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Register a new userAccuracy of one-dimensional collision integral in the rigid spheres approximation
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The accuracy of calculation of spectral line shapes in one-dimensional approximation is studied analytically in several limiting cases for arbitrary collision kernel and numerically in the rigid spheres model. It is shown that the deviation of the line profile is maximal in the center of the line in case of large perturber mass and intermediate values of collision frequency. For moderate masses of buffer molecules the error of one-dimensional approximation is found not to exceed 5%.
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We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different d
iscretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case.
Three-dimensional (3D) artificial metacrystals host rich topological phases, such as Weyl points, nodal rings and 3D photonic topological insulators. These topological states enable a wide range of applications, including 3D robust waveguide, one-way fiber and negative refraction of surface wave. However, these carefully designed metacrystals are usually very complex, hindering their extension to nanoscale photonic systems. Here, we theoretically proposed and experimentally realized an ideal nodal ring in visible region using a simple 1D photonic crystal. The pi Berry phase around the ring is manifested by a 2pi reflection phases winding and the resultant drumhead surface states. By breaking the inversion symmetry, the nodal ring can be gapped and the pi-Berry phase would diffuse into a toroidal shaped Berry flux, resulting in photonic ridge states (the 3D extension of quantum valley Hall states). Our results provide a simple and feasible platform for exploring 3D topological physics and their potential applications in nanophotonics.
We study ultra-cold bosons out of equilibrium in a one-dimensional (1D) setting and probe the breaking of integrability and the resulting relaxation at the onset of the crossover from one to three dimensions. In a quantum Newtons cradle type experiment, we excite the atoms to oscillate and collide in an array of 1D tubes and observe the evolution for up to 4.8 seconds (400 oscillations) with minimal heating and loss. By investigating the dynamics of the longitudinal momentum distribution function and the transverse excitation, we observe and quantify a two-stage relaxation process. In the initial stage single-body dephasing reduces the 1D densities, thus rapidly drives the 1D gas out of the quantum degenerate regime. The momentum distribution function asymptotically approaches the distribution of quasimomenta (rapidities), which are conserved in an integrable system. In the subsequent long time evolution, the 1D gas slowly relaxes towards thermal equilibrium through the collisions with transversely excited atoms. Moreover, we tune the dynamics in the dimensional crossover by initializing the evolution with different imprinted longitudinal momenta (energies). The dynamical evolution towards the relaxed state is quantitatively described by a semiclassical molecular dynamics simulation.
We calculated the phase diagram of a continuous system of hard spheres loaded in a quasi-one dimensional bichromatic optical lattice. The wavelengths of both lattice-defining lasers were chosen to model an incommensurate arrangement. Densities of one particle and half a particle per potential well were considered. Our results can be compared directly to those of the experimental system [Fallani et al. PRL, {bf 98} 130404 (2007)] from which our initial parameters were taken. The phase diagrams for both densities are significatively different to those obtained by describing the same experimental setup with a Bose-Hubbard model.
The coefficient of restitution of colliding viscoelastic spheres is analytically known as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While beeing analytically exact, this result is not suitable for applications in efficient event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on the analytic result, here we derive expressions for the coefficient of restitution which allow for an application in efficient eMD and MC simulations of granular Systems.
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