Related papers: Lattice vibrations in the harmonic approximation

In a one-dimensional lattice, the induced metric (from a noncommutative geometry calculation) breaks translation invariance. This leads to some inconsistencies among different spectator frames, in the observation of the hoppings of a test…

When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such…

A semiclassical model is used to investigate oscillations of atomic fermions in a combined magnetic trap and one dimensional optical lattice potential following axial displacement of the trap. The oscillations are shown to have a…

Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to…

We study the propagation of a hole in degenerate (paramagnetic) spin environments. This canonical problem has important connections to a number of physical systems, and is perfectly suited for experimental realization with ultra-cold atoms…

The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac equation on the lattice are presented with the help of the difference equations and the orthogonal polynomials of discrete variable. This area of research is…

We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency…

Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…

Using the Taylor expansion method, we show that it is possible to improve the lattice Boltzmann method for acoustic applications. We derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the…

In this paper we examine the excitations observable in atoms confined in an optical lattice around the superfluid-insulator transition. We use increases in the number variance of atoms, subsequent to tilting the lattice as the primary…

We propose a lattice counterpart of diffeomorphism symmetry in the continuum. A functional integral for quantum gravity is regularized on a discrete set of space-time points, with fermionic or bosonic lattice fields. When the space-time…

We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The error reduction techniques, referred…

Intrinsic fluctuations around the solution of the lattice Boltzmann equation are described or modeled by addition of a white Gaussian noise source. For stationary states a fluctuation-dissipation theorem relates the variance of the…

We introduce an alternative discretization for static quarks on the lattice retaining the O(a) improvement properties of the Eichten-Hill action. In this formulation, statistical fluctuations are reduced by a factor which grows…

We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to…

In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…

A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it…

We present a simple and efficient scheme to reduce atom-number fluctuations in optical lattices. The interaction-energy difference for atoms in different vibrational states is used to remove excess atomic occupation. The remaining vacant…

As an application of perfect lattice perturbation theory, we construct an O(\lambda) perfect lattice action for the anharmonic oscillator analytically in momentum space. In coordinate space we obtain a set of 2-spin and 4-spin couplings…

We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbour sites of the dice lattice accompanied by the…