Coherent Destruction of Photon Emission from a Single Molecule Source

The behavior of a single molecule driven simultaneously by a laser and by an electric radio frequency field is investigated using a non-Hermitian Hamiltonian approach. Employing the renormalization group method for differential equations we calculate the average waiting time for the first photon emission event to occur, and determine the conditions for the suppression and enhancement of photon emission. An abrupt transition from localization-like behavior to delocalization behavior is found.Comment: 5 pages, 4 figure

О построении циркулянтных матриц, связанных с MDS-матрицами

The objective of this paper is to suggest a method of the construction of circulant ma-trices, which are appropriate for being MDS (Maximum Distance Separable) matrices utilising in cryptography. Thus, we focus on designing so-called bi-regular circulant matrices, and furthermore, impose additional restraints on matrices in order that they have the maximal number of some element occurrences and the minimal number of distinct elements. The reason to construct bi-regular matrices is that any MDS matrix is necessarily the bi-regular one, and two additional restraints on matrix elements grant that matrix-vector multiplication for the samples constructed may be performed effciently. The results obtained include an upper bound on the number of some ele-ment occurrences for which the circulant matrix is bi-regular. Furthermore, necessary and sucient conditions for the circulant matrix bi-regularity are derived. On the ba-sis of these conditions, we developed an effcient bi-regularity verication procedure. Additionally, several bi-regular circulant matrix layouts of order up to 31 with the maximal number of some element occurrences are listed. In particular, it appeared that there are no layouts of order 32 with more than 5 occurrences of any element which yield a bi-regular matrix (and hence an MDS matrix)

Majorana fermions in pinned vortices

Exploiting the peculiar properties of proximity-induced superconductivity on the surface of a topological insulator, we propose a device which allows the creation of a Majorana fermion inside the core of a pinned Abrikosov vortex. The relevant Bogolyubov-de Gennes equations are studied analytically. We demonstrate that in this system the zero-energy Majorana fermion state is separated by a large energy gap, of the order of the zero-temperature superconducting gap $\Delta$, from a band of single-particle non-topological excitations. In other words, the Majorana fermion remains robust against thermal fluctuations, as long as the temperature remains substantially lower than the critical superconducting temperature. Experimentally, the Majorana state may be detected by measuring the tunneling differential conductance at the center of the Abrikosov vortex. In such an experiment, the Majorana state manifests itself as a zero-bias anomaly separated by a gap, of the order of $\Delta$, from the contributions of the nontopological excitations.Comment: 9 pages, 2 eps figures, new references are added, several typos are correcte

Instabilities of the AA-stacked graphene bilayer

Tight-binding calculations predict that the AA-stacked graphene bilayer has one electron and one hole conducting bands, and that the Fermi surfaces of these bands coincide. We demonstrate that as a result of this degeneracy, the bilayer becomes unstable with respect to a set of spontaneous symmetry violations. Which of the symmetries is broken depends on the microscopic details of the system. We find that antiferromagnetism is the more stable order parameter. This order is stabilized by the strong on-site Coulomb repulsion. For an on-site repulsion energy typical for graphene systems, the antiferromagnetic gap can exist up to room temperatures.Comment: 4 pages, 2 eps figure, submitted to Phys. Rev. Let

Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity

Using bosonization-fermionization transformation we map the Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the model of fermionic quasiparticles whose interaction is irrelevant in the renormalization group sense. Such mapping allows us to set up an expansion for the density-density propagator of the original Tomonaga-Luttinger Hamiltonian in orders of the (irrelevant) quasiparticle interaction. The lowest order term in such an expansion is proportional to the propagator for free fermions. The next term is also evaluated. The propagator found is used for calculation of the Coulomb drug resistivity $r$ in a system of two capacitively coupled one-dimensional conductors. It is shown that $r$ is proportional to $T^2$ for both free and interacting fermions. The marginal repulsive in-chain interaction acts to reduce $r$ as compared to the non-interacting result. The correction to $r$ due to the quasiparticle interaction is found as well. It scales as $T^4$ at low temperature.Comment: 5 pages, 1 eps figure; the new version of the e-print corrects an error, which exists in the original submission; fortunately, all important conclusions of the study remain vali

Aggregated estimation of the basic parameters of biological production and the carbon budget of Russian terrestrial ecosytems: 2. Net primary production

The estimated net primary production (NPP) of Russian terrestrial ecosystems (annual average over the period from 1988 to 1992) is 9544 Tg of dry matter, or 4353 Tg of carbon. Of the total amount, forests account for approximately 39.2% (here and below, comparisons are made with respect to carbon content); natural grasslands and brushwoods, for 27.6%; farmlands (arable land and cultivated pastures), for 22.0%; and wetlands, for 11.2%. The average NPP density on lands covered with vegetation (1629.8 million hectares in Russia) is 267 g C/m2per year. The highest value (498 g C/m2per year) is characteristic of arable lands. Other land-use/land-cover (LULC) classes have the following NPP densities (in areas covered with vegetation): grasslands and brushwoods, 278 g C/m2; forests, 224 g C/m2; and wetlands, 219 g C/m2per year. In general, Russian terrestrial ecosystems accumulate 59.7% of the total NPP in the aboveground phytomass (47.8% in green parts and 11.9% in wood) and 40.3% in the underground phytomass. The latter parameter differs significantly in different LULC classes and bioclimatic zones. According to calculations, the uncertainty in estimating the total NPP is 11% (a priori confidential probability 0.9)

Suspensions of supracolloidal magnetic polymers: self-assembly properties from computer simulations

We study self-assembly in suspensions of supracolloidal polymer-like structures made of crosslinked magnetic particles. Inspired by self-assembly motifs observed for dipolar hard spheres, we focus on four different topologies of the polymer-like structures: linear chains, rings, Y-shaped and X-shaped polymers. We show how the presence of the crosslinkers, the number of beads in the polymer and the magnetic interparticle interaction affect the structure of the suspension. It turns out that for the same set of parameters, the rings are the least active in assembling larger structures, whereas the system of Y- and especially X-like magnetic polymers tend to form very large loose aggregates

A nearly closed ballistic billiard with random boundary transmission

A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary, and optical cavities with random surface refractive index. The specific example we study is a circular (integrable) billiard with no internal impurities weakly coupled to the exterior by a large number of leads with one channel open in each lead. We construct a supersymmetric nonlinear $\sigma$-model by averaging over the random coupling strengths between bound states and channels. The resulting theory can be used to evaluate the statistical properties of any physically measurable quantity in a billiard. As an illustration, we present results for the local density of states.Comment: 5 pages, 1 figur

Stem-technologies: mathematics and informatics

Algorithms solutions of tasks in the field of the theory of numbers within implementation of the STEM project are proposed and realized. Calculations in a package of computer algebra on an open code in the environment of Linux DebianПредложены и реализованы алгоритмы решения задач в области теории чисел в рамках реализации проекта STEM. Вычисления в пакете компьютерной алгебры на открытом коде в среде Linux Debia

Experimental (computing) theory of numbers

Carrying out numerical experiments with Euler's function. Specification of the theorem of Mertens. Calculations in a package of computer algebra on an open code in the environment of Linux DebianПроведение численных экспериментов с функцией Эйлера. Уточнение теоремы Мертенса. Вычисления в пакете компьютерной алгебры на открытом коде в среде Linux Debia