Operator Spreading, Duality, and the Noisy Long-Range FKPP Equation

This is the data required for plotting figure 4 and 5 in the paper "Operator Spreading, Duality, and the Noisy Long-Range FKPP Equation"[1]. The folder fig_4a contains data for alpha close to 1.5, and fig_4bc contains data for alpha close to 1 (also used in plotting figure 5). 

Files with name *_b and *_r correspond to soft constraint and hard constraind, respectively. These two constraints are defined in the paper.

In each data file, one can find the following variables: 

't': time;

'M': he distance to the furthest occupied site;

'Np': the total population;

'Ns': the total number of occupied sites;

'l': typical size of the light cone;

'X_int': integral of X(\{tau})*X(t-\{tau})d \{tau} from 0 to t;

'X_half_t': the value of X at time t/2;

Note 1: X can be one of M, Np, Ns, and l.

Note 2: figure 5 is the first figure in the supplementary material.

[1] Zhou, T., Brunet, É. and Qi, X., 2025. Operator Spreading, Duality, and the Noisy Long-Range FKPP Equation. arXiv preprint arXiv:2505.06353.