arXiv preprints from January 1, 2026 through September 21, 2026 — 04:22:58 EST
Let $Δ_k$ be the Dunkl Laplacian associated with an arbitrary root system and a nonnegative multiplicity function. For every $0<p\leq1$, a Coifman-Weiss type atomic characterization of the Hardy space $H^p_{\mathrm{Dunkl}}$ is established. More precisely, it is proved that the space $H^p_{\mathrm{Dunkl}}$, which is originally defined...
We study the far-field behavior of solutions of the one-phase Bernoulli free boundary problem in the exterior of a ball, and of entire solutions with a single compactly supported inhomogeneity of the free boundary condition, which we call a defect. For solutions which blow down to a half-plane solution (proper solutions) we establish...
We develop an extension of Deligne--Lusztig theory to certain (possibly infinite type) disconnected reductive groups arising from the special fibers of point stabilizers in the Bruhat--Tits building, which we call \emph{paraductive}. We then compute explicit lower bounds for the Tate cohomology of representations of paraductive...
We establish a weighted extension of the Bishop-Gromov volume comparison theorem for complete Riemannian manifolds with Ricci curvature bounded below. Given a point $p$ and positive radial weights $f$ and $h$, we consider the weighted volume of a geodesic ball and a corresponding model weighted volume in the simply connected space...
Let $U,V$ be matrix $\mathcal A_p$ weights, $1<p<\infty$, and let $B$ be a matrix-valued function. For Calderón--Zygmund operators $T$ with scalar standard kernels, we characterize boundedness and compactness of $[M_B,T\otimes I_m]:L^p(U)\to L^p(V)$ by two-matrix BMO and vanishing oscillation conditions. The converse statements...
We introduce forward recursive aggregator systems in It__o-diffusion markets, bridging the theories of recursive utilities and of forward performance criteria. We derive the associated HJB SPDE and sufficient conditions for consistency and admissibility. We also develop a convex duality theory based on state price densities and...
Simulating nuclear magnetic resonance (NMR) spectra is a promising application of quantum simulation. Using Quantinuum's System Model H2, a trapped-ion quantum computer, we demonstrate an end-to-end, large-scale digital NMR simulation of a classically challenging benchmark molecule, 1,2-di-tert-butyl-diphosphane. We implement a...
Stable ternary compounds lie below every competing phase on a conventional convex hull, but this does not reveal whether their stability is inherited from already favorable binaries or created by bringing three elements into one crystal. We define the emergent ternary stabilization energy, delta E3, as the energy by which a stable...
This course on two-dimensional quantum gases, prepared for the S{ã}o Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, is organized into three lectures. The first introductory lecture addresses Bose-Einstein condensation in an ideal gas, the effect of interactions in the weakly interacting limit, Gross-Pitaevskii equation and its...
In order to solve practical problems on a quantum computer, it is necessary to use fault-tolerant quantum error correction schemes to overcome noise: the errors arising from imperfections in physical components. The Gottesman-Kitaev-Preskill (GKP) code aims at achieving this in a hardware efficient manner by encoding...
We address three-dimensional (3D) solitons maintained by spin-orbit coupling (SOC) in the binary self-interacting Bose-Einstein condensate (BEC) held in the 3D optical lattice (OL). The analysis reveals that the SOC-OL interplay results in the formation of stable full-vortex (FV) soli-tons, built as sets of four density peaks residing...
The conformal boundary of asymptotically flat spacetime is null and therefore carries a Carrollian rather than Lorentzian geometry. This changes the relation between symmetry, variational principles and evolution equations in an essential way: unlike a Lorentzian Levi-Civita connection, a torsion-free Carrollian connection compatible...
CeRh$_2$As$_2$ has been receiving considerable attention due to its unusual two-phase superconductivity. The superconducting (SC) phase appears at $T_{\mathrm{c}}$ = 0.35 K in an ordered state (phase I) of the Ce-4$f$ moments, which develops below $T_{\mathrm{0}}$ = 0.55 K. The microscopic nature of phase I has not been fully...
Pseudospectral analysis provides a powerful way to probe the spectral stability of non-self-adjoint operators and has been widely used in black hole physics, but its application to braneworld scenarios has not yet been explored. In this work, we apply this method to tensor gravitational perturbations in a representative...
We proof the existence of the Integrated Density of States (IDS) for fractional random Schrödinger operators with Gaussian potential based on the theory of isotropic $α$-stable Lévy processes. Further we show that the IDS exhibits Lifshitz tails and determine its asymptotics at the right end of the spectrum. Isotropic$α$-stable Lévy...
Recent studies of the superconducting proximity effect in quasicrystalline and topological systems have opened up a new research direction for exploring how quasiperiodicity and topology influence proximity induced superconductivity. In this work, we investigate spatial variation of the proximity induced pairing amplitude in a hybrid...
Muon-spin rotation/relaxation is one of the most powerful microscopic probes for understanding magnetic order, spin dynamics, superconductivity, and complex magnetic phases in emerging quantum materials. Quantitative interpretation depends critically on the accurate identification of the muon stopping site, a problem traditionally...
Multi-state HLL-type approximate Riemann solutions of ideal magnetohydrodynamics (MHD) typically assume that the medium within the Riemann fan is incompressible, and thus the slow magnetoacoustic mode cannot be included in their space-time wave configurations for the approximated states. We propose a new strategy to design multi-state...
The mechanical response of a moving probe in an active bath reflects both the dynamics of the bath and how the probe couples to it. For a probe moving at velocity $\mathbf V$ and interacting weakly with an ideal active bath, we show that the trajectory statistics of a free bath particle determine a density response from which the bath...
Disk fractions in star-forming clusters decline with stellar age, and are routinely read as the lifetime distribution of primordial protoplanetary disks. We argue that this reading is not warranted, because late infall can replenish or reform disks after collapse. To formalize this, we model the disk fraction as a superposition of...
In order to circumvent that no universal set of gates can be achieved on a given quantum error-correcting codes, additional gates can be performed through magic state injection. This however requires to have access to high fidelity magic state, which can be obtained by the distillation of low quality states to fewer higher quality...
In the present work, we study the radiative decays of the P-wave $D\bar{D}^*$ molecular state $G_0$ with $I^G(J^{PC})=0^+(0^{-+})$ using a phenomenological Lagrangian approach. The molecular coupling is fixed by the compositeness condition with a Gaussian form factor. The partial widths for $G_0\to γγ$, $γJ/ψ$, $γψ(2S)$, $γh_c$, $γρ$,...
Eigenstate thermalization constrains the smooth dependence of observables on energy, but it does not by itself fix the microscopic statistics of the overlaps between many-body eigenstates and a chosen basis: the smooth envelope is a one-point statement, and the fluctuation field it leaves undetermined carries a structured two-point...
Binding energies of molecules on ice mantles are important to understand the evolution of molecular complexity in molecular clouds. Binding energies are often computed using density functional theory (DFT) calculations, typically on either small amorphous ice clusters or crystalline slabs. Since these calculations require an accurate...
For a nontrivial finite abelian group $G$, let $ν(G)$ be the smallest integer $\ell$ such that every zero-sum free sequence $T$ over $G$ of length at least $\ell$ has the following property: all nonzero elements of $G$ that do not occur as a subsequence sum of $T$ lie in a proper coset of some subgroup of $G$. It is easy to check that...