相关论文: Minimal Soft Lattice Theta Functions

We prove that the hexagonal lattice is a local minimizer, among all point configurations, of the interaction energy per unit volume for pair potentials that are completely monotonic functions of the square distance. This includes Gaussian…

$U(1)$ gauge theories, including conventional Maxwell electromagnetism, allow $\theta$-terms when parity and time-reversal symmetry are broken. In condensed matter systems, the physics of $\theta$ as a magnetoelectric response has been…

Single crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice $\rm Tb_2Ir_3Ga_9$. While the…

We study the pair interaction on flat tori of functions whose Fourier coefficients are positive and decay sufficiently rapidly. In dimension one we find that the minimizer, up to translation, is the equidistant point set. In dimension two,…

We investigate the local and global optimality of the triangular, square, simple cubic, face-centred-cubic (FCC), body-centred-cubic (BCC) lattices and the hexagonal-close-packing (HCP) structure for a potential energy per point generated…

In this Ph.D. thesis a model for graphene in presence of quantized electromagnetic interactions is introduced. The zero and low temperature properties of the model are studied using rigorous renormalization group methods and lattice Ward…

Due to remarkable advances in colloid synthesis techniques, systems of squares and cubes, once an academic abstraction for theorists and simulators, are nowadays an experimental reality. By means of a free minimization of the free-energy…

We extend density functional perturbation theory for lattice dynamics with fully relativistic ultrasoft pseudopotentials to magnetic materials. Our approach is based on the application of the time-reversal operator to the Sternheimer linear…

Let $L =\sqrt{\frac{1}{\Im(z)}}\Big({\mathbb Z}\oplus z{\mathbb Z}\Big)$ where $z \in \mathbb{H}=\{z= x+ i y\;\hbox{or}\;(x,y)\in\mathbb{C}: y>0\}$ be the two dimensional lattices with unit density. Assuming that $\alpha\geq1$, we prove…

We study the lattice version of higher-form symmetries on tensor-product Hilbert spaces. Interestingly, at low energies, these symmetries may not flow to the topological higher-form symmetries familiar from relativistic quantum field…

We consider the most general neutrino mass matrix which leads to $\theta_{13} = 0$, and present the formulae needed for obtaining the neutrino masses and mixing parameters in that case. We apply this formalism to a model based on the lepton…

Let $\zeta(s,z)=\sum_{(m,n)\in\mathbb{Z}^2\backslash\{0\}}\frac{(\Im(z))^s}{|mz+n|^{2s}}$ be the Eisenstein series/Epstein Zeta function. Motivated by widely used Lennard-Jones potential \begin{equation}\aligned\nonumber…

We have developed and implemented a self-consistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical LCAO basis set, which includes multiple-zeta and polarization orbitals. Exchange and…

We study random one-Lipschitz integer functions $f$ on the vertices of a finite connected graph, sampled according to the weight $W(f) = \prod_{\langle v, w \rangle \in E} \mathbf{c}^{ \mathbb{I} \{ f(v) = f(w) \} }$ where $\mathbf{c} \geq…

The modelling of minimum bias interactions is a crucial ingredient to learn about the description of soft QCD processes. It has also a significant relevance for the simulation of the environment at the LHC with many concurrent pp…

We offer the Skyrme model on a lattice as an effective field theory - fully quantized - of baryon-meson interactions at temperatures below the chiral phase transition. We define a local topological density that involves the volumes of…

We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…

Mimicking the idea of the generalized Hamming weight of linear codes, we introduce a new lattice invariant, the generalized theta series. Applications range from identifying stable lattices to the lattice isomorphism problem. Moreover, we…

This paper is devoted to the rigorous study of the low temperature properties of the two-dimensional weakly interacting Hubbard model on the honeycomb lattice in which the renormalized chemical potential $\mu$ has been fixed such that the…

We present the extension of Rosenfeld's fundamental measure theory to lattice models by constructing a density functional for d-dimensional mixtures of parallel hard hypercubes on a simple hypercubic lattice. The one-dimensional case is…