Related papers: Optimal lattice configurations for interacting spa…
We consider a simple two-dimemsional harmonic lattice with random, independent and identically distributed masses. Using the methods of stochastic homogenization, we show that solutions with long wave initial data converge in an appropriate…
We consider translationally invariant tight-binding all-bands-flat networks which lack dispersion. In a recent work [arXiv:2004.11871] we derived the subset of these networks which preserves nonlinear caging, i.e. keeps compact excitations…
The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge…
Open lattices are characterized by low volume-fraction arrangements of building blocks, low coordination number, and open spaces between building blocks. The self-assembly of these lattices faces the challenge of mechanical instability due…
The existence of flat bands is generally thought to be physically possible only for dimensions larger than one. However, by exciting a system with different orthogonal states this condition can be reformulated. In this work, we demonstrate…
We present and analyze mechanisms for the patterned deposition of particles in a spatio-temporally driven lattice. The working principle is based on the breaking of the spatio-temporal translation symmetry, which is responsible for the…
We study the area-dependent entropy and two-site entanglement for two state Bose-Einstein condensates in a 2D optical lattice. We consider the case where the array of two component condensates behave like an ensemble of spin-half particles…
The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111)…
The most energetically favourable arrangement of low-density electrons in an infinite two-dimensional plane is the ordered triangular Wigner lattice. However, in most instances of contemporary interest one deals instead with finite clusters…
Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have…
We demonstrate the directed transport of underdamped particles in two dimensional lattices of arbitrary geometry driven by an unbiased ac-driving force. The direction of transport can be controlled via the lattice geometry as well as the…
We propose to extend the d'Humi\'eres version of the lattice Boltzmann scheme to triangular meshes. We use Bravais lattices or more general lattices with the property that the degree of each internal vertex is supposed to be constant. On…
We experimentally study the effect of inter-particle interactions on the flat-band states of a two-dimensional Lieb lattice with drive and dissipation. Exploiting the giant nonlinear interactions of exciton polaritons we observe compactly…
Few-body physics plays a central role in many branches of physics, such as nuclear physics and atomic physics. Advances in controlling ultra-cold quantum gases provide an ideal testbed for few-body physics theory. In this work, we study…
The propagation of elastic waves on discrete periodic Euler-Bernoulli mass-beam lattices is characterised by the competition between coupled translational and rotational degrees-of-freedom at the mass-beam junctions. We influence the…
The spectral density of bound pairs in ideal 1D, 2D and Bethe lattices is computed for weak and strong interactions. The computations are performed with Green's functions by an efficient recursion method in real space. For the range of…
This paper examines the propagation of time-harmonic waves in a two-dimensional triangular lattice with a lattice constant $a = 1$. The sources are positioned along line segments within the lattice. Specifically, we investigate the discrete…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…
We consider a 1D lattice gas model in which the atoms interact via an infinite number of cluster interactions within contiguous atomic chains plus the next nearest neighbor pairwise interaction. All interactions are of arbitrary strength.…
We propose a model for a two dimensional, associative water-like lattice gas with one single variable representing both long and short-range interactions. The corresponding hamiltonian was solved exactly, by state enumeration in a finite…