Elliptic operators in even subspaces

In the paper we consider the theory of elliptic operators acting in subspaces defined by pseudodifferential projections. This theory on closed manifolds is connected with the theory of boundary value problems for operators violating Atiyah-Bott condition. We prove an index formula for elliptic operators in subspaces defined by even projections on odd-dimensional manifolds and for boundary value problems, generalizing the classical result of Atiyah-Bott. Besides a topological contribution of Atiyah-Singer type, the index formulas contain an invariant of subspaces defined by even projections. This homotopy invariant can be expressed in terms of the eta-invariant. The results also shed new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure

Recombination limited energy relaxation in a BCS superconductor

We study quasiparticle energy relaxation at sub-kelvin temperatures by injecting hot electrons into an aluminium island and measuring the energy flux from electrons into phonons both in the superconducting and in the normal state. The data show strong reduction of the flux at low temperatures in the superconducting state, in qualitative agreement with the presented quasiclassical theory for clean superconductors. Quantitatively, the energy flux exceeds that from the theory both in the superconducting and in the normal state, possibly suggesting an enhanced or additional relaxation process

Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method of uniformization: We assign to the nonlocal problem a pseudodifferential operator with the same index, acting in sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah-Singer index theorem.Comment: 16 pages, no figure

Wandering breathers and self-trapping in weakly coupled nonlinear chains: classical counterpart of macroscopic tunneling quantum dynamics

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly-moving: the periodic transverse translation (wandering) of low-amplitude breather between the chains, and the one-chain-localization of high-amplitude breather. These two modes of coupled nonlinear excitations, which involve large number of anharmonic oscillators, can be mapped onto two solutions of a single pendulum equation, detached by a separatrix mode. We also study two-chain breathers, which can be considered as bound states of discrete breathers with different symmetry and center locations in the coupled chains, and bifurcation of the anti-phase two-chain breather into the one-chain one. Delocalizing transition of 1D breather in 2D system of a large number of parallel coupled nonlinear chains is described, in which the breather, initially excited in a given chain, abruptly spreads its vibration energy in the whole 2D system upon decreasing breather frequency or amplitude below the threshold one. The threshold breather frequency is above the cut off phonon frequency in 2D system, and the threshold breather amplitude scales as square root of the inter-chain coupling constant. Delocalizing transition of discrete vibrational breather in 2D and 3D systems of coupled nonlinear chains has an analogy with delocalizing transition for Bose-Einstein condensates in 2D and 3D optical lattices.Comment: 33 pages, 16 figure

Methodological approaches to the formation of a unified national system of monitoring and accounting of carbon balance and greenhouse gas emissions on lands of the agricultural fund of the Russian Federation

Methodological approaches to the formation of a unified national system for monitoring and accounting the balance of carbon and greenhouse gas emissions are considered. The purpose, typification, requirements for the spatial placement of “carbon” polygons, assessment of the carbon absorption capacity of forests and agricultural ecosystems in the Russian Federation, the standard methodology recommended by the international community for assessing carbon stocks in soils, which should be applied in the Russian Federation to ensure comparability of the results of greenhouse gas accounting between countries, determination of the carbon absorption capacity of natural ecosystems and soils are discussed. The potential of carbon uptake by agricultural soils is shown. The list of indicators for assessing soil carbon according to the IPCC methodology for Tiers 2 and 3 is given. Taking into account the analysis of international practice, as well as on the basis of theoretical and applied experience of national science, the priority measures have been developed, they are aimed at working out and implementation of the national strategy for the use of terrestrial ecosystems in order to regulate greenhouse gas emissions to mitigate climate change

Poincare isomorphism in K-theory on manifolds with edges

The aim of this paper is to construct the Poincare isomorphism in K-theory on manifolds with edges. We show that the Poincare isomorphism can naturally be constructed in the framework of noncommutative geometry. More precisely, to a manifold with edges we assign a noncommutative algebra and construct an isomorphism between the K-group of this algebra and the K-homology group of the manifold with edges viewed as a compact topological space.Comment: 15 pages, no figure

Noncommutative elliptic theory. Examples

We study differential operators, whose coefficients define noncommutative algebras. As algebra of coefficients, we consider crossed products, corresponding to action of a discrete group on a smooth manifold. We give index formulas for Euler, signature and Dirac operators twisted by projections over the crossed product. Index of Connes operators on the noncommutative torus is computed.Comment: 23 pages, 1 figur

Динамика неньютоновского осциллятора

For an explanation of curves of rotation of spiral galaxies the changed form of the second law of Newton is offered. For the purpose of possible experimental registration in terrestrial conditions of the changed law the model of non-newtonian oscillator is offered. Precisely and in various approximations the task about oscillations of non-newtonian oscillator is solved.Для объяснения наблюдаемых кривых вращения спиральных галактик предложена измененная форма второго закона Ньютона. С целью возможной экспериментальной проверки в земных условиях справедливости предлагаемого закона движения рассматривается модель неньютоновского осциллятора. Точно и в различных приближениях решена задача о колебаниях неньютоновского осциллятора

Global climate and soil cover – implications for land use in Russia

The necessity of a comprehensive description of greenhouse gas fluxes on different types of soils, the methodology for creating “carbon polygons” and “carbon farms” with the use of modern methods for assessing carbon fluxes in ecosystems, taking into account the specifics of the natural conditions of Russia and competitive advantages, are substantiated. Directions for developing national methods for calculating carbon fluxes are given, which should be subjected to verification by the interested parties of the Paris Agreement adopted by the Russian Federation. Such issues are considered as the role and potential of the Russian soil cover in the carbon balance of the planet, factors of reducing carbon stocks from the upper 1 meter depth layer of the soil, competitive edge in the EU and the Western world in the questions of natural and climatic changes, the use of remote sensing of the Earth from space in order to obtain regular, complete and reliable estimates of the absorption of greenhouse gases

Simulation of dimensionality effects in thermal transport

The discovery of nanostructures and the development of growth and fabrication techniques of one- and two-dimensional materials provide the possibility to probe experimentally heat transport in low-dimensional systems. Nevertheless measuring the thermal conductivity of these systems is extremely challenging and subject to large uncertainties, thus hindering the chance for a direct comparison between experiments and statistical physics models. Atomistic simulations of realistic nanostructures provide the ideal bridge between abstract models and experiments. After briefly introducing the state of the art of heat transport measurement in nanostructures, and numerical techniques to simulate realistic systems at atomistic level, we review the contribution of lattice dynamics and molecular dynamics simulation to understanding nanoscale thermal transport in systems with reduced dimensionality. We focus on the effect of dimensionality in determining the phononic properties of carbon and semiconducting nanostructures, specifically considering the cases of carbon nanotubes, graphene and of silicon nanowires and ultra-thin membranes, underlying analogies and differences with abstract lattice models.Comment: 30 pages, 21 figures. Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.