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Density Matrix Theories in Quantum Physics

  • ID: 5215258
  • Book
  • November 2020
  • Bentham Science Publishers Ltd
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, super fluidity, 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.
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Preface

Introduction

Chapter 1 New Theory of Step Kinetics
1. Step Kinetics of Reactions in Solids Correlation Theory
1.1. Introduction
1.2. Kinetic Theory of Solid-Phase Reactions
1.3. Uniform Distribution of Particles in the Matrix
1.4. Conclusion
2. Influence of Hydrogen Atom Tunnel Junction on the Step Kinetics of Solid-Phase Reactions with Participation of Radicals In Organic Substances
2.1. Introduction
2.2. Tunnel Junction
2.3. Conclusion
2.4. Experimental Data Processing
3. Death Kinetics of Stabilized Electrons in Polyethylene
3.1. Introduction
3.2. Study of Loss of Electrons
3.3. Explanation Experiment Theory
3.4. Conclusion
  • References
  • Additional Literature
Chapter 2 Density Matrix
2.1. Equation for Density Matrix Derivation of Quantum Markov Kinetic Equation from the Liouville − Von Neumann Equation
2.1.1 Introduction
2.1.2. Method of Density Matrix and Non-Stationary Perturbation Theory
2.1.3. Quantum Markov Kinetic Equation
2.1.4. Unitary Transformation
2.1.5. Conclusion
  • References
  • Additional Literature
Chapter 3 New Theory of Superconductivity
3.1. History of Superconductivity
3.1.1. Discovery of Superconductivity
3.1.2. Meissner - Ochsenfeld Effect. Silsbee Effect
3.1.3. Energy Gap
3.2. Density Matrix Method Variational Principle For Equilibrium Fermions System
3.2.1. Lagrange Method
3.2.2. the Hierarchy of Density Matrices
3.2.3. Introduction of the Occupation Numbers
3.2.4. the Unitary Transformation
3.2.5. Internal Energy of Fermions System
3.2.6. Entropy
3.2.7. Fermi − Dirac Function
3.2.8. Mean-Field Approximation for Fermions System
3.2.9. Multiplicative Approach of Second Order
3.3. Energy of Electrons in Crystal Lattice
3.3.1. Unitary Transformation
3.3.2. Hamiltonian of Fermions System
3.3.3. the Energy of the Electrons in the Crystal Lattice
3.3.4. Fermi − Dirac Function and Distribution of Electrons Over the Wave Vectors
3.3.5. We Also Need to Find the Thermodynamic Functions
3.4. Anisotropy and Superconductivity
3.4.1. Equation for Probability and Model Hamiltonian
3.4.2. Anisotropy
3.4.3. Mean-Field Approximation
3.4.4. Isotropic Distribution of Electrons
3.4.5. Anisotropic Distribution of Electrons
3.4.6. Electron Distribution at T = 0
3.4.7. Superconductivity
3.4.8. Normalization Condition and Electron Energy
3.4.9. Electron Energy Calculation at T = 0
3.4.10. Real Distribution Function
3.4.11. Electron Mean Energy
3.4.12. Type-I and Type-Ii Superconductors
3.4.13. Density Matrix
3.4.14. Silsby Effect
3.4.15. Conclusion
3.5. Superconductivity Disappears
3.5.1. the Mean-Field Approximation for I = 0
3.5.2. Real Distribution of the Electrons
3.5.3. Energy Gap
3.5.4. Medium Electron Energy
3.6. Superconductivity Type-Ii
3.6.1. Mean-Field Approximation for J = 0
3.6.2. Distribution of Electrons at T = 0
3.6.3. Superconductivity Energy of States
3.6.4. Order Parameter
3.6.5. Mean Energy Dependence of Single Electron
3.7. Magnetic Field in Superconductor
3.7.1. Wave Function
3.7.2. the Kinetic Energy of Electrons in the Crystal Lattice
3.7.3. the Magnetic Field-Dependent Unitary Transformation
3.7.4. Electrons Energy in Wave Vector Space
3.7.5. Equation for Electron Wave Vector Distribution Function
3.7.6. Meissner - Osnfeld Effect
3.7.8. the Magnetic Field in a Flat Superconductor
3.7.9. the Magnetic Field in the Superconducting Sphere
3.7.10. Magnetic Field in the Flat Disc of Superconductor
3.7.11. Supercurrent Flowing Through the Coil
3.7.12. Superconductivity Flowing Through the Solenoid
3.7.13. Quantum Levitation and Quantum Trapping
  • References
  • Additional Literature
Chapter 4 New Theoflury of Super-Fluidty
4.1. New Theory of Super-Fluidity Equilibrium Density Matrix Method
4.1.1. Liquid Helium
4.1.2. Uniform Distribution of Particles in Space
4.1.3. Kinetic Energy of Particle
4.1.4. Particle Interaction Energy
4.1.5. Gas Internal Energy
4.1.6. Particle Pulse Distribution Function
4.1.7. Chemical Potential
4.1.8. Order Parameter
4.1.9. Gas Internal Energy Dependence on Temperature
4.1.10. Heat Capacity of Gas
4.1.11. Energy Spectrum of Particles
4.1.12. Superfluidity
4.1.13. Conclusion
  • References
  • Additional Literature
Chapter 5 New Theory of Arbitrary Atom
5.1. Мethod of Density Matrix New Calculation of Energy Level Of Electrons in Atom
5.1.1. Introduction
5.1.2. Statistical Operator
5.1.3. Density Matrix
5.1.4. Hamiltonian of the Electron System
5.1.5. Matrix Elements of the Hamiltonian
5.1.6. Wave Function of One Electron Moving Around an Arbitrary Nucleus
5.1.7. Matrix Elements of the Electron Interaction Hamiltonian
5.1.8. the Energy of the Electrons in Core is Recorded Using Density Matrix
5.1.9. the Pure State of Electrons in Atom
5.1.10. Conclusion
5.1.11. Comment
  • References
  • Additional Literature
Chapter 6 New Theory of Laser
6.1. Density Matrix Method in Two-Level Laser Theory
6.1.1. Introduction
6.1.2. Kinetics of Quantum Transitions
6.1.3. Density Matrix
6.1.4. Equation for the Density Matrix
6.1.5. Equation for Density Matrix of the First-Order Approximation
6.1.6. Equation for the Density Matrix of Zero-Order
6.1.7. Diagonal Hamiltonian
6.1.8. Density Matrix in Κ-Representation
6.1.9. the Transition Density Matrix from 𝜅-Representation in Initial Α-Representation
6.1.10. Dissipative Matrix
6.1.11. the Equation for the Density Matrix in 𝜅-Representation
6.1.12. Kinetics of Laser
6.1.13. Equation for Non-Diagonal Density Matrix
6.1.14. Kinetics of Radiation
6.1.15. Conclusion
  • References
Chapter 7 Dissipative Operator
7.1. Lindblad Equation for Harmonic Oscillator Uncertainty Relation Depending on Temperature
7.1.1. Lindblad Equation
7.1.2. Energy Representation
7.1.3. Mean Value of the Coordinate
7.1.4. Mean Oscillator Energy
7.1.5. Kinetic Equation Expressed in Terms of Coordinate and Momentum Operators
7.1.6. Coordinate Representation
7.1.7. Momentum Representation
7.1.8. Wigner Function
7.1.9. Lindblad Equation is First-Order Approximation
7.1.10. Conclusion
7.2. Statistical Operator in Theory of Quantum Oscillator Dissipative Operator Damping
7.2.1. Introduction
7.2.2. Equation for Statistical Operator That Describes Damped Oscillations
7.2.3. Average Values of Position and Momentum
7.2.4. the Average Values of Squares of Position and Momentum
7.2.5. Conclusion
7.3. Particle in a Stochastic Environment Dissipative Matrix
7.3.1. Particle in a Homogeneous Isotropic Continuum
7.3.2. Equation for the Density Matrix
7.3.3. Equation for the Wigner Function
7.3.4. Conclusion
7.4. Density Matrix Method in Quantum Theory of Light Emitting Diode (Led)
7.4.1. Introduction
7.4.2. Light-Diode
7.4.3. Connect Led
7.4.4. Equilibrium Distribution of Electron Energy
7.4.5. Impurity Semiconductors of P -Type
7.4.6. N -Type Impurity Semiconductors
7.4.7. P-N Transition
7.4.8. Lindblad Equation. Statistical Operator
7.4.9. Density Matrix
7.4.10. Lindblad Equation Dissipative Operator
7.4.11. Equations for Density Matrix
7.4.12. Wigner Equation
7.4.13. Wigner Equations for Light Diode
7.5. Theory of Ball Lightning
7.5.1. Introduction
7.5.2. Interaction of Electrons with Nuclei
7.5.3. Lindblad Equation
7.5.4. Dissipative Diffusion and Attenuation Operators
7.5.5. Equation for Statistical Operator of Atomic Nuclei
7.5.6. Average Values of Atomic Nucleus Coordinates
7.5.7. Average Value of Atomic Nucleus Pulse
7.5.8. Equation of Motion of Average Value of Nucleus Coordinates
7.5.9. Equation for Average Value 〈𝑟̂2〉
7.5.10. Equation for Average Value of 〈𝑝̂2〉
7.5.11. Equation for Average Value of Operator 𝑟̂ 𝑝̂+ 𝑝̂ 𝑟̂
7.5.12. Solution of Obtained Equations
7.5.13. Equation for Atomic Nucleus Density Matrix in Coordinate Representation
7.5.14. Wigner Equation
7.5.15. Distribution of Atomic Nucleus by Coordinates
7.6. Theory of Tunnel Transitions
7.6.1. Introduction
7.6.2. Lindblad Equation and Dissipative Damping Operator
7.6.3. the Probability of Increasing the Crystal with Increasing Temperature
  • References
  • Additional Literature
Chapter 8. the Beginning of Theoretical Nanophysics
8.1. Equation for Density Matrix Systems of Identical Particles
8.1.1. Introduction
8.1.2. Equation for the Density Matrix of One Particle
8.1.3. the Hierarchy for Statistical Operators
8.1.4. the Equation for Statistical Operators
8.1.5. the Equation for Density Matrix
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  • Boris V. Bondarev
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