Related papers: Densities in Fabry's theorem

It has only recently been possible to study the superconducting state in the attractive Hubbard Hamiltonian via a direct observation of the formation of a gap in the density of states N(w). Here we determine the effect of random chemical…

We study the fate of density perturbations in an Universe dominate by the Chaplygin gas, which exhibit negative pressure. We show that it is possible to obtain the value for the density contrast observed in large scale structure of the…

Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations are…

We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic…

We discuss the relation between density matrices and the uncertainty principle; this allows us to justify and explain a recent statement by Man'ko et al. We thereafter use Hardy's uncertainty principle to prove a new result for Wigner…

It was shown that if in Quantum Theory a fundamental length exists and a well-known measurement procedure is used, then the density matrix at the Planck scale cannot be defined in the usual way, because in this case density matrix trace is…

Using the finite Fourier transform, we introduce a generalization of Pauli-spin matrices for $d$-dimensional spaces, and the resulting set of unitary matrices $S(d) $ is a basis for $d\times d$ matrices. If $N=d_{1}\times…

The probability density function of single-point velocity fluctuations in turbulence is studied systematically using Fourier coefficients in the energy-containing range. In ideal turbulence where energy-containing motions are random and…

Malliavin calculus is implemented in the context of [M. Hairer, A theory of regularity structures, Invent. Math. 2014]. This involves some constructions of independent interest, notably an extension of the structure which accomodates a…

We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove…

Log-Sobolev inequalities (LSIs) upper-bound entropy via a multiple of the Dirichlet form (i.e. norm of a gradient). In this paper we prove a family of entropy-energy inequalities for the binary hypercube which provide a non-linear…

Let $X=\{x_i:i\in\mathbb{Z}\}$, $\dots<x_{i-1}<x_i<x_{i+1}<\dots$, be a sampling set which is separated by a constant $\gamma>0$. Under certain conditions on $\phi$, it is proved that if there exists a positive integer $\nu$ such that…

A general formulation of the equilibrium state of a many-electron system in terms of a (mixed-state, ensemble) density matrix operator in the Fock space, based on the maximum entropy principle, is introduced. Various characteristic…

We reformulate and generalize the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed point…

We use an upper bound on Jacobsthal's function to complete a proof of a known density result. Apart from the bound on Jacobsthal's function used here, the proof we are completing uses only elementary methods and Dirichlet's theorem on the…

The classical problem of maximizing the Shannon entropy of a sum of independent random variables supported on a finite alphabet is considered and settled in the ternary case. Namely, the following theorem is established: if…

We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $\alpha$-dimensional density with respect to some norm, then $\alpha$ must be an integer.

We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory…

A degenerate fermionic vacuum population is suggested. Based on the abundance of the dark energy density in the Universe the vacuum particle mass and number density are estimated. The obtained mass is in reasonable agreement with…

We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.