Related papers: Lattice vibrations in the harmonic approximation
On approaching the glass transition, the microscopic kinetic unit spends increasing time rattling in the cage of the first neighbours whereas its average escape time, the structural relaxation time $\tau_\alpha$, increases from a few…
We consider a classical, two-dimensional system of identical particles which interact via a finite-ranged, repulsive pair potential. We assume that the system is in a crystalline phase. We calculate the normal vibrational modes of a…
We study the scattering of matter-waves from interacting bosons in a one-dimensional optical lattice, described by the Bose-Hubbard Hamiltonian. We derive analytically a formula for the inelastic cross section as a function of the atomic…
Lattice refinement in LQC, its meaning and its necessity are discussed. The r\^ole of lattice refinement for the realisation of a successful inflationary model is explicitly shown. A simple and effective numerical technique to solve the…
This note has no new results and is therefore not intended to be submitted to a "research" journal in the foreseeable future, but to be available to the numerous individuals who are interested in this issue. The Debye-Waller factor is the…
Estimating decay parameters in lattice simulations is a computationally demanding problem, requiring several volumes and momenta. We explore an alternative approach, where the transition amplitude can be extracted from the spectral…
We generalize, and then use, a recently introduced formalism to study thermal fluctuations of atomic displacements in several two and three dimensional crystals. We study both close packed as well as open crystals with multi atom bases.…
This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a…
Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine the structure of the…
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant…
Atom interferometers provide a powerful tool for measuring physical constants and testifying fundamental physics with unprecedented precision. Conventional atom interferometry focuses on the phase difference between two paths and utilizes…
The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is…
We study dissipative transport of spontaneously emitting atoms in a 1D standing-wave laser field in the regimes where the underlying deterministic Hamiltonian dynamics is regular and chaotic. A Monte Carlo stochastic wavefunction method is…
This work generalizes our previous works on fcc-bcc martensitic transformations to the larger family of transformations in the fcc-bcc-hcp system and to fcc-fcc mechanical twinning. The analytical expressions of the atomic displacements and…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
Atomic wave packets loaded into a phase-modulated vertical optical-lattice potential exhibit a coherent delocalization dynamics arising from intraband transitions among Wannier-Stark levels. Wannier-Stark intraband transitions are here…
Consider a point process in Euclidean space obtained by perturbing the integer lattice with independent and identically distributed random vectors. Under mild assumptions on the law of the perturbations, we construct a translation-invariant…
A straightforward analytical scheme is proposed for computing the long-time, asymptotic mean velocity and dispersivity (effective diffusivity) of a particle undergoing a discrete biased random walk on a periodic lattice amongst an array of…
We investigate a new type of quantum ratchet which may be realised by cold atoms in a double-well optical lattice which is pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate $D$ is…