DATASET J. Stat. Mech. (2022) 053209: "Virtual double-well potential for an underdamped oscillator created by a feedback loop"

Matlab Figures: 

Fig_i.fig corresponds to the source file used to plot the figures of the article

Simulation and Model codes: Matlab script

Simu_and_Model.m is the code used to:

1) Simulate trajectories of the underdamped cantilever in the virtual double well potential with hysteresis at the comparator switches.

2) Compute from the simulation the steady state temperature and the crossing rate.

2) Compute and plot the model's prediction regarding the steady state temperature and the crossing rate. 

static_hyst_XX.mat : Matlab dataset

It is experimental data of the underdamped cantilever in vacuum trapped in a double well potential with hysteresis at the switches. It is not the data used in the article. Indeed:

1) The velocity distributions of the article were the ones of the analogical implementation of the feedback loop with hysteresis. Here we propose as an example a more recent dataset from the numerical implementation of the feedback loop with a chosen hysteresis.

2) Besides the in this dataset the cantilever is evolving in vacuum so that the cooling effect observed is much more important for a given hysteresis.

But as the data treatment to obtain the velocity distribution and the cooling observed are similar to the one detailed in the article, this dataset should be enough for any person interested.

Each data file contains in particular: x the  position in sigma units (z in the article), X_1 the wells centers position in sigma units (z_1 in the article), x0 the barrier position in sigma units (z_0 in the article), sigma_m the position variance calibrated before the experiment and sigma_protocol the position variance calibrated before every data file. 

Analyse_velocity_distribution.m : Matlab Script

It is the code to treat datasets such as the one provided here "static_hyst". The code recover the data from the files and compute the velocity distributions for different distances between the wells. The velocity variance is deduced from the velocity distributions and matches the variance computed using the velocity power spectrum. The velocity and position spectrums are also displayed.