Related papers: On the Pair Correlation Density for Hyperbolic Ang…
We show that for each $n \geq 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty)$. We also show that for any $n\geq 2$ and any Salem number $\lambda$, there is a closed arithmetic hyperbolic…
Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments whereas in cold-gases systems,…
We theoretically investigate the thermodynamics of an interacting inhomogeneous two-component Fermi gas in an optical lattice. Motivated by a recent experiment by L. Hackerm\"uller et al., Science, 327, 1621 (2010), we study the effect of…
We construct cross sections for the geodesic flow on the orbifolds $\Gamma\backslash H$ which are tailor-made for the requirements of transfer operator approaches to Maass cusp forms and Selberg zeta functions. Here, $H$ denotes the…
A possibility to measure the energy and polarization distributions of high intensity gamma-beams is considered. This possibility is based on measurements of the number of electron-pozitron pairs in such media as laser waves and single…
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…
We study the vortex formation in optical lattices submitted to artificial gauge potentials. We compute the superfluid density for Abelian and non-Abelian gauge potentials with a mean-field approach of the Bose-Hubbard model and we determine…
A dense form of matter is formed in relativistic heavy ion collisions. The constituent degrees of freedom in this dense matter are currently unknown. Long-range, forward-backward multiplicity correlations (LRC) are expected to arise due to…
Strong correlations can dramatically modify the thermodynamics of a quantum many-particle system. Especially intriguing behaviour can appear when the system adiabatically enters a strongly correlated regime, for the interplay between…
We investigate two density questions for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) for an open set $\Omega\subset\mathbb R^n$,…
We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the…
We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always {\it…
A planar square lattice model with 3-d spins interacting with nearest neighbours through a potential -$\epsilon P_4 (cos \theta_{ij})$ is studied by Monte Carlo technique. Lattice sizes from 10$\times$10 to 30$\times$30 are considered for…
The availability of ultrafast pulses of coherent hard x-rays from the Linac Coherent Light Source opens new opportunities for studies of atomic-scale dynamics in amorphous materials. Here we show that single ultrafast coherent x-ray pulses…
We realize and study the ionic Hubbard model using an interacting two-component gas of fermionic atoms loaded into an optical lattice. The bipartite lattice has honeycomb geometry with a staggered energy-offset that explicitly breaks the…
We compute the pair entanglement between two interacting bosons in a two dimensional (2D)isotropic harmonic trap. The interaction potential is modeled by a 2D regularized pseudo-potential. By analytically decomposing the wave function into…
The two-particle momentum correlation between the Omega-baryon ($\Omega$) and the $^{4}He (\alpha) $ in high-energy heavy ion collisions is explored. Such correlations as an alternative source of information can help us further understand…
The Hessian Topology is a subject with interesting relations with some classical problems of analysis and geometry. In this article we prove a conjecture on this subject stated by V.I. Arnold concerning the number of connected components of…
Let $K$ be a convex body in $\mathbb{R}^n$, let $L$ be a lattice with covolume one, and let $\eta>0$. We say that $K$ and $L$ form an $\eta$-smooth cover if each point $x \in \mathbb{R}^n$ is covered by $(1 \pm \eta) vol(K)$ translates of…
Let \Gamma be a lattice in G=SL(n,R) and X=G/S a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish uniform distribution of orbits of \Gamma in X…