Related papers: Minimizing Lattice Energy and Hexagonal Crystalliz…

We present two-dimensional crystallization results in the square lattice for finite particle systems consisting of two different atomic types. We identify energy minimizers of configurational energies featuring two-body short-ranged…

We revisit a classical question: how large is the minimal logarithmic energy of $n$ points on $\mathbb{S}^2$ $$ \mathcal{E}_{\log}(n) = \min_{x_1, \dots, x_n \in \mathbb{S}^2} \quad \sum_{i,j =1 \atop i \neq j}^{n}{…

Particles interacting through long-range attraction and short-range repulsion given by power-laws have been widely used to model physical and biological systems, and to predict or explain many of the patterns they display. Apart from rare…

We consider the minimization of theta functions $\theta\_\Lambda(\alpha)=\sum\_{p\in\Lambda}e^{-\pi\alpha|p|^2}$ amongst lattices $\Lambda\subset \mathbb R^d$, by reducing the dimension of the problem, following as a motivation the case…

We investigate the minimization of the energy per point $E\_f$ among $d$-dimensional Bravais lattices, depending on the choice of pairwise potential equal to a radially symmetric function $f(|x|^2)$. We formulate criteria for minimality and…

We prove a nontrivial circuit-depth lower bound for preparing a low-energy state of a locally interacting quantum many-body system in two dimensions, assuming the circuit is geometrically local. For preparing any state which has an energy…

We calculate the energy of a homogeneous one component plasma and find that the energy is lower for correlated motions of the particles as compared to uncorrelated motion. Our starting point is the conserved approximately relativistic…

We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H.~Montgomery. Minimal theta functions. \textit{Glasgow Mathematical Journal}, 30(1):75--85, 1988]. The studied…

Let $\mathcal{P} \subset \mathbb{R}^d$ be a lattice polytope of dimension $d$. Let $b(\mathcal{P})$ denote the number of lattice points belonging to the boundary of $\mathcal{P}$ and $c(\mathcal{P})$ that to the interior of $\mathcal{P}$.…

We study the $\Lambda$-nucleon ($\Lambda N$) force by using lattice QCD. The Bethe-Salpeter amplitude is calculated for the lowest scattering state of the $\Lambda N$ so as to obtain the $\Lambda N$ potential. The numerical calculation is…

We study $\phi^4$ lattice field theory at finite chemical potential $\mu$ in two and four dimensions, using a worldline representation that overcomes the complex action problem. We compute the particle number at very low temperature as a…

We present a short review of our most recent high statistics lattice determinations in the HQET of the following important parameters in B physics: the B--meson binding energy, $\overline{\Lambda}$ and the kinetic energy of the b quark in…

The Riesz potential $f_s(r)=r^{-s}$ is known to be an important building block of many interactions, including Lennard-Jones type potentials $f_{n,m}^{\rm{LJ}}(r):=a r^{-n}-b r^{-m}$, $n>m$ that are widely used in Molecular Simulations. In…

We compute the energy density at arbitrary temperature of the half plane Ising lattice with a boundary magnetic field $H_b$ at a distance $M$ rows from the boundary and compare limiting cases of the exact expression with recent calculations…

We review one of the most accurate low-energy determinations of $\alpha_s$. Comparing at short distances the QCD static energy at three loops and resummation of the next-to-next-to leading logarithms with its determination in 2+1-flavor…

We calculate the one-, two- and three-particle energy levels for different lattice volumes in the complex $\varphi^4$ theory on the lattice. We argue that the exponentially suppressed finite-volume corrections for the two- and…

We describe an extremal property of the hexagonal lattice $\Lambda \subset \mathbb{R}^2$. Let $p$ denote the circumcenter of its fundamental triangle (a so-called deep hole) and let $A_r$ denote the set of lattice points that are at…

In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…

We argue that the lower bound to the barrier energy to flip an up/down spin domain embedded in a down/up spin environment for Ising spin glass is independent of the size of the system. The argument shows the existence of at least one…

We consider the minimum energy problem on the unit sphere $\mathbb S^{d-1}$ in the Euclidean space $\mathbb R^d$, $d\geq 3$, in the presence of an external field $Q$, where the charges are assumed to interact according to Newtonian…