Quantum Mechanics of Non Hamiltonian and Dissipative Systems Book

Quantum Mechanics of Non Hamiltonian and Dissipative Systems


  • Author : Vasily Tarasov
  • Publisher : Elsevier
  • Release Date : 2008-06-06
  • Genre: Science
  • Pages : 530
  • ISBN 10 : 0080559719

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Quantum Mechanics of Non Hamiltonian and Dissipative Systems Excerpt :

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. • Requires no preliminary knowledge of graduate and advanced mathematics • Discusses the fundamental results of last 15 years in this theory • Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences

Applications in Physics Book

Applications in Physics


  • Author : Vasily E. Tarasov
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2019-02-19
  • Genre: Mathematics
  • Pages : 327
  • ISBN 10 : 9783110571721

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Applications in Physics Excerpt :

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

Fractional Dynamics Book

Fractional Dynamics


  • Author : Vasily E. Tarasov
  • Publisher : Springer Science & Business Media
  • Release Date : 2011-01-04
  • Genre: Science
  • Pages : 505
  • ISBN 10 : 9783642140037

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Fractional Dynamics Excerpt :

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Fractional Dynamics Book

Fractional Dynamics


  • Author : Joseph Klafter
  • Publisher : World Scientific
  • Release Date : 2012
  • Genre: Mathematics
  • Pages : 530
  • ISBN 10 : 9789814340595

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Fractional Dynamics Excerpt :

This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.

Quantum Mechanics Between Ontology and Epistemology Book

Quantum Mechanics Between Ontology and Epistemology


  • Author : Florian J. Boge
  • Publisher : Springer
  • Release Date : 2018-10-24
  • Genre: Science
  • Pages : 432
  • ISBN 10 : 9783319957654

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Quantum Mechanics Between Ontology and Epistemology Excerpt :

This book explores the prospects of rivaling ontological and epistemic interpretations of quantum mechanics (QM). It concludes with a suggestion for how to interpret QM from an epistemological point of view and with a Kantian touch. It thus refines, extends, and combines existing approaches in a similar direction. The author first looks at current, hotly debated ontological interpretations. These include hidden variables-approaches, Bohmian mechanics, collapse interpretations, and the many worlds interpretation. He demonstrates why none of these ontological interpretations can claim to be the clear winner amongst its rivals. Next, coverage explores the possibility of interpreting QM in terms of knowledge but without the assumption of hidden variables. It examines QBism as well as Healey’s pragmatist view. The author finds both interpretations or programs appealing, but still wanting in certain respects. As a result, he then goes on to advance a genuine proposal as to how to interpret QM from the perspective of an internal realism in the sense of Putnam and Kant. The book also includes two philosophical interludes. One details the notions of probability and realism. The other highlights the connections between the notions of locality, causality, and reality in the context of violations of Bell-type inequalities.

Fractional Quantum Mechanics Book

Fractional Quantum Mechanics


  • Author : Laskin Nick
  • Publisher : World Scientific
  • Release Date : 2018-05-25
  • Genre: Science
  • Pages : 360
  • ISBN 10 : 9789813223813

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Fractional Quantum Mechanics Excerpt :

Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.

Entropy in Foundations of Quantum Physics Book

Entropy in Foundations of Quantum Physics


  • Author : Marcin Pawłowski
  • Publisher : MDPI
  • Release Date : 2020-12-15
  • Genre: Computers
  • Pages : 266
  • ISBN 10 : 9783039289516

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Entropy in Foundations of Quantum Physics Excerpt :

This book is a collection of outstanding papers on various aspects of entropy at the foundation of quantum physics. The covered topics range from purely foundational issues such as contextuality and Bell and Leggett–Garg inequalities to applications such as quantum key distribution, teleportation, and image encoding. The main ingredient binding them together in this book is that in all of the contained papers, entropy plays a key role either as a mathematical tool or as a link which bridges the gap between different fields of science.

The Problem of Time Book

The Problem of Time


  • Author : Edward Anderson
  • Publisher : Springer
  • Release Date : 2017-09-18
  • Genre: Science
  • Pages : 920
  • ISBN 10 : 9783319588483

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The Problem of Time Excerpt :

This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon entertaining background independence in classical (rather than quantum) physics. By this development, and interpreting shape theory as modelling background independence, this book further establishes background independence as a field of study. Background independent mechanics, as well as minisuperspace (spatially homogeneous) models of GR and perturbations thereabout are used to illustrate these points. As hitherto formulated, the different facets of the Problem of Time greatly interfere with each others' attempted resolutions. This book explains how, none the less, a local resolution of the Problem of Time can be arrived at after various reconceptualizations of the facets and reformulations of their mathematical implementation. Self-contained appendices on mathematical methods for basic and foundational quantum gravity are included. Finally, this book outlines how supergravity is refreshingly different from GR as a realization of background independence, and w

Geometric Methods in Physics XXXVIII Book

Geometric Methods in Physics XXXVIII


  • Author : Piotr Kielanowski
  • Publisher : Springer Nature
  • Release Date : 2020-10-27
  • Genre: Mathematics
  • Pages : 381
  • ISBN 10 : 9783030533052

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Geometric Methods in Physics XXXVIII Excerpt :

The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Mathematical Economics Book

Mathematical Economics


  • Author : Vasily E. Tarasov
  • Publisher : MDPI
  • Release Date : 2020-06-03
  • Genre: Business & Economics
  • Pages : 278
  • ISBN 10 : 9783039361182

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Mathematical Economics Excerpt :

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

Symmetries in Science X Book

Symmetries in Science X


  • Author : Bruno Gruber
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Mathematics
  • Pages : 454
  • ISBN 10 : 9781489915375

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Symmetries in Science X Excerpt :

Proceedings an International Symposium held in Bregenz, Austria, July 13-18, 1997

Applications in Physics Book

Applications in Physics


  • Author : Vasily E. Tarasov
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2019-02-19
  • Genre: Mathematics
  • Pages : 314
  • ISBN 10 : 9783110571707

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Applications in Physics Excerpt :

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics.

Lagrangian and Hamiltonian Methods for Nonlinear Control 2003 Book

Lagrangian and Hamiltonian Methods for Nonlinear Control 2003


  • Author : A Astolfi
  • Publisher : Elsevier
  • Release Date : 2003-10-07
  • Genre: Mathematics
  • Pages : 318
  • ISBN 10 : 0080442781

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Lagrangian and Hamiltonian Methods for Nonlinear Control 2003 Excerpt :

This is the second of a series of IFAC Workshops initiated in 2000. The first one chaired and organized by Profs. N. Leonard and R. Ortega, was held in Princeton in March 2000. This proceedings volume looks at the role-played by Lagrangian and Hamiltonian methods in disciplines such as classical mechanics, quantum mechanics, fluid dynamics, electrodynamics, celestial mechanics and how such methods can be practically applied in the control community. *Presents and illustrates new approaches to nonlinear control that exploit the Lagrangian and Hamiltonian structure of the system to be controlled *Highlights the important role of Lagrangian and Hamiltonian Structures as design methods

Quantum Mechanics Book

Quantum Mechanics


  • Author : Harish Parthasarathy
  • Publisher : CRC Press
  • Release Date : 2021-10-01
  • Genre: Science
  • Pages : 325
  • ISBN 10 : 9781000465389

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Quantum Mechanics Excerpt :

This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classifica

Transport of Information Carriers in Semiconductors and Nanodevices Book

Transport of Information Carriers in Semiconductors and Nanodevices


  • Author : El-Saba, Muhammad
  • Publisher : IGI Global
  • Release Date : 2017-03-31
  • Genre: Technology & Engineering
  • Pages : 677
  • ISBN 10 : 9781522523130

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Transport of Information Carriers in Semiconductors and Nanodevices Excerpt :

Rapid developments in technology have led to enhanced electronic systems and applications. When utilized correctly, these can have significant impacts on communication and computer systems. Transport of Information-Carriers in Semiconductors and Nanodevices is an innovative source of academic material on transport modelling in semiconductor material and nanoscale devices. Including a range of perspectives on relevant topics such as charge carriers, semiclassical transport theory, and organic semiconductors, this is an ideal publication for engineers, researchers, academics, professionals, and practitioners interested in emerging developments on transport equations that govern information carriers.