Tootfinder

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…

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…

This https://arxiv.org/abs/2411.07189 has been replaced.
initial toot: https://mastoxiv.page/@…

Scale-invariant dynamics in a purely deterministic Game of Life model
Scale invariance is a key feature that characterizes criticality in complex dynamical systems, which often organize into structures exhibiting no typical size and/or lifespan. While random external inputs or tunable stochastic interactions are typically required for showcasing such criticality, the question of whether scale-invariant dynamics can emerge from purely deterministic interactions remains unclear. In this work, we discover highly affirmative signatures of critical dynamics in equal-s…

This https://arxiv.org/abs/2408.01155 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Efficient conversion from fermionic Gaussian states to matrix product states
Fermionic Gaussian states are eigenstates of quadratic Hamiltonians and are widely used in quantum many-body problems. We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems with translation invariance. If the ground states of a topologically ordered system on infinite cylinders are expressed as matrix…