Stability of Matter

from atoms in the microscopic world to stars in astrophysical scale

This web site will be soon moved to http://www.cc.matsuyama-u.ac.jp/~dan/stability/

We investigate the mathematical analysis of quantum mechanics for many-body systems, a large number of elements interacting with each other. Our research project will contribute

Analysis Seminar

The $N$-Representability Problem for Reduced Density Operators

Analysis Seminar

References

Monday Friday Seminar

Seminar blackboard

Textbook

Seminar Notes

  1. Slater determinant is the simplest example of antisymmetric functions
  2. The Space of Wave Function (24 Oct. 2016)
  3. Density Matrices (31 Oct. 2016)
  4. Trace of Operators (21 Nov. 2016)
  5. Density Matrices (21 Nov. 2016)
  6. Reduced Density Matrices (28 Nov. 2016)
  7. Admissible One-Body Density Matrices (5 Dec. 2016)
  8. Admissible One-Body Density Matrices for Fermions (12 Dec. 2016)
  9. Under consideration (19 Dec. 2016)
  10. Under construction (16 Jan. 2017)
  11. Sufficiency (15 Feb. 2017)
  12. A completion of the proof (24 Feb. 2017)
  13. Many Body Hamiltonian (3 Mar. 2017)
  14. Gamma function (30 Mar. 2017)
  15. Coulomb Potential (2 May 2017)
  16. Basic Electrostatic Inequality (12 May 2017)
  17. Baxter's Inequality (19 May 2017)
  18. Refined Electrostatic Inequality (26 May 2017)
  19. The Method of Image Charge (2 June 2017)
  20. Stability of Non-Relativistic Matter (23 June 2017)
  21. Alternative Proof (30 June 2017)
  22. Extensivity and Bosonic Instability (21 July 2017)
  23. The N7/5 Law (28 July 2017)[New!]
  1. Prologue
  2. Introduction to Elementary Quantum Mechanics and Stability of the First Kind
    1. Introduction
    2. Brief Outline of the Book
  3. Many-Particle Systems and Stability of the Second Kind
  4. Lieb-Thirring and Related Inequalities
  5. Electrostatic Inequalities
  6. An Estimation of the Indirect Part of the Coulomb Energy
  7. Stability of Non-Relativistic Matter
  8. Stability of Relativistic Matter
  9. Magnetic Fields and the Pauli Operator
  10. The Dirac Operator and the Brown-Ravenhall Model
  11. Quantized Electromagnetic Fields and Stability of Matter
  12. The Inonization Problem, and the Dependance of the Energy on N and M Separately
  13. Gravitational Stability of White Dwarfs and Neutron Stars
  14. The Thermodynamic Limit for Coulomb Systems
Arnold Sommerfeld, the fine structure constant

Research Review around PDE

Research Review

"Lieb-Thirring inequalities for eigenvalues of Schrödinger and Dirac operators," Seminar on Spectral Theory at Gakushuin University, Japan

Seminar

"The approach to Lieb-Thirring inequalities for Schrödinger operators," Talk at Gakushuin University, Japan

Talk

References

Stability of Matter

Ice-type model

The ionization conjecture

Entropy and Entanglement

Recent upcomming results

Density Matrices and N-Representability Problem

Stability of Matter

Combinatorial Analysis

Water H2O Molecule and Snow Crystals

Quantum Pigeonhole Principle

Physics

Other materials