Description
The eigenvalues of Hermitian matrices are fundamental to understanding the statistical and dynamical properties of quantum systems. Traditionally, this involves diagonalizing the Hamiltonian, with the diagonal elements representing its eigenvalues. In this presentation, I propose an alternative method: tridiagonalizing the Hamiltonian. Utilizing the Krylov space approach, I will explore the characteristics and distributions of the tridiagonal matrix elements within the framework of random matrix theory and the Double-Scaled SYK model. The spectrum of the bulk Lanczos coefficients is believed to govern the late-time boundary physics and provides insights into the non-perturbative aspects of bulk gravity theory.
Speaker
Pratik Nandy
(iTHEMS, RIKEN (Kyoto) & YITP, Kyoto U)
