Anomalous Hall effect in disordered Weyl semimetals

We study the anomalous Hall effect in a disordered Weyl semimetal. While the intrinsic contribution is expressed solely in terms of Berry curvature, the extrinsic contribution is given by a combination of the skew scattering and side jump terms. For the model of small size impurities, we are able to express the skew scattering contribution in terms of scattering phase shifts. We identify the regime in which the skew scattering contribution dominates the side-jump contribution: the impurities are either strong or resonant, and at dilute concentration. In this regime, the Hall resistivity $\rho_{xy}$ is expressed in terms of two scattering phases, analogous to the s-wave scattering phase in a non-topological metal. We compute the dependence of $\rho_{xy}$ on the chemical potential, and show that $\rho_{xy}$ scales with temperature as $T^2$ in low temperatures and as $T^{3/2}$ in the high temperature limit

Heat transport in Weyl semimetals in the hydrodynamic regime

We study heat transport in a Weyl semimetal with broken time-reversal symmetry in the hydrodynamic regime. At the neutrality point, the longitudinal heat conductivity is governed by the momentum relaxation (elastic) time, while longitudinal electric conductivity is controlled by the inelastic scattering time. In the hydrodynamic regime this leads to a large longitudinal Lorenz ratio. As the chemical potential is tuned away from the neutrality point, the longitudinal Lorenz ratio decreases because of suppression of the heat conductivity by the Seebeck effect. The Seebeck effect (thermopower) and the open circuit heat conductivity are intertwined with the electric conductivity. The magnitude of Seebeck tensor is parametrically enhanced, compared to the non-interacting model, in a wide parameter range. While the longitudinal component of Seebeck response decreases with increasing electric anomalous Hall conductivity $\sigma_{xy}$, the transverse component depends on $\sigma_{xy}$ in a non-monotonous way. Via its effect on the Seebeck response, large $\sigma_{xy}$ enhances the longitudinal Lorenz ratio at a finite chemical potential. At the neutrality point, the transverse heat conductivity is determined by the Wiedemann-Franz law. Increasing the distance from the neutrality point, the transverse heat conductivity is enhanced by the transverse Seebeck effect and follows its non-monotonous dependence on $\sigma_{xy}$

Mesoscopic conductance fluctuations and noise in disordered Majorana wires

Superconducting wires with broken time-reversal and spin-rotational symmetries can exhibit two distinct topological gapped phases and host bound Majorana states at the phase boundaries. When the wire is tuned to the transition between these two phases and the gap is closed, Majorana states become delocalized leading to a peculiar critical state of the system. We study transport properties of this critical state as a function of the length $L$ of a disordered multichannel wire. Applying a non-linear supersymmetric sigma model of symmetry class D with two replicas, we identify the average conductance, its variance and the third cumulant in the whole range of $L$ from the Ohmic limit of short wires to the regime of a broad conductance distribution when $L$ exceeds the correlation length of the system. In addition, we calculate the average shot noise power and variance of the topological index for arbitrary $L$. The general approach developed in the paper can also be applied to study combined effects of disorder and topology in wires of other symmetries.Comment: 21 pages, 7 figure

Analysis of Mechanical Safety of Stadiums for the World Cup 2018

It is obvious that contemporary design and construction of unique buildings and structures is unthinkable without mathematical (numerical) and computer modelling and advanced analysis ofload-bearing structures under various kinds ofloads and impacts. One of the most ambitious and important construction projects is the uniquelarge-span structures. These are, in particular, stadiums, sports palaces and water parks, shopping malls, pedestrian, road and railway bridges of various design solutions. The distinctive paper is devoted to theoretical foundations and results of mathematical (numerical) modeling of the state (in terms of the analysis of stress-strain state, strength and stability) of football stadiums built for the 2018 FIFA World Cup in Russia. Finite element method is used for approximation and high-precision numerical solution of corresponding boundary problems of structural mechanics. It is the most universal and powerful numerical method of mechanics. The paper, in particular, describes some features of development of finite element models and the main results of the analysis of the mechanical (structural) safety of three- dimensionallarge-span systems "soil foundation - reinforced concrete structures of foundations and stands - steel structures of the coating and facades" of these football stadiums with the basic and specialload combinations. In addition, the key procedures of scientific support during the corresponding expertise and assessments are outlined. Generally, socially significant and knowledge-intensive problem of providing mechanical (constructive) safety of unique combined objects of construction (three-dimensional systems "foundation - reinforced concrete structures of foundations and stands - steel structures of coating and facades") has been solved at a new level as a result of the performed complex of research works

Quantum corrections to the polarizability and dephasing in isolated disordered metals

We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop-expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated (canonical ensemble) systems appears only in subleading terms of the expansion, and can be neglected if the frequency of the external field, $\omega$, is of the order of (or even slightly smaller than) the mean level spacing, $\Delta$. If $\omega \ll \Delta$, the two-loop correction becomes important. We calculate it by systematically evaluating the ballistic parts (the Hikami boxes) of the corresponding diagrams and exploiting electroneutrality. Our theory allows one to take into account a finite dephasing rate, $\gamma$, generated by electron interactions, and it is complementary to the non-perturbative results obtained from a combination of Random Matrix Theory (RMT) and the $\sigma$-model, valid at $\gamma \to 0$. Remarkably, we find that the two-loop result for isolated systems with moderately weak dephasing, $\gamma \sim \Delta$, is similar to the result of the RMT+$\sigma$-model even in the limit $\omega \to 0$. For smaller $\gamma$, we discuss the possibility to interpolate between the perturbative and the non-perturbative results. We compare our results for the temperature dependence of the polarizability of isolated rings to the experimental data of Deblock \emph{et al} [\prl \ {\bf 84}, 5379 (2000); \prb \ {\bf 65}, 075301 (2002)], and we argue that the elusive 0D regime of dephasing might have manifested itself in the observed magneto-oscillations. Besides, we thoroughly discuss possible future measurements of the polarizability, which could aim to reveal the existence of 0D dephasing and the role of the Pauli blocking at small temperatures.Comment: 12+ pages, 10 figures; version published in PR

High Performance Fuel Design for Next Generation PWRs: 11th Quarterly Report

Quarterly Report for Project DE-FG03-01SF22329 April 2004 – June 2004I. Technical Narrative: The overall objective of this NERI project is to examine the potential for a high performance advanced fuel for Pressurized Water Reactors (PWRs), which would accommodate a substantial increase of core power density while simultaneously providing larger thermal margins than current PWRs. This advanced fuel will have an annular geometry that allows internal and external coolant flow and heat removal. The project is led by the Massachusetts Institute of Technology (MIT), with collaboration of four industrial partners – Gamma Engineering Corporation, Westinghouse Electric Corporation, Framatome ANP (formerly Duke Engineering & Services), and Atomic Energy of Canada Limited

High Performance Fuel Design for Next Generation PWRs 2nd Annual Report

Progress Report for Work August 2002 through July 2003The overall objective of this NERI project is to examine the potential for a high performance advanced fuel design for Pressurized Water Reactors (PWRs), which would accommodate a substantial increase of core power density while simultaneously providing larger thermal margins than current PWRs. This advanced fuel employs an annular geometry that allows internal and external coolant flow and heat removal. The project is led by the Massachusetts Institute of Technology (MIT), with the collaboration of four industrial partners – Gamma Engineering Corporation, Westinghouse Electric Corporation, Framatome ANP DE & S (formerly Duke Engineering & Services), and Atomic Energy of Canada Limited. The project is organized into five tasks: 1. Task 1 Assess the thermal hydraulic performance of the internally and externally cooled annular fuel to identify the configuration with the highest potential for power density increase while maintaining ample thermal margins, as well as key aspects of mechanical design to ensure that new fuel will not perform outside established hydraulic and mechanical constraints, 2. Task 2 Determine the neutronic performance of the new fuel, and the design that will minimize fuel cycle cost and assures that reactor physics safety parameters are as good or better than those of current PWRs, 3. Task 3 Explore various methods of manufacturing of this advanced fuel, including new innovative fabrication processes to produce annular fuel elements with the required product characteristics, 4. Task 4 Evaluate fuel cycle cost and capital cost implications of high power density to determine the economic viability of the high-performance fuel, and 5. Task 5 Analyze fuel performance of the new UO2 annular fuel obtained by various production technologies including irradiation testing in the MIT reactor