Energy Current Correlations For Weakly Anharmonic Lattices

Following approach of Iorgov--Lisovyy--Teschner, we construct solutions of the (modified) Riemann--Hilbert problem using conformal blocks of $(1,k)$ Virasoro models. For $k>1$ case, the solution of this Riemann--Hilbert problem is not unique due to more singular behavior at punctures. On the CFT side the dimension of the space of conformal blocks also increases. We specifically study the $k=2$ case, which corresponds to the central charge $c=-2$ and symplectic fermions. We explicitly construct a corresponding solution of the modified Riemann--Hilbert problem in the case of 3 punctures and prove its uniqueness under suitable initial data conditions. We also obtain new bilinear relations for $c=-2$ tau functions.

math-ph↗

arXiv2026

Uniformity theory of weighted composites

By including spatially varying volume fractions of the constituents, composites are obtained that are akin to functionally graded media. An extension of the mathematical apparatus of double groupoids is proposed to incorporate these materials with the aim of eventually classifying defects of misalignment and their time evolution.

math-ph↗

arXiv2026

Extended States on the Bethe Lattice Revisited

We give a short proof of the classical weak-disorder result that the Anderson model on the Bethe lattice has purely absolutely continuous spectrum on compact intervals in the interior of the free spectrum. This note continues [6], where we gave a minimal proof of the existence of a nontrivial absolutely continuous component using the cyclicity criterion of [8]. There, Hellinger overlap yields the required non-cyclicity. Here, a stability argument for the forward Green function, followed by the zero--one law for the tree recursion, yields positivity of its boundary imaginary part. This positivity already gives absolutely continuous spectrum throughout the interval; the structural result of [7] excludes singular spectrum and yields purity. We also observe that the same structural argument shortens the final passage from boundary positivity to purity in the recent OpenAI preprint on the weak-disorder Anderson model on $\zz^d$, $d\geq3$ [10].

math-ph↗