Related papers: An explicit formula for the number of tunnels in d…
Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The…
This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…
We define a plane curve to be threadable if it can rigidly pass through a point-hole in a line L without otherwise touching L. Threadable curves are in a sense generalizations of monotone curves. We have two main results. The first is a…
We consider systems of simple closed curves on surfaces and their total number of intersection points, their so-called crossing number. For a fixed number of curves, we aim to minimise the crossing number. We determine the minimal crossing…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
Taking the convex hull of a curve is a natural construction in computational geometry. On the other hand, path signatures, central in stochastic analysis, capture geometric properties of curves, although their exact interpretation for…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
How much time does a wave packet spent in tunneling a barrier? Quantum mechanical calculations result in zero time inside a barrier. In the nineties analogous tunneling experiments with microwaves were carried out confirming quantum…
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…
Tunneling times in atomic ionization are studied theoretically by a virtual detector approach. A virtual detector is a hypothetical device that allows one to monitor the wave function's density with spatial and temporal resolution during…
In this paper we present unsolved problems that involve infinite tunnels of recursive triangles or recursive polygons, either in a decreasing or in an increasing way. The "nedians or order i in a triangle" are generalized to "nedians of…
A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…
The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of…
Quantum computers are the promising candidates for simulation of large quantum systems, which is a daunting task to perform in a classical computer. Here, we report the experimental realization of quantum tunneling of a single particle…
A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A…
A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to…
A method of a non-stationary description of tunneling of a particle through the one-dimensional and spherically symmetric rectangular barriers on the basis of analisis of multiple internal reflections of wave packets in relation on the…
I propose to consider photon tunneling as a space-time correlation phenomenon between the emission and absorption of a photon on the two sides of a barrier. Standard technics based on an appropriate counting rate formula may then be applied…
The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…
This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing the concept of level of visibility, we are able to analyze…