Analysis & PDE · Mathematics & Statistics
Spectral Theory
The newest papers in Spectral Theory that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
20 papers, from 8 September 2026 to 4 November 2026: 20 arXiv preprints.
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Newest papers
Beyond the Gap: What Imaginary-Time Evolution Reveals About the Edge of the Continuum
The spectral gap, the energy separating the ground state from the first excitation, governs many quantum phenomena, yet it is far harder to compute than the ground state.Spectral properties of twisted soft waveguides
We discuss a model of a soft waveguide described by Schrödinger operator whose potential is a twisted straight channel of non-circular profile.Persistence of Unitary Almost Mathieu Operator Gaps Ten Dry Martinis, Five on the Rim
We determine exactly which gap labels are realized by open spectral gaps for the unitary almost Mathieu operator at every irrational frequency and all coupling constants ($0<λ_1,λ_2\leq1$).Threshold Criteria for Bosonic and Fermionic Trimers on a Square Lattice: A Birman--Schwinger Comparison
We compare two three-particle lattice models on the square lattice at total quasimomentum zero: three identical bosons with attractive contact interactions, and a two-fermion plus one…Every route counts, but some count more: a max-plus view of the C. elegans brain
Brains do not simply add up every signal they receive: they select which routes dominate.Kernelised covariance matrices, dimension reduction and imbalanced spectral clustering
The Gaussian Mixture Model (abbrv.A sharp gradient-corrected Lieb--Thirring inequality in one dimension with applications to density functional theory
We first prove a sharp Lieb-Thirring inequality with semi-classical constant and gradient correction in one dimension.Lieb-Robinson bounds via the Combes-Thomas estimate
This paper studies quantum spin systems: networks of spins coupled by local interactions.Upper Bound on the Correlation Energy of a Dense Fermi Gas in the Thermodynamic Limit
We prove that the random phase approximation provides an upper bound on the correlation energy of a three-dimensional, weakly interacting, Fermi gas in the thermodynamic limit at high density.Why Shallow Neural Networks Learn Sinusoidal Components First: An Orthogonal Polynomial Dynamics Framework
Neural networks often learn low-frequency components before high-frequency ones --- a phenomenon called spectral bias or termed F-principle.A note on the A.C. spectrum of limit-periodic Jacobi matrices
We show that limit-periodic Jacobi matrices in the weak exponential class $EC(η)$ have purely absolutely continuous spectral type when $η$ is sufficiently large, depending only on the…An optimization problem for $δ'$ leaky stars
We consider singular Schrödinger operators with an attractive $δ'$ interaction of strength $β$ supported by a star graph and prove that the ground-state eigenvalue is uniquely maximized by stars of…Harmonic analysis and circuit approximation of Sobolev functions on quantum input spaces
We derive approximation rates for Sobolev functions defined on the complex unit sphere and complex projective space, representing quantum states, and on the special and projective unitary groups…Wasserstein Gradient Flows and Forward-Only Diffusion Are Not Enough for Multimodal Sampling
There has been a proliferation of sampling algorithms based on Wasserstein gradient flows (WGF) and forward-only diffusion processes (FODP), often accompanied by theoretical guarantees of…Smooth perturbation theory and generic Cantor spectrum for multi-dimensional monotone quasiperiodic operators
We consider multi-dimensional quasiperiodic Schrödinger operators with monotone sawtooth-type potentials in the perturbative localization regime.A polylogarithmic higher-order Cheeger inequality
Let $λ_k(G)$ be the $k$th eigenvalue of the normalized Laplacian of a finite undirected weighted graph, and let $ρ_G(k)$ be the minimum possible maximum conductance of $k$ disjoint nonempty vertex…Effective atom-dimer bands of three-body lattice systems at strong coupling: exact critical mass ratios and a statistics-quasimomentum duality
We study three particles on the square lattice with contact interactions of infinite strength, for all total quasimomenta, for three statistics: three identical bosons, two identical fermions plus a…On attention heads and bilinear forms
We study the symmetric and antisymmetric parts of bilinear forms in the attention heads of trained large language models.Eigenvalue-Decomposition Cost Denoising as an Alternative to Predict-then-Optimize for Shortest-Path Problems
Predict-then-optimize methods such as Smart "Predict, then Optimize" (SPO+) of Elmachtoub and Grigas (2022) learn a mapping from contextual features to unknown edge costs and then solve the induced…Beyond Cut Balance: Spectral Sparsification of the Nonlinear Directed Laplacian
Digraphs with constant cut balance admit nearly linear directed cut sparsifiers.