### Working paper

## Quench-controlled frictionless motion of an impurity in a quantum medium

The workshop *Tropical Aspects in Geometry, Topology and Physics* was devoted to a wide discussion and exchange of ideas between the leading experts representing various points of view on the subject. The development of tropical geometry is based on deep links between problems in real and complex enumerative geometry, symplectic geometry, quantum fields theory, mirror symmetry, dynamical systems and other research areas. On the other hand, new interesting phenomena discovered in the framework of tropical geometry (like refined tropical enumerative invariants) pose the problem of a conceptual understanding of these phenomena in the “classical” geometry and mathematical physics.

The article is devoted to the philosophical interpretation of the several approaches to the creation of a quantum theory of gravity. The analysis of the key aspects of the General theory of relativity and the Standard Model, the clarification of the relevant concepts contents (gravity, particle, field, space, etc.) are conducted for this purpose. We establish the causes and origins of the creation of the quantum theory of gravity problematical character, give the interpretation of the existing problems. Therefore, the article shows a fundamental difference between realities described by the two leading modern physical theories.

Classical science is based on common sense and intuitive representability, while the microcosm cannot be directly observed and therefore is out of the representable sphere. This is probably the part of the reason for the incompatibility of the equations of quantum theory and general relativity. On the basis of the philosophical analysis of the results of some modern theoretical physics concepts, the article presents the direction of creation a quantum theory of gravity. This direction appears to be the combination of the consequences of several concepts of the string theory and the holographic principle to the properties of the quantum-mechanical entanglement. The entanglement is most likely dually connected with gravity, and the non-locality is a characteristic of the multidimensional space.

The problem lies in the fact that this result is not literally applicable to our reality and describes the possible worlds (in the context of the diversity of the laws of physics). The article establishes that, despite the mentioned, the theory remains scientific and still appears to be a good approximation to the observed physical reality.

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research.

This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed.

Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments.

This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

We calculate one--loop corrections to the vertexes and propagators of photons and charged particles in the strong electric field backgrounds. We use the Schwinger--Keldysh diagrammatic technique. We observe that photon's Keldysh propagator receives growing with time infrared contribution. As the result, loop corrections are not suppressed in comparison with tree--level contribution. This effect substantially changes the standard picture of the pair production. To sum up leading IR corrections from all loops we consider the infrared limit of the Dyson--Schwinger equations and reduce them to a single kinetic equation.

In this paper we introduce a notion of Feynman geometry on which quantum field theories could be properly defined. A strong Feynman geometry is a geometry when the vector space of A-infinity structures is nite dimensional. A weak Feynman geometry is a geometry when the vector space of A-infinity structures is innite dimensional while the relevant operators are of trace-class. We construct families of Feynman geometries with "continuum" as their limit.

We explain the Dirac–Segal approach to quantum field theory. We study local observables in this approach and the theory of deformations. We found out that this theory of deformation in the second-order coincides with the renormalization of the same theory, would it be considered in Polyakov approach. We conjecture that it is still true to all orders.

This volume presents new results in the study and optimization of information transmission models in telecommunication networks using different approaches, mainly based on theiries of queueing systems and queueing networks .

The problem of management of the nonlinear object which is exposed to impact of uncontrollable indignations, is considered in a key of differential game. Synthesis of optimum managements is made with application of transformation of the nonlinear equation of initial object in the differential equation with the parameters depending on a condition. The square-law functional of quality allows to formulate synthesis conditions in the form of need of search of solutions of the equation of Rikkati. The solution of the equation of Rikkati with the parameters depending on a condition, is in a symbolical view with application of algebraic methods that allows to generalize a number of earlier published theoretical results, to receive rather constructive decisions in a number of statements of problems of management.

The Handbook of CO₂ in Power Systems' objective is to include the state-of-the-art developments that occurred in power systems taking CO₂ emission into account. The book includes power systems operation modeling with CO₂ emissions considerations, CO₂ market mechanism modeling, CO₂ regulation policy modeling, carbon price forecasting, and carbon capture modeling. For each of the subjects, at least one article authored by a world specialist on the specific domain is included.

The article is based upon the fact that the growing demand for master data management systems has not yet produced a commonly accepted metodology for their design and development/ The article offers two mathematical models? that allow a master data management systems designer a way to formally describe their system before development and verify the system quality by measurements? unique to master data management systems.

Many electronic devices operate in a cyclic mode. This should be considered when forecastingreliability indicators at the design stage.The accuracy of the prediction and the planning for the event to ensure reliability depends on correctness of valuation and accounting greatest possiblenumber of factors. That in turn will affect the overall progress of the design and, in the end,result in the quality and competitiveness of products

Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables