Notes on density matrix perturbation theory

Canonical density matrix perturbation theory.

Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equat...

Notes on Random Matrix Theory

3 Universality 4 3.1 Macroscopic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Wigner’s semicircle law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Microscopic behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2.1 Bulk universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Matrix Perturbation Theory

Ren-Cang Li University of Texas at Arlington 15.1 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-1 15.2 Singular Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-6 15.3 Polar Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-7 15.4 Generalized Eigenvalue Problems . . . . . . . . . . . . . . . . . . . 15-...

Notes on Branes in Matrix Theory

We study the effective actions of various brane configurations in Matrix theory. Starting from the 0 + 1 dimensional quantum mechanics, we replace coordinate matrices by covariant derivatives in the large N limit, thereby obtaining effective field theories on the brane world volumes. Even for noncompact branes, these effective theories are of Yang-Mills type, with constant background magnetic f...

Notes 32 : Time - Dependent Perturbation Theory