Related papers: One-dimensional s-p superlattice
We consider a single particle tunnelling in a tight-binding model with nearest-neighbour couplings, in the presence of a periodic high-frequency force. An effective Hamiltonian for the particle is derived using an averaging method…
In Pedersen et al. (2011) we proposed a method to utilize a temporally dependent superlattice potential to mediate spin-selective transport, and thereby probe long and short range magnetic correlations in optical lattices. Specifically this…
Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and continues to attract significant international attention. This…
Density of Lipschitz functions in Newtonian spaces based on quasi-Banach function lattices is discussed. Newtonian spaces are first-order Sobolev-type spaces on abstract metric measure spaces defined via (weak) upper gradients. Our main…
Flat bands have become a pillar of modern condensed matter physics and photonics owing to the vanishing group velocity and diverging density of states. Here, we present a paradigmatic scheme to construct arbitrary flat bands on demand by…
The existence of quasi-bi-Hamiltonian structures for a two-dimensional superintegrable $(k_1,k_2,k_3)$-dependent Kepler-related problem is studied. We make use of an approach that is related with the existence of some complex functions…
The moir\'e superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability. In this work, we propose a photonic analog of the moir\'e superlattice based on dielectric resonator…
One key feature of the multi-orbital superconducting Sr$_2$RuO$_4$ is the presence of nodal or near-nodal quasiparticle excitations revealed in a wide variety of experiments. Typically, a nodal gap structure in a two-dimensional model would…
The gap symmetries of superconductivity are studied in this work. It is found that the gap symmetries are simply determined by the 4-fold rotational symmetries of the coupling potential on neighbor sites. A local on-site coupling potential…
We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not…
Motivated by experimental measurements, we investigate the $p$-$\Omega$ correlation functions and interactions on the basis of a quark model. By solving the inverse scattering problem with channel coupling, we renormalize the coupling to…
The behavior of ultracold atomic gases depends crucially on the two-body scattering properties of these systems. We develop a multichannel scattering theory for atom-atom collisions in quasi-one-dimensional (quasi-1D) geometries such as…
We propose a new class of tight-binding models where a flat band is either gapped from or crossing right through a dispersive band on two-band (i.e., two sites/unit cell) tetragonal and honeycomb lattices. By imposing a condition on the…
We analyze the effective Hamiltonian arising from a suitable power series expansion of the overlap integrals of Wannier functions for confined bosonic atoms in a 1d optical lattice. For certain constraints between the coupling constants, we…
We investigate the interplay of band structure topology and localization properties of Wannier functions. To this end, we extend a recently proposed compressed sensing based paradigm for the search for maximally localized Wannier functions…
We report a first-principles Wannier function study of the electronic structure of PdTe. Its electronic structure is found to be a broad three-dimensional Fermi surface with highly reduced correlations effects. In addition, the higher…
Single particle localization of an ultra-cold atom is studied in one dimension when the atom is confined by an optical lattice and by the incommensurate potential of a high-finesse optical cavity. In the strong coupling regime the atom is a…
In this paper, we consider a class of two-particle tight-binding Hamiltonians, describing pairs of interacting quantum particles on the lattice $\Z^d$, $d\ge 1$ subject to a common external potential $V(x)$ which we assume quasi-periodic…
We present a technique for partitioning the total energy from a semi-local density functional theory calculation into contributions from individual electronic states in a localized Wannier basis. We use our technique to reveal the key role…
Static vortices close together are studied for two different models in 2-dimen- sional Euclidean space. In a simple model for one complex field an expansion in the parameters describing the relative position of two vortices can be given in…