Tootfinder

Improved geometric and recollision estimates for the invariance principle of the random Lorentz gas
Raphael Winter, Karsten Matthies
https://arxiv.org/abs/2506.18539

Improved geometric and recollision estimates for the invariance principle of the random Lorentz gas
By improving geometric recollision estimates for a random Lorentz gas, we extend the timescale $T(r)$ of the invariance principle for a Lorentz gas with particle size $r$ obtained by Lutsko and Toth (2020) from $\lim_{r \rightarrow 0} T(r) r^{2} |\log(r)|^2 =0$ to $\lim_{r \rightarrow 0} T(r) r^{2} |\log(r)| =0$. We show that this is the maximal reachable timescale with the coupling of stochastic processes introduced in the original result. In our improved geometric estimate…

Full extremal process in four-dimensional membrane model
Hao Ge, Xinyi Li, Jiaxi Zhao
https://arxiv.org/abs/2507.19554 https://arxiv.org/pdf/2507.19554

Full extremal process in four-dimensional membrane model
We investigate the extremal process of four-dimensional membrane models as the size of the lattice $N$ tends to infinity. We prove the cluster-like geometry of the extreme points and the existence as well as the uniqueness of the extremal process. The extremal process is characterized by a distributional invariance property and a Poisson structure with explicit formulas. Our approach follows the same philosophy as the two-dimensional Gaussian free field (2D GFF) via the comparison with the modi…

Geometric Superfluid Weight in Quasicrystals
Junsong Sun, Huaiming Guo, Bohm-Jung Yang
https://arxiv.org/abs/2507.20540 https://arxiv.org/pdf/2507.20540

Geometric Superfluid Weight in Quasicrystals
We study the geometric contribution to the superfluidity in quasicrystals in which the conventional momentum-space quantum geometric tensor cannot be defined due to the lack of translational invariance. Based on the correspondence between the momentum and magnetic flux, we introduce the flux-space quantum metric in finite-size closed systems and reveal its contribution to the superfluid weight in quasicrystalline superconductors. As a toy model, we study the attractive Hubbard model on the Fibo…