# Engineered Swift Equilibration of brownian particles: consequences of hydrodynamic coupling

### Submission summary

 As Contributors: Ludovic Bellon · DAGO Salambô · Emmanuel Trizac Arxiv Link: https://arxiv.org/abs/2005.04939v2 (pdf) Date accepted: 2020-10-06 Date submitted: 2020-09-23 19:27 Submitted by: Bellon, Ludovic Submitted to: SciPost Physics Academic field: Physics Specialties: Statistical and Soft Matter Physics Approaches: Theoretical, Experimental

### Abstract

We present a detailed theoretical and experimental analysis of Engineered Swift Equilibration (ESE) protocols applied to two hydrodynamically coupled colloids in optical traps. The second particle disturbs slightly (10% at most) the response to an ESE compression applied to a single particle. This effect is quantitatively explained by a model of hydrodynamic coupling. Then we design a coupled ESE protocol for the two particles, allowing the perfect control of one target particle while the second is enslaved to the first. The calibration errors and the limitations of the model are finally discussed in detail.

Published as SciPost Phys. 9, 064 (2020)

We thank the referees for their positive reviews of our submission. In this minor revision, we address the two points that were raised by both of them: English has been reviewed, and we did our best to improve the figures .

### List of changes

- We proofread the text of the article to improve the English, with an increased attention to the specific points mentioned by referee 2.

- All of the figures were reworked with the goal of improving their readability. To this aim, a new notation $\sigma_n$ has been introduced in the main text, figures and their captions to better explain the main quantity we are plotting. This normalized variance of the first particle $\sigma_n=(\sigma(t)-\sigma_{f})/(\sigma_{i}-\sigma_{f})$ describes the evolution of the variance of particle under control, normalised so that $\sigma_n=0$ at initial time, and $\sigma_n=1$ at the end of the protocol.

- The left panel of figure 2 has been changed according to the suggestion of referee 2, to use the same unit for the time variable on the two panels of this figure.

### Submission & Refereeing History

Resubmission 2005.04939v2 on 23 September 2020
Submission 2005.04939v1 on 12 May 2020