# Towards a "hydrodynamic" approach to density matrices in quantum chaotic systems

### APA

Lashkari, N. (2017). Towards a "hydrodynamic" approach to density matrices in quantum chaotic systems. Perimeter Institute. https://pirsa.org/17030054

### MLA

Lashkari, Nima. Towards a "hydrodynamic" approach to density matrices in quantum chaotic systems. Perimeter Institute, Mar. 07, 2017, https://pirsa.org/17030054

### BibTex

@misc{ pirsa_17030054, doi = {10.48660/17030054}, url = {https://pirsa.org/17030054}, author = {Lashkari, Nima}, keywords = {Quantum Fields and Strings}, language = {en}, title = {Towards a "hydrodynamic" approach to density matrices in quantum chaotic systems}, publisher = {Perimeter Institute}, year = {2017}, month = {mar}, note = {PIRSA:17030054 see, \url{https://pirsa.org}} }

Nima Lashkari McGill University

## Abstract

We study the eigenstate thermalization hypothesis in chaotic conformal ﬁeld theories (CFTs) of arbitrary dimensions by computing the reduced density matrices of small size in energy eigenstates. We show that in the inﬁnite volume limit this operator is well-approximated by a “universal” density matrix which is its projection to the primary operators that have nonzero thermal one-point functions. These operators in all two-dimensional CFTs and holographic higher-dimensional CFTs are the polynomials of stress tensor. We compute the time-dependent two-point correlators and Renyi entropies of the universal density martix, and compare the results to the thermal Gibbs state and black holes in various dimensions. We demonstrate that the two-dimensional universal density matrix is close in trace distance to the reduced Gibbs state. We put forward the truncation of density matrix to the stress tensor sector as a “hydrodynamic” method to study the out-of-equilibrium dynamics of strong-coupled ﬁeld theories