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Random Matrices and Statistical Mechanics

Random Matrices and Statistical Mechanics. by Kevin Phillips Advisor: Dr. Michael K.-H. Kiessling. Goals:. Add to the understanding of the interplay of Random Matrix Theory and Statistical Mechanics. Statistical Mechanics:. Goals:. Statistical Mechanics:.

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Random Matrices and Statistical Mechanics

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  1. Random Matrices and Statistical Mechanics by Kevin Phillips Advisor: Dr. Michael K.-H. Kiessling

  2. Goals: Add to the understanding of the interplay of Random Matrix Theory and Statistical Mechanics. Statistical Mechanics:

  3. Goals: Statistical Mechanics: For specific Uint , Uext and b, these are identical! Understanding the interplay of Random Matrix Theory and Statistical Mechanics. Random Matrix Theory:

  4. Classical Gas of Charges

  5. Classical Gas of Charges

  6. The Gibbs Canonical Ensemble Consider an ensemble of systems with the same Hamiltonian each in different states (Q,P) but distributed according to a probability measure which depends only on the Hamiltonian: exponential- Gibbs Measure.

  7. The Configuration Gas Integrate out momentum, ask questions only about position! Where:

  8. Particle-Particle interaction arising from electric fields. Interaction with positive background. Hamiltonian of Point Charges in 2D For specific Uint , Uext and b, these are identical! Gibbs Canonical Measure Joint Eigenvalue Distribution

  9. Gibbs Canonical Ensemble : Point Charges in 2D Ok, we have Uint and Uext, but what b should we try?

  10. Overlap: Random Matrices and 2D Ensembles

  11. My Project 1.) From the previous chart… I Would like to set this in stone. 2.) Normal Matrices : Real and Complex, Gaussian and non-Gaussian.

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