This book is devoted to the fundamental principles of quantum physics, which are based on the study of the statistical operator and the density matrix, related to each other by an integral representation. The basic equation used in this book is the Lindblad equation for the statistical operator, in which the dissipative operator describes the effect of a thermostat on a quantum system. For the case, when the system is in equilibrium (the density matrix does not depend on time), the author applies the variational principle, which makes it possible to construct new quantum theories. The book consists of 9 chapters.
Chapter 1 is devoted to the stepwise kinetics of solid-phase reactions, when the reaction suddenly stops at a constant temperature. When the temperature rises, the reaction resumes. The author assumes that tunneling transitions of reagents are possible in solids. He developed the theory of stepwise kinetics, applied this theory to a specific reaction and proved that this reaction holds Arrhenius law.
In Chapter 2, the author considered a nonequilibrium quantum system, which is surrounded by a large equilibrium thermostat. For the composite system, the Liouville – von Neumann equation is fulfilled, from which the equation for the density matrix is derived and, as the author proves, this equation is equivalent to the Lindblad equation. In the diagonal form of the matrix, this equation reduces to a quantum kinetic equation.
In Chapter 3, a new theory of superconductivity is developed. Since this phenomenon is observed at a constant temperature, Bondarev has applied the variational principle to describe it. The considered electrons are fermions, that is two electrons cannot be in the same state, which is confirmed by the antisymmetry of the Hamiltonian matrix of the interaction of these two electrons. Based on these two principles, the author has derived an equation for the interaction energy of two electrons. The obtained anisotropic solution shows that electric currents flowing in opposite directions are not equal to each other, determining the phenomenon of superconductivity. The corresponding phenomena observed experimentally are described later in this chapter.
In Chapter 4, the phenomenon of superfluidity is investigated. Bondarev has deduced the heat capacity of this substance, which tends to infinity when the temperature approaches from the left to the value.
Chapter 5 presents a theory about a new calculation of the energy levels of an arbitrary atom. Here Bondarev has proposed a new formula for the energy, defined in terms of the Hamiltonian of one electron, the Hamiltonian of the interaction of two electrons, and statistical operators. The antisymmetry of the matrix is achieved by writing it through the antisymmetric Slater function.
Chapter 6 examines the operation of a two-level laser. It is found that the well-known kinetic equation is located aside from the quantum equation. In Chapter 2, it was proved that the kinetic equation is obtained from the quantum one when the density matrix has a diagonal form. First, a unitary matrix is found that makes the transition from the coordinate representation, where the original Hamiltonian has four components in the size of 2 × 2, to some representation of the Hamiltonian in a diagonal form. The density matrix in the new representation will also have a diagonal form. As a result, an equation is written for the spectral energy density of laser radiation, the solution of which determines the laser radiation density.
Chapter 7 presents the theory of the quantum harmonic oscillator and the Heisenberg relation. Bondarev finds the dissipative operators of diffusion and damping and with their help shows that the Wigner equation coincides with the Fokker – Planck equation. Further, the author investigates the equation for the statistical operator with a dissipative damping operator, which describes damped oscillations. This chapter also presents theories of ball lightning and LED.
In the Chapter 8, an equation for the density matrix of a system of identical particles is derived, on the base of which the quantum theories of the spaser and graphene are constructed.
Final Chapter 9 presents the author’s view of the future of quantum physics. The author discusses the advantages and shortcomings of the currently used basic equations and establishes promising directions for further research in the field of quantum physics.
In general, the monograph under review presents interesting approaches and new theories based on the physical principles of quantum physics and the corresponding mathematical apparatus. The book can be useful for students, graduate students and theoretical physicists who study complex physical phenomena such as superconductivity, superfluidity, ball lightning, laser and LED operation.
Ivan A. Parinov, ,
Dr. Sc., Chief Researcher of the I. I. Vorovich Institute Mathematics,
Mechanics and Computer Science, Southern Federal University, Rostov-on-Don, Russia
Book Information:
Title: Density Matrix Theories in Quantum Physics
Author: Boris V. Bondarev
ISBN: 9789811475399 (Print)
ISBN: 9789811475412 (Ebook)
Year of Publication: 2020
Website link: https://benthambooks.com/book/9789811475412/
Bentham Books Bulletin 