Related papers: Complex median method and Schatten class membershi…
We develop a new method for obtaining bounds on the negative eigenvalues of self-adjoint operators B in terms of a Schatten norm of the difference of the semigroups generated by A and B, where A is an operator with non-negative spectrum.…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
We apply the Marchenko method of quantum inverse scattering to study nucleon scattering problems. Assuming a $\beta/r^2$ type repulsive core and comparing our results to the Reid93 phenomenological potential we estimate the constant…
Conventional approaches to describe dark matter phenomenology at collider and (in)direct detection experiments in the form of dark matter effective field theory or simplified models suffer in general from drawbacks regarding validity at…
We give an alternative proof of several sharp commutator estimates involving Riesz transforms, Riesz potentials, and fractional Laplacians. Our methods only involve harmonic extensions to the upper half-space, integration by parts, and…
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
In this paper, we systematically study the Fefferman-Stein inequality and Coifman-Fefferman inequality for the general commutators of singular integral operators that satisfy H\"{o}rmander conditions of Young type. Specifically, we first…
This paper is concerned with local cohomology sheaves on generalized flag varieties supported in closed Schubert varieties, which carry natural structures as (mixed Hodge) D-modules. We employ Kazhdan--Lusztig theory and Saito's theory of…
A simple and elegant mechanism is proposed to resolve the problem of having a light scalar mediator for self-interacting dark matter and the resulting disruption to the cosmic microwave background (CMB) at late times by the former's…
The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of…
We consider a multi-component dark matter model where the dark sector contains a scalar doublet and a complex scalar singlet. We impose a discrete $Z_4$ symmetry to ensure such that the lightest component of the doublet, $\tilde{A}$, and…
We characterize the Schatten class $S^p$ of the commutator of Riesz transforms $[b,R_j]$ in $\mathbb R^n$ ($j=1,\ldots, n$) in the two weight setting for $n< p<\infty$, by introducing the condition that the symbol $b$ being in Besov spaces…
Let $K_\theta$ be a model space generated by an inner function $\theta$. We study the Schatten class membership of embeddings $I : K_\theta \to L^2(\mu)$, $\mu$ a positive measure, and of composition operators $C_\phi:K_\theta\to…
Even if Dark Matter (DM) is neutral under electromagnetism, it can still interact with the Standard Model (SM) via photon exchange from higher-dimensional operators. Here we classify the general effective operators coupling DM to photons,…
We present a new and explicit method for lifting a tilting complex to a bimodule complex. The key ingredient of our method is the notion of a strong homotopy action in the sense of Stasheff.
We obtain combinatorial model categories of parametrised spectra, together with systems of base change Quillen adjunctions associated to maps of parameter spaces. We work with simplicial objects and use Hovey's sequential and symmetric…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
Recently published works have shown that the Multiple Temporal Compression (MTC) method is a more efficient approach for generation of multiple bright solitons in stacked waveguides, in comparison to the traditional soliton-fission…
The Fredholm-Hammerstein integral equations (FHIEs) with weakly singular kernels exhibit multi-point singularity at the endpoints or boundaries. The dense discretized matrices result in high computational complexity when employing numerical…