Mathematical Modeling of Wave Phenomena: 3rd Conference on Mathematical Modeling of Wave Phenomena, 20th Nordic Conference on Radio Science and Communications
Börje Nilsson, Louis Fishman, Anders Karlsson, Sven Nordebo
This conference illuminates and benefits from relations between different types of waves, i.e., quantum physics methods in classical wave modeling. The proceedings are intended for researchers and graduate students in fundamental as well as applied sciences. The preface classifies and summarizes the conference, giving relations between the papers.
This conference illuminates and benefits from relations between different types of waves, i.e., quantum physics methods in classical wave modeling. The proceedings are intended for researchers and graduate students in fundamental as well as applied sciences. The preface classifies and summarizes the conference, giving relations between the papers.
The conference brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantically methods, and other computer science techniques applied to the study of physical behaviour in general. Work that applies structures and methods inspired by quantum theory to other fields (including computer science) is also welcome. With members from around the world focused on Quantum physics and Nuclear Engineering this is your best opportunity to reach the largest assemblage of participants from the universities, colleges, research centres, societies, institutions, labs, associations, communities and companies etc. We want to make a worldwide meet in which data between researchers from the different controls can be effectively traded. The explanation behind bringing the general population at the meetings together is to catalyse empowering trades and connections between experts in different fields, from physical science to engineering. It will make new interdisciplinary systems and permit members to trade know-how and data to accomplish speedier and better results.
The 10th Quantum Mathematics International Conference (Qmath10) gave an opportunity to bring together specialists interested in that part of mathematical physics which is in close connection with various aspects of quantum theory. It was also meant to introduce young scientists and new tendencies in the field.This collection of carefully selected papers aims to reflect recent techniques and results on Schroedinger operators with magnetic fields, random Schroedinger operators, condensed matter and open systems, pseudo-differential operators and semiclassical analysis, quantum field theory and relativistic quantum mechanics, quantum information, and much more. The book serves as a concise and well-documented tool for the more experimented scientists, as well as a research guide for postgraduate students.
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes the dynamics of the respective wave. Different wave phenomena are thus governed by different differential equations. Here we want to emphasize the experimental approach to matter waves, but before doing so we will discuss and test the procedure for other types of waves, in particular water waves.
In recent decades, substantial theoretical and experimental progress was achieved in understanding the quantum nature of physical phenomena that serves as the foundation of present and future quantum technologies. Quantum correlations like the entanglement of the states of composite systems, the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, connected with these phenomena, uncertainty relations for conjugate variables and entropies, like Shannon and Rényi entropies, and the inequalities for spin states, like Bell inequalities, reflect the recently understood quantum properties of micro and macro systems. The mathematical methods needed to describe all quantum phenomena mentioned above were also the subject of intense studies in the end of the last, and beginning of the new, century. In this section of CAMOP 'Mathematical Methods of Studying Physical Phenomena' new results and new trends in the rapidly developing domain of quantum (and classical) physics are presented. Among the particular topics under discussion there are some reviews on the problems of dynamical invariants and their relations with symmetries of the physical systems. In fact, this is a very old problem of both classical and quantum systems, e.g. the systems of parametric oscillators with time-dependent parameters, like Ermakov systems, which have specific constants of motion depending linearly or quadratically on the oscillator positions and momenta. Such dynamical invariants play an important role in studying the dynamical Casimir effect, the essence of the effect being the creation of photons from the vacuum in a cavity with moving boundaries due to the presence of purely quantum fluctuations of the electromagnetic field in the vacuum. It is remarkable that this effect was recently observed experimentally. The other new direction in developing the mathematical approach in physics is quantum tomography that provides a new vision of quantum states. In the tomographic picture of quantum mechanics, the states are identified with fair conditional probability distributions, which contain the same information on the states as the wave function or the density matrix. The mathematical methods of the tomographic approach are based on studying the star-product (associative product) quantization scheme. The tomographic star-product technique provides an additional understanding of the associative product, which is connected with the existence of specific pairs of operators called quantizers and dequantizers. These operators code information on the kernels of all the star-product schemes, including the traditional phase-space Weyl–Wigner–Moyal picture describing the quantum-system evolution. The new equation to find quantizers, if the kernel of the star product of functions is given, is presented in this CAMOP section. For studying classical systems, the mathematical methods developed in quantum mechanics can also be used. The case of paraxial-radiation beams propagating in waveguides is a known example of describing a purely classical phenomenon by means of quantum-like equations. Thus, some quantum phenomenon like the entanglement can be mimicked by the properties of classical beams, for example, Gaussian modes. The mathematical structures and relations to the symplectic symmetry group are analogous for both classical and quantum phenomena. Such analogies of the mathematical classical and quantum methods used in research on quantum-like communication channels provide new tools for constructing a theoretical basis of the new information–transmission technologies. The conventional quantum mechanics and its relation to classical mechanics contain mathematical recipes of the correspondence principle and quantization rules. Attempts to find rules for deriving the quantum-mechanical formalism starting from the classical field theory, taking into account the influence of classical fluctuations of the field, is considered in these papers. The methods to solve quantum equations and formulate the boundary conditions in the problems with singular potentials are connected with the mathematical problems of self-adjointness of the Hamiltonians. The progress and some new results in this direction are reflected in this CAMOP section. The Gaussian states of the photons play an important role in quantum optics. The multimode electromagnetic field and quantum correlations in the Gaussian states are considered in this section. The new results in the statistical properties of the laser radiation discussed here are based on applications of mathematical methods in this traditional domain of physics. It is worth stressing that the universality of the mathematical procedures permitted to consider the physical phenomena in the ocean is on the same footing as the phenomena in the microworld. In this CAMOP section, there are also papers devoted to traditional problems of solving the Schrödinger equation for interesting quantum systems. Recently obtained results related to different domains of theoretical physics are united by applying mathematical methods and tools, that provide new possibilities to better understand the theoretical foundations needed to develop new quantum technologies like quantum computing and quantum communications. The papers are arranged alphabetically by the name of the first author. We are grateful to all authors who accepted our invitation to contribute to this CAMOP section.
This special volume of Journal of Physics: Conference Series is dedicated to the proceedings of "International Conference on Quantum Science and Applications (ICQSA-2016)". The conference was organized by the Centre for Quantum Research and Applications at Eskisehir Osmangazi University, Eskisehir, Turkey. It was held in Eskisehir Osmangazi University Congress and Culture Centre during May 25-27, 2016 http://icqsa2016.ogu.edu.tr . It gathered actively 143 participants from different disciplines in natural and applied sciences coming from 16 different countries from all over the word. It was the first international conference in its content on the scientific research fields of quantum science and applications in Turkey. It also consisted of 12 plenary lectures and 119 contributed oral presentations covering interdisciplinary fields of research. The ICQSA-2016 conference focused on recent modern theoretical and experimental developments of quantum science in multi-disciplinary aspects of areas of mathematics, physics, statistics, chemistry, biology, computer science, electronics, informatics, medicine, education, etc. It served as an interaction platform for students, researchers, public, and private sector delegates for sharing new scientific and technological ideas on quantum applications in science and technology. The topics of the conference were: Quantum theory and quantum computing, quantum information theory and its applications, quantum statistics and its applications, quantum thermodynamics, quantum cryptography, classical and quantum symmetries, quantum calculus in science, engineering, medicine, education, etc., classical and quantum integrable systems, modeling and numerical methods in quantum systems, other modern mathematical methods in science and technology. Each of the submitted papers for this special volume of the proceedings of ICQSA-2016 has been reviewed by external referees. There are 36 accepted papers. Besides, it is worth pointing out that a great deal of interest shown by the participants of the ICQSA-2016 conference gives hope for the continuation of this meeting in the following years. The conference organization was sponsored by Eskisehir Osmangazi University (ESOGU), Eskisehir Tepebasi Municipality, the Scientific and Technological Research Council of Turkey (TUBITAK) under the project number 113F226. Other supporters of this organization were: Eskisehir Metropolitan Municipality, Eskisehir Governorship Provincial Directorate of Culture and Tourism, Pegem Academy Publishing Company. In addition, this special volume is supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the project number 113F226. Finally, our special thanks go to the Scientific and Organizing Committee members, to the sponsors and supporters, and to all of the participants. We hope this special volume will provide a useful resource for students, experts, and other participants, who are interested in interdisciplinary fields of quantum science and applications.