Tootfinder

Quantum Latin squares with all possible cardinalities
Ying Zhang, Xin Wang, Lijun Ji
https://arxiv.org/abs/2507.05642 https://arxiv.o…

Quantum Latin squares with all possible cardinalities
A quantum Latin square of order $n$ (denoted as QLS$(n)$) is an $n\times n$ array whose entries are unit column vectors from the $n$-dimensional Hilbert space $\mathcal{H}_n$, such that each row and column forms an orthonormal basis. Two unit vectors $|u\rangle, |v\rangle\in \mathcal{H}_n$ are regarded as identical if there exists a real number $θ$ such that $|u\rangle=e^{iθ}|v\rangle$; otherwise, they are considered distinct. The cardinality $c$ of a QLS$(n)$ is the numbe…

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Certain Upper Bounds on the $A$-Numerical Radius of Operators in Semi-Hilbertian Spaces and Their Applications
M. H. M. Rashid
https://arxiv.org/abs/2507.05398

Certain Upper Bounds on the $A$-Numerical Radius of Operators in Semi-Hilbertian Spaces and Their Applications
Consider a complex Hilbert space $\left(\mathcal{H}, \langle \cdot, \cdot \rangle\right)$ equipped with a positive bounded linear operator $A$ on $\mathcal{H}$. This induces a semi-norm $\|\cdot\|_A$ through the semi-inner product $\langle x, y \rangle_A = \langle Ax, y \rangle$ for $x, y \in \mathcal{H}$. In this semi-Hilbertian space setting, we investigate the $A$-numerical radius $w_A(T)$ and $A$-operator semi-norm $\|T\|_A$ of bounded operators $T$. This paper presents …

Parallel spin wave for the Villain model
Paul Dario, Wei Wu
https://arxiv.org/abs/2507.04098 https://arxiv.org/pdf/2507.04098

Parallel spin wave for the Villain model
In this paper, we study the Villain model in $\mathbb{Z}^d$ in dimension $d\geq 3$. It is conjectured, that the parallel correlation function in the infinite volume Gibbs state, i.e., the map $$ x \mapsto \langle \cosθ(0) \cosθ(x) \rangle_{μ_{\mathrm{Vil}, β}} -\left( \langle \cosθ(0) \rangle_{μ_{\mathrm{Vil}, β}} \right)^2, $$ decays like $|x|^{-2(d-2)}$ as $|x| \to \infty$ at low temperature. The results of Bricmont, Fontaine, Lebowitz, Lieb, and Spencer (19…

Narrowing the Gap: Supervised Fine-Tuning of Open-Source LLMs as a Viable Alternative to Proprietary Models for Pedagogical Tools
Lorenzo Lee Solano, Charles Koutcheme, Juho Leinonen, Alexandra Vassar, Jake Renzella
https://arxiv.org/abs/2507.05305

Narrowing the Gap: Supervised Fine-Tuning of Open-Source LLMs as a Viable Alternative to Proprietary Models for Pedagogical Tools
Frontier Large language models (LLMs) like ChatGPT and Gemini can decipher cryptic compiler errors for novice programmers, but their computational scale, cost, and tendency to over-assist make them problematic for widespread pedagogical adoption. This work demonstrates that smaller, specialised language models, enhanced via Supervised Fine-Tuning (SFT), present a more viable alternative for educational tools. We utilise a new dataset of 40,000 C compiler error explanations, derived from real in…

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Phase-Induced Particle Creation in the Kappa-Gamma Vacuum
Arash Azizi
https://arxiv.org/abs/2507.05299 https://arxiv.org/pdf/2507.052…

Phase-Induced Particle Creation in the Kappa-Gamma Vacuum
We introduce a two-parameter ($κ, γ$) family of field modes in flat spacetime that generalizes the recently developed $κ$-plane wave modes, which correspond to real squeezing. By incorporating a phase parameter, $γ$, our new kappa gamma plane wave modes describe a vacuum state, $| 0_{κ,γ} \rangle$, characterized by continuous-mode phase squeezing, where $κ$ governs the squeezing magnitude and $γ$ sets its angle. This generalization reveals a novel physical effect: particle creation…

QCD condensates and $\alpha_s$ from $e^ e^-$ and $\tau$-decays
Stephan Narison (LUPM-CNRS Montpellier-FR,iHEPMAD-Univ. Antananarivo-MG)
https://arxiv.org/abs/2508.05434 https://…

QCD condensates and $α_s$ from $e^+e^-$ and $τ$-decays
In this talk, I review the determinations of the QCD condensates and $α_s$ within the SVZ expansion using the ratio of Laplace sum rule (LSR) and $τ$-like moments in $e^+e^-\to I=1$ Hadrons and in $τ\to ν_τ+$Hadrons Axial-vector (A) and V-A channels. Some misprints in the original papers [1-3] have been corrected. We found that the value of the gluon condensate agrees with the one $\langle α_s G^2\rangle=(6.35\pm 0.35)\times 10^{-2}$ GeV$^4$ from quarkonia and some other sum rules but les…