Linear Stability Analysis

[0.1.2] - 2016-11-21

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• Linear stability analysis.

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A Prerelease with plentiful contents

Table of Contents

1. Preliminary
   1.1. Common Sense
   1.1.1. Units
   1.1.2. Useful Conversions in Neutrino Physics
   1.1.3. Diagrams
   1.1.4. Refs and Notes
   1.2. Physics
   1.2.1. Reactions Related to Neutrinos
   1.2.2. What is a Neutrino Particle?
   1.2.3. Chirality and Helicity
   1.2.4. Majorana or Dirac
   1.2.5. States
   1.2.6. Statistics
   1.2.7. Refs & Notes
   1.3. Mathematics Related
   1.3.1. Pauli Matrices
   1.3.2. The Equations
   1.3.3. Equation Solving
   1.3.4. Qualitative Analysis
   1.4. Questions
   1.4.1. Astrophysics
2. Masses of Neutrinos
   2.1. Theories of Neutrino Mass
   2.1.1. Majorana Particle
   2.1.2. Refs & Notes
   2.2. Determine Neutrino Mass
   2.2.1. Experiments
3. Experiments
   3.1. Neutrino Sources
   3.2. Concepts in Experiments
   3.2.1. Prediction of Theory
   3.2.2. Sensitivity
   3.2.3. Review of Experiments
   3.2.4. Low Energy Neutrino Detection
   3.2.5. Refs & Notes
   3.3. List of Neutrino Experiments
4. Oscillations
   4.1. How Do Neutrinos Propagate
   4.1.1. Wave Packet Treatment
   4.2. Two-flavor and Three-flavor
   4.2.1. Oscillation Scales
   4.2.2. Refs & Notes
   4.3. Evidence of Oscillations
   4.3.1. Results of Experiments
   4.3.2. Hamiltonian, Equation of Motion and Solution
   4.3.3. Matter Effect - An Introduction
   4.3.4. Q&A
   4.4. Vacuum Oscillation
   4.4.1. Survival Problem
   4.4.2. Two Flavor States
   4.4.3. The Standard Math for 2 Flavor Neutrino
   4.4.4. Numerical Results for 2 Flavor Neutrino Oscillations
   4.4.5. 3 Flavor Oscillations
   4.4.6. Ternary Diagram
   4.4.7. Understanding the Mixing Angles
   4.4.8. Refs and Notes
5. Interaction With Matter
   5.1. MSW Effect
   5.1.1. An Introduction to MSW Effect
   5.1.2. Solar Neutrinos and MSW Effect
   5.1.3. Numerical Results
   5.1.4. Experiments
   5.1.5. MSW Triangle
   5.1.6. Refs and Notes
   5.2. MSW Refraction, Resonance and Non-adiabacity
   5.2.1. 2 Flavor Neutrino Oscillations and Matter Effect
   5.2.2. Constant Electron Number Density
   5.2.3. Adiabatic Limit
   5.2.4. General Discussion of Matter Effect
   5.2.5. Landau-Zener Transition of Neutrinos
   5.3. Parametric Resonance
   5.3.1. Parametric Resonance
   5.3.2. Castle Wall Potential
   5.3.3. Refs and Notes
   5.4. Matter as Driven Energy
   5.4.1. Oscillation in Matter and Vacuum
   5.4.2. Rabi-like Transition
   5.4.3. Analytical Attack
   5.4.4. Period Matter Potential (NON-PHYSICAL)
   5.4.5. Constant Matter with Periodic Perturbation
   5.4.6. Resoances
   5.4.7. Refs & Notes
6. Collective Behavior
   6.1. Collective Phenomenon
   6.1.1. Spectral Split
   6.2. Bipolar Model
   6.3. Dense Homogeneous Isotropic Neutrino Gas
   6.4. Refs & Notes
7. Instability
   7.1. Self-Interaction Instability
   7.1.1. Linear Stability Analysis
   7.1.2. Neutrino Self Interaction and Instability
   7.1.3. Refs & Notes
   7.2. List of Instabilities
   7.2.1. Bimodal Instability
   7.2.2. Multi-angle Instability
   7.2.3. MAA
   7.3. Bimodal Oscillations
8. Pictures
   8.1. Some Useful Physics Pictures
   8.1.1. Magnetic Spin
   8.1.2. Coupled Pendulum
   8.1.3. Gyroscope or Spinning Top Picture
   8.1.4. Polarization Vector
   8.1.5. Neutrino-neutrino Interaction and BCS Theory
   8.2. Flavor Isospin
   8.2.1. Neutrino Flavour Isospin
   8.2.2. Graphical Representation of Flavor Isospin
   8.2.3. Refs & Notes
9. Models
   9.1. Homogeneous and Isotropic Neutrino Gas
   9.1.1. What to expect?
   9.1.2. Solving Eqns
10. Statistical Physics
    10.1. Neutrino Oscillation And Master Equation
    10.1.1. Quantum Master Equation
    10.1.2. Vacuum Oscillation Master Equation
    10.1.3. Neutrino Oscillation in Matter - A Possible Master Equation Approach
    10.1.4. Self Interaction Between Neutrinos
    10.1.5. Refs & Notes
11. Geometric Phase
    11.1. Review of Geometric Phases
    11.1.1. Berry Phase
    11.1.2. Refs & Notes
    11.2. Neutrino Oscillations and Berry Phase
    11.2.1. Notes & References
12. Astrophysics
    12.1. Stars as Neutrino Factories
    12.1.1. Neutrinos in Astrophysics
    12.1.2. Solar Neutrino Spectrum
    12.1.3. Neutrino Spectrum with Thermal and Relativistic Modifications
    12.1.4. Supernova Neutrinos and Conclusion
    12.1.5. Refs & Notes
    12.2. Supernova
    12.2.1. Neutrino Oscillations
13. Gravity
    13.1. Effect of Gravitation
    13.1.1. Evaluation
    13.1.2. Refs & Notes
14. Neutrinos and Cosmology
    14.1. Baryon Asymmetry in the Univserse
    14.2. Cosmic Neutrino Background
    14.2.1. Cosmic Neutrino Background
    14.2.2. Refs & Notes
15. Other Topics
    15.1. Basis
    15.1.1. Rotation of States
    15.1.2. Rotation of Pauli Matrices
    15.1.3. Rotation of Hamiltonian
    15.1.4. Examples of Rotating Basis
    15.1.5. Refs & Notes
    15.2. Qualitative Analysis
    15.2.1. Oscillation Period, Frequency and Energy
    15.2.2. Refs and Notes
    15.3. Neutrino Cheat Sheet
    15.3.1. Refs & Notes
    15.4. Frequently Asked Questions
    15.4.1. Refs & Notes
16. References
17. Acknowledgement

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