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We apply general methods to generate upper and lower bounds for the essential minimum of a specific family of height functions. In particular, the results shown in this article apply to the case of the Zhang-Zagier height. Furthermore, we…

Number Theory · Mathematics 2022-02-02 Marcos Isai Morales Inostroza

Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express…

General Relativity and Quantum Cosmology · Physics 2009-10-31 Zdzislaw A. Golda , Andrzej Woszczyna

We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 S. Lafortune , B. Grammaticos , A. Ramani , P. Winternitz

Gibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many…

Probability · Mathematics 2023-05-26 Ujan Gangopadhyay , Subhro Ghosh , Kin Aun Tan

Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a…

Strongly Correlated Electrons · Physics 2015-05-20 Roger Haydock , C. M. M. Nex

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of amorphous many-particle configurations that…

Statistical Mechanics · Physics 2007-05-23 S. Torquato , F. H. Stillinger

Determining the maximal density $m_1(\mathbb{R}^2)$ of planar sets without unit distances is a fundamental problem in combinatorial geometry. This paper investigates lower bounds for this quantity. We introduce a novel approach to…

Metric Geometry · Mathematics 2025-04-14 Alexander Tolmachev

We prove a rigorous inequality estimating the purity of a reduced density matrix of a composite quantum system in terms of cross-correlation of the same state and an arbitrary product state. Various immediate applications of our result are…

Quantum Physics · Physics 2009-11-10 Tomaz Prosen , Thomas H. Seligman , Marko Znidaric

The densities of small linear structures (such as arithmetic progressions) in subsets of Abelian groups can be expressed as certain analytic averages involving linear forms. Higher-order Fourier analysis examines such averages by…

Number Theory · Mathematics 2014-05-09 Hamed Hatami , Pooya Hatami , Shachar Lovett

We calculate the properties of a one-dimensional $Z_2$ lattice gauge theory in different Gauss law sectors, corresponding to different configurations of static charges set by the orientations of the gauge spins. Importantly, in quantum…

Quantum Gases · Physics 2024-09-20 Vaibhav Sharma , Erich J Mueller

For a given finitely generated multiplicative subgroup of the rationals which possibly contain negative numbers, we derive, subject to GRH, formulas for the densities of primes for which the index of the reduction group has a given value.…

Number Theory · Mathematics 2020-06-04 Herish Abdullah , Andam Ali Mustafa , Francesco Pappalardi

We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…

Number Theory · Mathematics 2016-01-26 Ryoichi Kunisada

By comparing the results from numerical microlensing simulations to the observed long-term variability of quasars, strong upper limits on the cosmological density of compact objects in the 0.0001-1 solar mass range may in principle be…

Astrophysics · Physics 2009-11-07 Erik Zackrisson , Nils Bergvall

For a hard-core Bose gas on a one-dimensional lattice we find characteristic oscillations in the density-density correlation function. Their wavelength diverges as the system undergoes a continuous transition from an incommensurate to a…

Statistical Mechanics · Physics 2016-08-31 C. Ates , Ch. Moseley , K. Ziegler

In this paper we analyse both the dynamics and the high density physics of the infinite dimensional lattice gas model for random heteropolymers recently introduced in \cite{jort}. Restricting ourselves to site-disordered heteropolymers, we…

Disordered Systems and Neural Networks · Physics 2009-11-07 H. Chakravorty , J. van Mourik , A. C. C. Coolen

Consider a Gaussian stationary sequence with unit variance $X=\{X_k;k\in {\mathbb{N}}\cup\{0\}\}$. Assume that the central limit theorem holds for a weighted sum of the form $V_n=n^{-1/2}\sum^{n-1}_{k=0}f(X_k)$, where $f$ designates a…

Probability · Mathematics 2015-09-30 Yaozhong Hu , David Nualart , Samy Tindel , Fangjun Xu

We derive exact density functionals for systems of hard rods with first-neighbor interactions of arbitrary shape but limited range on a one-dimensional lattice. The size of all rods is the same integer unit of the lattice constant. The…

Statistical Mechanics · Physics 2013-12-17 Benaoumeur Bakhti , Gerhard Müller , Philipp Maass

For an odd prime $p$, we determine the lower central series of a large family of non-periodic GGS-groups, which has a density of roughly $(\frac{p-1}{p})^2$ within all GGS-groups. This means a significant extension of the knowledge…

Group Theory · Mathematics 2024-10-11 Gustavo A. Fernández-Alcober , Mikel E. Garciarena , Marialaura Noce

We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a ``no go'' for simulating the original continuum classical gauge fields over a long time…

High Energy Physics - Theory · Physics 2008-02-03 Holger Bech Nielsen , Hans Henrik Rugh , Svend Erik Rugh

Abstract upper densities are monotone and subadditive functions from the power set of positive integers to the unit real interval that generalize the upper densities used in number theory, including the upper asymptotic density, the upper…

Number Theory · Mathematics 2017-09-12 Mauro Di Nasso , Renling Jin