Download or read book Density Matrix Theories in Quantum Physics written by Boris V. Bondarev and published by Bentham Science Publishers. This book was released on 2020-11-03 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Density Matrix Theories in Quantum Physics, the author explores new possibilities for the main quantities in quantum physics – the statistical operator and the density matrix. The starting point in this exploration is the Lindblad equation for the statistical operator, where the main element of influence on a system by its environment is the dissipative operator. Bondarev has developed the theory of the harmonic oscillator, in which he finds the density matrix and proves the Heisenberg relation. Bondarev has written the dissipative diffusion and attenuation operators and proven the equivalence of the Wigner and Fokker–Planck equations using them. He further develops theories of the light-emitting diode and ball lightning. Bondarev also derives equations for the density matrix of a single particle and a system of identical particles. These equations have a remarkable property: when the density matrix has a diagonal shape they turn into a quantum kinetic equation for probability. Additional chapters in the book present new theories of experimentally discovered phenomena, such as the step kinetics of bimolecular reactions in solids, superconductivity, superfluidity, the energy spectrum of an arbitrary atom, lasers, spasers, and graphene. Density Matrix Theories in Quantum Physics is an informative reference for theoretical physicists interested in new theories on the subject of complex physical phenomena, quantum theory and density matrices.
Download or read book Density Matrix Theory and Applications written by Karl Blum and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary vari ables. The use of density matrix methods also has the advantage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incom~'\etely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.
Download or read book Statistical Operator and Density Matrix written by Boris Vladimirovich Bondarev and published by Scientific Research Publishing, Inc. USA. This book was released on 2022-03-29 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Theory and Quantum Mechanics written by Valter Moretti and published by Springer. This book was released on 2018-01-30 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."
Download or read book Consistent Quantum Theory written by Robert B. Griffiths and published by Cambridge University Press. This book was released on 2003-11-13 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.
Download or read book Lectures on Quantum Statistics written by Werner Ebeling and published by Springer. This book was released on 2019-05-11 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most of the matter in our universe is in a gaseous or plasma state. Yet, most textbooks on quantum statistics focus on examples from and applications in condensed matter systems, due to the prevalence of solids and liquids in our day-to-day lives. In an attempt to remedy that oversight, this book consciously focuses on teaching the subject matter in the context of (dilute) gases and plasmas, while aiming primarily at graduate students and young researchers in the field of quantum gases and plasmas for some of the more advanced topics. The majority of the material is based on a two-semester course held jointly by the authors over many years, and has benefited from extensive feedback provided by countless students and co-workers. The book also includes many historical remarks on the roots of quantum statistics: firstly because students appreciate and are strongly motivated by looking back at the history of a given field of research, and secondly because the spirit permeating this book has been deeply influenced by meetings and discussions with several pioneers of quantum statistics over the past few decades.
Download or read book Lectures On Quantum Theory Mathematical And Structural Foundations written by Chris J. Isham and published by Allied Publishers. This book was released on 2001 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Open Quantum Systems written by Heinz-Peter Breuer and published by Oxford University Press, USA. This book was released on 2002 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented. The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.
Download or read book Laser Cooling and Trapping written by Harold J. Metcalf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for advanced undergraduates and beginning graduates with some basic knowledge of optics and quantum mechanics, this text begins with a review of the relevant results of quantum mechanics, before turning to the electromagnetic interactions involved in slowing and trapping atoms and ions, in both magnetic and optical traps. The concluding chapters discuss a broad range of applications, from atomic clocks and studies of collision processes, to diffraction and interference of atomic beams at optical lattices and Bose-Einstein condensation.
Download or read book Random Matrices and the Statistical Theory of Energy Levels written by M. L. Mehta and published by Academic Press. This book was released on 2014-05-12 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Matrices and the Statistical Theory of Energy Levels focuses on the processes, methodologies, calculations, and approaches involved in random matrices and the statistical theory of energy levels, including ensembles and density and correlation functions. The publication first elaborates on the joint probability density function for the matrix elements and eigenvalues, including the Gaussian unitary, symplectic, and orthogonal ensembles and time-reversal invariance. The text then examines the Gaussian ensembles, as well as the asymptotic formula for the level density and partition function. The manuscript elaborates on the Brownian motion model, circuit ensembles, correlation functions, thermodynamics, and spacing distribution of circular ensembles. Topics include continuum model for the spacing distribution, thermodynamic quantities, joint probability density function for the eigenvalues, stationary and nonstationary ensembles, and ensemble averages. The publication then examines the joint probability density functions for two nearby spacings and invariance hypothesis and matrix element correlations. The text is a valuable source of data for researchers interested in random matrices and the statistical theory of energy levels.
Download or read book Statistical Physics of Particles written by Mehran Kardar and published by Cambridge University Press. This book was released on 2007-06-07 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.
Download or read book Statistical Mechanics written by R.K. Pathria and published by Elsevier. This book was released on 2017-02-21 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Mechanics discusses the fundamental concepts involved in understanding the physical properties of matter in bulk on the basis of the dynamical behavior of its microscopic constituents. The book emphasizes the equilibrium states of physical systems. The text first details the statistical basis of thermodynamics, and then proceeds to discussing the elements of ensemble theory. The next two chapters cover the canonical and grand canonical ensemble. Chapter 5 deals with the formulation of quantum statistics, while Chapter 6 talks about the theory of simple gases. Chapters 7 and 8 examine the ideal Bose and Fermi systems. In the next three chapters, the book covers the statistical mechanics of interacting systems, which includes the method of cluster expansions, pseudopotentials, and quantized fields. Chapter 12 discusses the theory of phase transitions, while Chapter 13 discusses fluctuations. The book will be of great use to researchers and practitioners from wide array of disciplines, such as physics, chemistry, and engineering.
Download or read book 2D NMR written by Gh. D. Mateescu and published by Prentice Hall. This book was released on 1993 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an experimentally-based, clear explanation of the density-matrix and product operator treatments, thus allowing non-experts to work out sequences of varying degrees of complexity.
Download or read book Statistical Mechanics of Nonequilibrium Processes written by Dmitriĭ Nikolaevich Zubarev and published by . This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantum Entropy and Its Use written by M. Ohya and published by Springer Science & Business Media. This book was released on 2004-03-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous fundamental properties of quantum information measurement are developed, including the von Neumann entropy of a statistical operator and its limiting normalized version, the entropy rate. Use of quantum-entropy quantities is made in perturbation theory, central limit theorems, thermodynamics of spin systems, entropic uncertainty relations, and optical communication. This new softcover corrected reprint contains summaries of recent developments added to the ends of the chapters.
Download or read book Quantum Kinetic Theory written by Michael Bonitz and published by Springer. This book was released on 2015-11-20 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.
Download or read book Lectures on Quantum Mechanics for Mathematics Students written by L. D. Faddeev and published by American Mathematical Soc.. This book was released on 2009 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the relation between classical and quantum mechanics. This book contains a discussion of problems related to group representation theory and to scattering theory. It intends to give a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework.
