# Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps

## TL;DR

This paper demonstrates that in driven quantum systems, topological quasi-steady states can have exponentially long lifetimes, maintaining topological features while losing non-universal details, with implications for quantum control.

## Contribution

The authors derive an analytical bound showing the lifetime of topological quasi-steady states grows exponentially as driving frequency decreases, revealing a new stabilization mechanism.

## Key findings

- Lifetime of quasi-steady states is exponentially large in inverse frequency.
- Topological properties persist while non-universal features are washed out.
- States are characterized by maximum entropy with fixed particle number in Floquet bands.

## Abstract

We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.