Charge and Spin Transport at the Quantum Hall Edge of Graphene

Landau level bending near the edge of graphene, described using 2d Dirac equation, provides a microscopic framework for understanding the quantum Hall Effect (QHE) in this material. We review properties of the QHE edge states in graphene, with emphasis on the novel phenomena that arise due to Dirac character of electronic states. A method of mapping out the dispersion of the edge states using scanning tunneling probes is proposed. The Zeeman splitting of Landau levels is shown to create a particularly interesting situation around the Dirac point, where it gives rise to counter-circulating modes with opposite spin. These chiral spin modes lead to a rich variety of spin transport phenomena, including spin Hall effect, spin filtering and injection, and electric detection of spin current. The estimated Zeeman spin gap, enhanced by exchange, of a few hundred Kelvin, makes graphene an attractive system for spintronics. Comparison to recent transport measurements near nu=0 is presented.Comment: 10 pages, 6 figures, invited pape

Physiological reactions of a passenger to transportation conditions

The effect of transportation conditions on the performance capacity of a passenger were studied, in order to establish the time for his most rapid inclusion in production activity after the trip. It was concluded that the transportation conditions impair the functional condition of the passenger's organism. The restoration of the functional state to the initial level occurs mainly in the space of one day. It is shown that it is necessary to take into consideration the adaptation of the organism during transfer to another climate zone

2D materials and van der Waals heterostructures

The physics of two-dimensional (2D) materials and heterostructures based on such crystals has been developing extremely fast. With new 2D materials, truly 2D physics has started to appear (e.g. absence of long-range order, 2D excitons, commensurate-incommensurate transition, etc). Novel heterostructure devices are also starting to appear - tunneling transistors, resonant tunneling diodes, light emitting diodes, etc. Composed from individual 2D crystals, such devices utilize the properties of those crystals to create functionalities that are not accessible to us in other heterostructures. We review the properties of novel 2D crystals and how their properties are used in new heterostructure devices

Formalization of the General Model of the Green Economy at the Regional Level

The paper focuses on the study of the problems of the economic and mathematical modeling of the green economy at the regional level. The purpose of the research is the development of economic and mathematical tools for the economic and ecological systems’ modeling at the regional level on the basis of the principles of green economy. The hypothesis of the research is based on the thesis that in the conditions of the exhaustion of natural resources and depletion of natural capital, the technogenic fields, production and consumption waste could be considered as a resource basis for modernization. Such factors’ use leads to the elimination of accumulated environmental damage and substitution of natural resources. The paper describes the approaches to the system modeling problem-solving in order to develop the green economy both in the country and its regions. The urgency of the transition to a green economy is confirmed by the theoretical and practical research on the cyclical development of the socio-eco-economic systems. A number of formalized models and methods for solving the current environmental and economic issues including the economic valuation of accumulated environmental damage, eco-economic assessment of the efficiency of natural resource substitution with resource-substitute are proposed as well as the choice of an optimal set of resources-substitutes taking into account the financial and natural resource constraints. The authors research the typical model of green growth considering the exhaustion of natural resources, technogenic resources deposits involving in economic circulation through the implementation of investment projects on the elimination of accumulated environmental damage. The results could be used in the different regions of Russia for the justification and implementation of investment projects within the framework of the federal target program “Elimination of accumulated environmental damage” in 2015–2026 years.The research has been supported by the Grant of the Russian Foundation for Humanities, Project №14–02–00235а

О вычислении группы классов идеалов мнимых мультиквадратичных полей

In the paper, we extend Biasse | van Vredendaal (OBS, 2019, vol. 2) implementation and experiments of the class group computation from real to imaginary multi-quadratic elds. The implementation is optimized by introducing an explicit prime ideal lift operation and by using LLL reduction instead of HNF computation. We provide examples of class group computation of the imaginary multiquadratic elds of degree 64 and 128, that has been previously unreachable

Hyperelliptic curves, Cartier-Manin matrices and Legendre polynomials

We investigate the hyperelliptic curves of the form C1 : y2 = x2g+1 + ax9+1 + bx and C2 : y2 = x2g+2 + ax9+1 + b over the finite field Fq, q = pn, p > 2. We transform these curves to the form C1,p : y2 = x2g+1 —2px9+1 + x and C2,p : y2 = x2g+2 — 2px9+1 + 1 and prove that the coefficients of corresponding Cartier — Manin matrices are Legendre polynomials. As a consequence, the matrices are centrosymmetric and, therefore, it’s enough to compute a half of coefficients to compute the matrix. Moreover, they are equivalent to block-diagonal matrices under transformation of the form S(p)WS-1 . In the case of gcd(p,g) = 1, the matrices are monomial, and we prove that characteristic polynomial of the Frobenius endomorphism x(A) (mod p) can be found in factored form in terms of Legendre polynomials by using permutation attached to the monomial matrix. As an application of our results, we list all the possible polynomials x(A) (mod p) for the case of gcd(p,g) = 1, g e {1,. . ., 7} and the curve C1 is over Fp or Fp2

Hyperelliptic curves, Cartier - Manin matrices and Legendre polynomials

Using hyperelliptic curves in cryptography requires the computation of the Jacobian order of a curve. This is equivalent to computing the characteristic polynomial of Frobenius x(A) e Z[A|. By calculating Cartier — Manin matrix, we can recover the polynomial x(A) modulo the characteristic of the base field. This information can further be used for recovering full polynomial in combination with other methods. In this paper, we investigate the hyperelliptic curves of the form C1 : y2 = x2g+1 + + ax9+1 + bx and C2 : y2 = x2g+2 + ax9+1 + b over the finite field Fq, q = pn, p > 2. We transform these curves to the form C1,p : y2 = x2g+1 — 2px9+1 + x and C2,p : y2 = x2g+2 — 2px9+1 +1, where p = —a/(2Vb), and prove that the coefficients of the corresponding Cartier — Manin matrices for the curves in this form are Legendre polynomials. As a consequence, the matrices are centrosymmetric and therefore, for finding the matrix, it’s enough to compute a half of coefficients. Cartier — Manin matrices are determined up to a transformation of the form S(p)WS- 1. It is known that centrosymmetric matrices can be transformed to the block-diagonal form by an orthogonal transformation. We prove that this transformation can be modified to have a form S(p)WS- 1 and be defined over the base field of the curve. Therefore, Cartier — Manin matrices of curves C1,p and C2,p are equivalent to block-diagonal matrices. In the case of gcd(p,g) = 1, Miller and Lubin proved that the matrices of curves C1 and C2 are monomial. We prove that the polynomial x(A) (mod p) can be found in factored form in terms of Legendre polynomials by using permutation attached to the monomial matrix. As an application of our results, we list all possible polynomials x(A) (mod p) in the case of gcd(p,g) = 1, g is from 2 to 7 and the curve C1 is over Fp if /b e Fp and over Fp2 if / b £ Fp

Raman Fingerprint of Charged Impurities in Graphene

We report strong variations in the Raman spectra for different single-layer graphene samples obtained by micromechanical cleavage, which reveals the presence of excess charges, even in the absence of intentional doping. Doping concentrations up to ~10^13 cm-2 are estimated from the G peak shift and width, and the variation of both position and relative intensity of the second order 2D peak. Asymmetric G peaks indicate charge inhomogeneity on the scale of less than 1 micron.Comment: 3 pages, 5 figure