Modern Theoretical Physics Research Articles

AN ANTHOLOGY OF THE DISTINGUISHED ACHIEVEMENTS IN SCIENCE AND TECHNIQUE. PART 53: NOBEL PRIZE LAUREATES IN PHYSICS FOR 2016-2019

Purpose. Brief presentation of the distinguished achievements of Nobel Prize Laureates in physics for current time period of 2016-2019. Methodology. Scientific methods of collection, analysis and analytical treatment of scientific and technical information of world level in area of astronomy, astrophysics, physicists of the condensed environments, laser physics, modern theoretical and experimental physics. Results. The brief analytical review of the scientific discovery and distinguished achievements of scientists-physicists in area of modern physical and technical problems which were marked the Nobel Prizes in physics for the period 2016-2019 is presented. In the number of such discovery and achievements of the best representatives of world scientific association entered: theoretical discovery of topology phase transitions and topology phases of matter, experimental discovery of gravity waves, revolutionary inventions in area of laser physics, astronomic discovery and contribution to our understanding of evolution of Universe and place of Earth in space. Originality. Systematization and analytical exposition is executed in short concentrated and accessible to the wide reader to the form of the known scientific and technical materials, awarded with the Nobel Prizes in physics for current time period of 2016-2019 and devoted to: the theoretical openings of topology phase transitions and topology phases of matter, experimental opening of gravity waves, revolutionary inventions in area of laser physics, astronomic discovery and contribution to our understanding of evolution of Universe and place of Earth in space. Practical value. Popularization and deepening of scientific and technical knowledge for students, engineer and technical specialists and research workers in area of astronomy, astrophysics, physicists of the condensed environments, laser physics, modern theoretical and experimental physics, extending their scientific range of interests and further development of scientific and technical progress in human society.

Superunified Theory of Quantum Fields & Fundamental Interactions

This is an introduction to what is anticipated to be the so called final theory of physics. The theory unifies pure (not applied) mathematics and the modern theoretical physics into a universal system of mathematical harmony. It describes the physical Universe as mathematical machine.

Physics needs nothing less than a Renaissance – On the relation between physics and philosophy

In this article, the fundamental inconsistencies of the mainstream theoretical physics has been analyzed in detail. It has been shown that relativity and quantum field theory have an array of fundamental problems in postulations, methodology, theory, experimental verification and philosophy. The modern theoretical physics represented by relativity and the standard model of particle physics has come to a dead end. To get out of the impasse, physics community must give up the theological pursuit of a theory of everything, return to scientific philosophy, logic, methodology and scientific mission. Physics needs nothing less than a renaissance.

On the Geometry of the Set of Orbits of Killing Vector Fields on Euclidean Space

Smooth orbifolds can be considered as a natural generalization of smooth manifolds, when model space is not ${\mathbb R}^n,$ but factor space $ {\mathbb R}^n/G$ by a finite group $G$ of diffeomorphisms. In modern theoretical physics, orbifolds are used as string propagation spaces and are motivated by the preference for models on orbifolds over models on ordinary manifolds. Orbifolds arise in the theory of foliations as ``good'' spaces of leaves. It is known that the existence of a proper leaf with a finite holonomy group for a transversally complete Riemannian foliation is a necessary and sufficient condition for the space of leaves to be an orbifold. The purpose of our paper is study the structure of the space of leaves of singular foliation which generated by orbits of Killing vector fields. Geometry of Killing vector fields is a object of many investigations due to their importance in geometry and physics. We will prove that the space of orbits of family of Killing vector fields on Euclidean space is a smooth orbifold.

QUANTUM ECONOPHYSICAL PRECURSORS OF CRYPTOCURRENCY CRASHES

This article demonstrates the possibility of constructing indicators of critical and crash phenomena in the volatile market of cryptocurrency. The possibility of constructing dynamic measures of complexity as quantum econophysical behaving in a proper way during actual pre-crash periods has been shown. This fact is used to build predictors of crashes and critical events phenomena on the examples of all the patterns recorded in the time series of the key cryptocurrency Bitcoin, the effectiveness of the proposed indicators-precursors of these falls has been identified. From positions, attained by modern theoretical physics the concept of economic Planсk's constant has been proposed. The theory on the economic dynamic time series related to the cryptocurrencies market has been approved. Then, combining the empirical cross-correlation matrix with the Random Matrix Theory, we mainly examine the statistical properties of cross-correlation coefficient, the evolution of the distribution of eigenvalues and corresponding eigenvectors of the global cryptocurrency market using the daily returns of cryptocurrencies price time series all over the world from 2013 to 2018. The result has indicated that the largest eigenvalue reflects a collective effect of the whole market, and is very sensitive to the crash phenomena. It has been shown that both the introduced economic mass and the largest eigenvalue of the matrix of correlations can act like quantum indicators-predictors of falls in the market of cryptocurrencies.

Operations and Actions of Lie Groups on Manifolds

As recounted in this paper, the idea of groups is one that has evolved from some very intuitive concepts. We can do binary operations like adding or multiplying two elements and also binary operations like taking the square root of an element (in this case the result is not always in the set). In this paper, we aim to find the operations and actions of Lie groups on manifolds. These actions can be applied to the matrix group and Bi-invariant forms of Lie groups and to generalize the eigenvalues and eigenfunctions of differential operators on Rn. A Lie group is a group as well as differentiable manifold, with the property that the group operations are compatible with the smooth structure on which group manipulations, product and inverse, are distinct. It plays an extremely important role in the theory of fiber bundles and also finds vast applications in physics. It represents the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. Here we did work flat out to represent the mathematical aspects of Lie groups on manifolds.

The variety of approaches to the problem of the derivation of Dirac equation

Purpose. The Dirac equation is one of the fundamental equations of modern theoretical physics. It is in service more than 90 years (1928–2018). The application today is much wider than the areas of quantum mechanics, quantum field theory, atomic and nuclear physics, solid state physics. The successful derivation of some equation of mathematical physics is the first step to successful application. In such process the essence of the corresponding model of nature, the mathematical principles and the physical foundations are visualized. Here we deal with the different approaches to the problem of the Dirac equation derivation. Methods. The quantum-mechanical, quantum field-theoretical, group-theoretical, algebraic, symmetrical, statistical, stochastical and numerical approaches are used. Results. The 26 different ways of the Dirac equation derivation are presented. The various physical principles and mathematical formalisms are used. Three original approaches of the authors to the problem are given. They are (i) the generalization of H. Sallhofer derivation, (ii) the obtaining of the massless Dirac equation from the Maxwell equations in maximally symmetrical form, (iii) the derivation of the Dirac equation with nonzero mass from the relativistic quantum mechanics of the fermion-antifermion spin s = 1/2 doublet. In some sense the role of the Dirac equation today is demonstrated. Conclusions. The original investigation of the problem of the Dirac equation derivation is presented. The different approaches, which are based on the various mathematical and physical principles, are considered (26 methods). Therole of the scientists from Uzhhorod is shown. The importance of place of the Dirac equation in modern theoretical physics is discussed.

About the Approximate Solutions to Linear and Non-Linear Pseudodifferential Reaction Diffusion Equations

Background. The concept of fractal is one of the main paradigms of modern theoretical and experimental physics, radiophysics and radar, and fractional calculus is the mathematical basis of fractal physics, geothermal energy and space electrodynamics. We investigate the solvability of the Cauchy problem for linear and nonlinear inhomogeneous pseudodifferential diffusion equations. The equation contains a fractional derivative of a Riemann–Liouville time variable defined by Caputo and a pseudodifferential operator that acts on spatial variables and is constructed in a homogeneous, non-negative homogeneous order, a non-smooth character at the origin, smooth enough outside. The heterogeneity of the equation depends on the temporal and spatial variables and permits the Laplace transform of the temporal variable. The initial condition contains a restricted function. Objective. To show that the homotopy perturbation transform method (HPTM) is easily applied to linear and nonlinear inhomogeneous pseudodifferential diffusion equations. To prove the solvability and obtain the solution formula for the Cauchy problem series for the given linear and nonlinear diffusion equations. Methods. The problem is solved by the NPTM method, which combines a Laplace transform with a time variable and a homotopy perturbation method (HPM). After the Laplace transform, we obtain an integral equation which is solved as a series by degrees of the entered parameter with unknown coefficients. Substituting the input formula for the solution into the integral equation, we equate the expressions to equal parameter degrees and obtain formulas for unknown coefficients. When solving the nonlinear equation, we use a special polynomial which is included in the decomposition coefficients of the nonlinear function and allows the homotopy perturbation method to be applied as well for nonlinear non-uniform pseudodifferential diffusion equation. Results. The result is a solution of the Cauchy problem for the investigated diffusion equation, which is represented as a series of terms whose functions are found from the parametric series. Conclusions. In this paper we first prove the solvability and obtain the formula for solving the Cauchy problem as a series for linear and nonlinear inhomogeneous pseudodifferential equations.

J. Robert Schrieffer (1931–2019)

With the passing away of Robert Schrieffer a few days ago, one of the pioneering figures in modern theoretical physics is no more. Schrieffer, as a Ph D student, working with his mentor John Bardeen and postdoctoral colleague Leon Cooper, gave to the world the microscopic theory of superconductivity in 1957. (Their theory, unbreakably supported by a host of experiments, is considered the gold standard for the atomic-level understanding of the behaviour of electrons in matter, indeed of all fermions.) The flow of electrical current without any resistance, suddenly turning on in a very cold metal (close to, but above the absolute zero of temperature) is one of the most spectacular and mysterious phenomena in physical sciences. Discovered in 1911, its seductive appeal lured almost all the great names of physics into (unsuccessful) efforts at making sense of the phenomenon.

Ring paradigm as Quantum Gravity

Construction of a model of Quantum Gravity, which will be one day in concordance with experiments, is one of the most fascinating tasks which we have in modern theoretical physics. There are common phenomenons for all of the approaches to quantum gravity, which were developed so far. We mention the non-locality, dark energy and dimensional reduction. Then we introduce the concept of nonlinear graviton and we suggest the mathematical apparatus for Quantum Gravity. We discuss further the problematics of Feynman path integral. We end with a possible experimental evidence for our approach and we pose a list of open questions.

Symmetries and local conservation laws of variational schemes for the surface plasmon polaritons

The relation between symmetries and local conservation laws, known as Noether's theorem, plays an important role in modern theoretical physics. As a discrete analog of the differentiable physical system, a good numerical scheme should admit the discrete local conservation laws and inherent mathematical structures. A class of variational schemes constructed for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasi-neutral background shows good properties in secular simulations of surface plasmon polaritons [Q. Chen et al., Phys. Rev. E 99, 023313 (2019)]. We show the discrete local conservation laws admitted by these schemes. Based on the gauge symmetry of the discrete action functional, a discrete charge conservation law is realized locally, which is consistent with the discrete Euler-Lagrange equations obtained from the variational schemes. Based on the discrete Euler-Lagrange equations, discrete local momentum and energy conservation laws are derived directly, which are rigorous in theory. The preservation of the discrete local conservation laws and Lagrangian symplectic structure ensure that the numerical scheme is correct in physics.

The evolving unity of physics

Modern theoretical physics is indivisible. Ideas flow freely and fruitfully across traditional boundaries separating materials physics, fundamental physics and cosmology. How did this state of affairs come to be? What are its outstanding results? Is there more to come? Frank Wilczek discusses the synergy between the different fields of physics.

Variational Approach in the Theory of Liquid-Crystal State

The variational calculus by Leonhard Euler is the basis for modern mathematics and theoretical physics. The efficiency of variational approach in statistical theory of liquid-crystal state and in general case in condensed state theory is shown. The developed approach in particular allows us to introduce correctly effective pair interactions and optimize the simple models of liquid crystals with help of realistic intermolecular potentials.

Supplement of differential equations of fraction order for forecasting of financial markets

In this paper, the analysis of capital markets takes place using the advection-diffusion equation. It should be noted that the methods used in modern theoretical physics have long been used in the analysis of capital markets. In particular, the Fokker-Planck equation has long been used in finding the probability density function of the return on equity. Throughout the study, a number of authors have considered the supplement of the Fokker-Planck equation in the forecasting of equity markets, as a differential equation of second order. In this paper, the first time capital markets analysis is performed using the fractional diffusion equation. The rationale is determined solely by the application nature, which consists in generation of trading strategy in equity markets with the supplement of differential equation of fractional order. As the subject for studies, the differential operator of fractional order in partial derivatives was chosen – the Fokker-Planck equation. The general solutions of equation are the basis for the forecast on the exchange rate of equities included in the Dow Jones Index Average (DJIA).

Institute of Theoretical Physics Akhiezer. Origins. The first attempt in the USSR

On the 100th anniversary of the National Academy of Sciences of Ukraine & the 90th anniversary of the founding of the NSC KIPT ... In Kharkov, a powerful school of modern theoretical physics was created ...

Complementary Function of Modern Theoretical Physics Represented in Christopher Nolan’s Interstellar

Complementary Function of Modern Theoretical Physics Represented in Christopher Nolan’s Interstellar

Exploring Interacting Topological Insulators with Ultracold Atoms: The Synthetic Creutz-Hubbard Model

Understanding the robustness of topological phases of matter in the presence of strong interactions, and synthesising novel strongly-correlated topological materials, lie among the most important and difficult challenges of modern theoretical and experimental physics. In this work, we present a complete theoretical analysis of the synthetic Creutz-Hubbard ladder, which is a paradigmatic model that provides a neat playground to address these challenges. We put special attention to the competition of correlated topological phases and orbital quantum magnetism in the regime of strong interactions. These results are furthermore confirmed and extended by extensive numerical simulations. Moreover we propose how to experimentally realize this model in a synthetic ladder, made of two internal states of ultracold fermionic atoms in a one-dimensional optical lattice. Our work paves the way towards quantum simulators of interacting topological insulators with cold atoms.

AN ANTHOLOGY OF THE DISTINGUISHED ACHIEVEMENTS IN SCIENCE AND TECHNIQUE. PART 39: NOBEL PRIZE LAUREATES IN PHYSICS FOR 2011-2015

Purpose. Implementation of brief analytical review of the distinguished scientific achievements of the world scientists-physicists, awarded the Nobel Prize on physics for the period 2011-2015. Methodology. Scientific methods of collection, analysis and analytical treatment of scientific and technical information of world level in area of astrophysics, physics of elementary particles, physics of high energies, of modern theoretical and experimental physics. Results. The brief analytical review of the scientific openings and distinguished achievements of scientists-physicists is resulted in area of modern physical and technical problems which were marked the Nobel Prizes on physics for the period 2011-2015. Originality. Systematization is executed with exposition in the short concentrated form of the known scientific and technical materials, devoted opening of acceleration of expansion of Universe, creation of breach technologies of manipulation the quantum systems, theoretical discovery of mechanism of origin of mass of under-atomic particles, invention of effective power sources of light − blue light-emitting diodes and opening of neutrino oscillations. Practical value. Popularization and deepening of scientific and technical knowledges for students, engineers and technical specialists and research workers in area of modern theoretical and experimental physics, extending their scientific range of interests and cooperation in further development of scientific and technical progress in human society.

AN ANTHOLOGY OF THE DISTINGUISHED ACHIEVEMENTS IN SCIENCE AND TECHNIQUE. PART 38: NOBEL PRIZE LAUREATES IN PHYSICS FOR 2005-2010

Purpose. Implementation of brief analytical review of the distinguished scientific achievements of the world scientists-physicists, awarded the Nobel Prize in physics for period 2005-2010 yy. Methodology. Scientific methods of collection, analysis and analytical treatment of scientific and technical information of world level in area of modern theoretical and experimental physics. Results. The brief analytical review of the scientific openings and distinguished achievements of scientists-physicists is resulted in area of modern physical and technical problems which were marked by the Nobel Prizes in physics for the period 2005-2010. Originality. Systematization is executed with exposition in the short concentrated form of the known scientific and technical materials, devoted creation of quantum theory of optical coherentness by scientists-physicists, development of laser exact spectroscopy, opening form of spectrum for a black body and anisotropy of space microwave base-line radiation, opening of effect of giant magnetoresistance, opening of mechanism of spontaneous violation of symmetry in subatomic physics, development of new technology of transmission of light in optical fibres, invention of a semiconductor circuit for registration of images and results of innovative experiments on research of 2D material of graphen. Practical value. Popularization and deepening of scientific and technical knowledges for students, engineers and technical specialists and research workers in area of modern theoretical and experimental physics, extending their scientific range of interests and collaboration in further development of scientific and technical progress in human society.

AN ANTHOLOGY OF THE DISTINGUISHED ACHIEVEMENTS IN SCIENCE AND TECHNIQUE. PART 37: NOBEL PRIZE LAUREATES IN PHYSICS FOR 2000-2004

Purpose. Implementation of brief analytical review of the distinguished scientific achievements of the world scientists-physicists, awarded the Nobel bonus on physics for period 2000-2004. Methodology. Scientific methods of collection, analysis and analytical treatment of scientific and technical information of world level in area of modern theoretical and experimental physics. Results. The brief analytical review of the scientific openings and distinguished achievements of scientists-physicists is resulted in area of modern physical and technical problems which were marked the Nobel Prizes on physics for period 2000-2004. Originality. Systematization is executed with exposition in the short concentrated form of the known scientific and technical materials, devoted creation of semiconductor geterostructures scientists-physicists, integral microcircuit, to the receipt of condensation of Boze-Einstein in rarefied gases of alkaline metals, finding out a space neutrino, opening of space sources of X-rays, development of theory of superconductors and superfluid liquids and opening of asymptotic freedom in the theory of strong interactions of elementary particles . Practical value. Popularization and deepening of scientific and technical knowledges for students, engineers and technical specialists and research workers in area of modern theoretical and experimental physics, extending their scientific range of interests and cooperant of further development of scientific and technical progress in human society .