Related papers: Relaxed Gabor expansion at critical density and a …
In flat space, the scattering amplitudes of certain scalar effective field theories exhibit enhanced soft limits due to the presence of hidden symmetries. In this paper, we show that this phenomenon extends to wavefunction coefficients in…
Building on the discussion in PRA 93, 042510 (2016), we present a systematic derivation of gradient corrections to the kinetic-energy functional and the one-particle density, in particular for two-dimensional systems. We derive the leading…
The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some…
A grand canonical system of hard-core bosons, subject to thermal fluctuations, is studied on a lattice. Starting from the slave-boson representation with fields for occupied and unoccupied sites, an effective field theory is derived in…
Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
We consider Gibbs measures on the configuration space $S^{\mathbb{Z}^d}$, where mostly $d\geq 2$ and $S$ is a finite set. We start by a short review on concentration inequalities for Gibbs measures. In the Dobrushin uniqueness regime, we…
The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase…
The present article proposes a rigorous derivation of the Boltzmann equation in the half-space. We show an analog of the Lanford's theorem in this domain, with specular reflection boundary condition, stating the convergence in the low…
Let $g\in L^2(\mathbb{R})$ be a strictly decreasing continuous function supported on $\mathbb{R}_+$ such that for all $t > 0$ we have $g(x+t)\le q(t)g(x)$ for some $q(t)<1$. We prove that the Gabor system…
Lattice relaxation profoundly reshapes electronic structures in twisted materials. Prevailing treatments, however, typically rely on large-scale density functional theory (DFT), which is computationally costly and mechanistically opaque.…
We prove that the density function of the gradient of a sufficiently smooth function $S : \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$, obtained via a random variable transformation of a uniformly distributed random variable, is…
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with…
In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…
The paper is concerned with the basis properties of root function systems of the Dirac operator with a complex-valued summable potential. We establish a necessary condition of convergence of corresponding spectral expansions.
We consider a lattice gas interacting by the exclusion rule in the presence of a random field given by i.i.d. bounded random variables in a bounded domain in contact with particles reservoir at different densities. We show, in dimensions $d…
It is shown that if the squeezing function tends to one at an h-extendible boundary point of a $\mathcal C^\infty$-smooth, bounded pseudoconvex domain, then the point is strictly pseudoconvex.
The Taylor expansion of thermodynamic observables at a finite baryon chemical potential $\mu_B$ is an oft-used method to circumvent the well-known sign problem of Lattice QCD. Owing to the associated difficulty and limitations of precision…
Let $g(x)=\chi_B(x)$ be the indicator function of a bounded convex set in $\Bbb R^d$, $d\geq 2$, with a smooth boundary and everywhere non-vanishing Gaussian curvature. Using a combinatorial appraoch we prove that if $d \neq 1 \mod 4$, then…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…