Response of quantum pure states

TL;DR

This paper demonstrates that in large quantum systems, most pure states respond to external forces similarly to statistical predictions, a phenomenon called dynamical typicality, supported by theoretical analysis and numerical simulations.

Contribution

It introduces the concept of dynamical typicality, showing that most pure states exhibit responses close to statistical responses in large Hilbert spaces.

Findings

Most pure states' responses align with statistical predictions as Hilbert space dimension grows.

Numerical simulations confirm relaxation to a thermal equilibrium after a quench.

The new equilibrium state is consistent with thermal equilibrium descriptions.

Abstract

The response of a quantum system in a pure state to an external force is investigated by reconsidering the standard statistical approach to quantum dynamics on the light of the statistical description of equilibrium based on typicality. We prove that the response of the large majority of quantum pure states subjected to the same arbitrary external perturbation tends to be close to the statistical response as the dimension of the Hilbert space increases. This is what we can term dynamical typicality. The theoretical analysis is substantiated by numerical simulations of the response of a spin system to a sudden quench of the external magnetic field. For the considered system we show that not only the system relaxes toward a new equilibrium state after the quench of the Hamiltonian but also that such a new equilibrium is compatible with the description of a thermal equilibrium.