Density Matrix Theories In Quantum Physics
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Density Matrix Theories in Quantum Physics
Author: Boris V. Bondarev
language: en
Publisher: Bentham Science Publishers
Release Date: 2020-11-03
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.
Density Matrix Theory and Applications
Author: Karl Blum
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-06-29
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 variables. The use of density matrix methods also has the advan tage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incompletely 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.
Many-Body Quantum Theory in Condensed Matter Physics
Author: Henrik Bruus
language: en
Publisher: Oxford University Press
Release Date: 2004-09-02
The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.