

We present two approaches for studying the uniformity of a tunnel barrier. The first approach is based on measuring single-electron and two-electron tunneling in a hybrid single-electron transistor. Our measurements indicate that the…

A calligraph is a graph that for almost all edge length assignments moves with one degree of freedom in the plane, if we fix an edge and consider the vertices as revolute joints. The trajectory of a distinguished vertex of the calligraph is…

To test the quality of a tunnel junction, one sometimes fits the bias-dependent differential conductance to a theoretical model, such as Simmons's formula. Recent experimental work by {\AA}kerman and collaborators, however, has demonstrated…

We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. The calculations of…

The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is studied from the viewpoint of quantum optics by considering the photon statistics of a single mode cavity field which is…

Tunneling is an iconic concept that captures the peculiarity of quantum dynamics but, despite its ubiquity, questions remain. We focus on strong-field tunneling, which is vital to all attosecond science. We find an unexpected optical…

Let K be a finite field. We know that a half of elements of K* is a square. So it is natural to ask how many of them appear as x-coordinate of points on an elliptic curve over K. We consider a specific class of elliptic curves over finite…

The paper is devoted to the problem of integer-valued estimating of information quantity in a pixel of digital image. The definition of an integer estimation of information quantity based on constructing of the certain binary hierarchy of…

We have studied the electrical conductivity of two-dimensional nanowire networks. An analytical evaluation of the contribution of tunneling to their electrical conductivity suggests that it is proportional to the square of the wire…

Low-dimensional materials have attracted significant attentions over the past decade. To discover new low-dimensional materials, high-throughout screening methods have been applied in different materials databases. For this purpose, the…

We prove explicit bounds on the number of lattice points on or near a convex curve in terms of geometric invariants such as length, curvature, and affine arclength. In several of our results we obtain the best possible constants. Our…

A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…