Quantum Quench in $c=1$ Matrix Model and Emergent Space-times

TL;DR

This paper studies quantum quenches in a large-N matrix model, revealing that adiabaticity is always broken and emergent space-times often have spacelike boundaries, with only finely tuned profiles avoiding singularities.

Contribution

It provides exact classical solutions for eigenvalue density during quenches and interprets emergent space-times, highlighting universal features and conditions for regularity.

Findings

Adiabaticity is always broken during the quench.

Emergent space-times typically have spacelike boundaries with diverging couplings.

Fine-tuned profiles can produce regular, non-singular space-times.

Abstract

We consider quantum quench in large-N singlet sector quantum mechanics of a single hermitian matrix in the double scaling limit. The time dependent parameter is the self-coupling of the matrix. We find exact classical solutions of the collective field theory of eigenvalue density with abrupt smooth quench profiles which asymptote to constant couplings at early and late times, and the system is initially in its ground state. With adiabatic initial conditions we find that adiabaticity is always broken regardless of the quench speed. In a class of quench profiles the saddle point solution for the collective field diverges at a finite time, and a further time evolution becomes ambiguous. However the underlying matrix model expressed in terms of fermions predict a smooth time evolution across this point. By studying fluctuations around the saddle point solution we interpret the emergent space-times. They generically have spacelike boundaries where the couplings of the fluctuations diverge. Only for very finely tuned quench profiles, the space-time is normal.