Transition from diffusive to ballistic dynamics for a class of finite quantum models

The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length scale, e. g., the introduced distinction between diffusive and ballistic transport appears to be a scale-dependent concept, especially since a transition from diffusive to ballistic behavior is found in the limit of small as well as in the limit of large length scales. All these results are derived by an application of the time-convolutionless projection operator technique and are verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization for a range of model parameters.Comment: 4 pages, 5 figures, approved for publication in Physical Review Letter

Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations

Recent work from our research group has demonstrated that symmetry-projected Hartree--Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C$_2$ dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model $C_{2v}$ insertion pathway for BeH$_2$. The variational excited state methodology developed in this work has two remarkable traits: it is fully black-box and will be applicable to fairly large systems thanks to its mean-field computational cost

Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length

Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This analysis particularly includes the dependence of characteristic transport quantities on the amount of disorder and the energy interval, e.g., the mean free path which separates ballistic and diffusive transport regimes. For these regimes mean velocities, respectively diffusion constants are quantitatively given. By the use of the Boltzmann equation in the limit of weak disorder we reveal the known energy-dependencies of transport quantities. By an application of the time-convolutionless (TCL) projection operator technique in the limit of strong disorder we find evidence for much less pronounced energy dependencies. All our results are partially confirmed by the numerically exact solution of the time-dependent Schroedinger equation or by approximative numerical integrators. A comparison with other findings in the literature is additionally provided.Comment: 23 pages, 10 figure

ExELS: an exoplanet legacy science proposal for the ESA Euclid mission. II. Hot exoplanets and sub-stellar systems

The Exoplanet Euclid Legacy Survey (ExELS) proposes to determine the frequency of cold exoplanets down to Earth mass from host separations of ~1 AU out to the free-floating regime by detecting microlensing events in Galactic Bulge. We show that ExELS can also detect large numbers of hot, transiting exoplanets in the same population. The combined microlensing+transit survey would allow the first self-consistent estimate of the relative frequencies of hot and cold sub-stellar companions, reducing biases in comparing "near-field" radial velocity and transiting exoplanets with "far-field" microlensing exoplanets. The age of the Bulge and its spread in metallicity further allows ExELS to better constrain both the variation of companion frequency with metallicity and statistically explore the strength of star-planet tides. We conservatively estimate that ExELS will detect ~4100 sub-stellar objects, with sensitivity typically reaching down to Neptune-mass planets. Of these, ~600 will be detectable in both Euclid's VIS (optical) channel and NISP H-band imager, with ~90% of detections being hot Jupiters. Likely scenarios predict a range of 2900-7000 for VIS and 400-1600 for H-band. Twice as many can be expected in VIS if the cadence can be increased to match the 20-minute H-band cadence. The separation of planets from brown dwarfs via Doppler boosting or ellipsoidal variability will be possible in a handful of cases. Radial velocity confirmation should be possible in some cases, using 30-metre-class telescopes. We expect secondary eclipses, and reflection and emission from planets to be detectable in up to ~100 systems in both VIS and NISP-H. Transits of ~500 planetary-radius companions will be characterised with two-colour photometry and ~40 with four-colour photometry (VIS,YJH), and the albedo of (and emission from) a large sample of hot Jupiters in the H-band can be explored statistically.Comment: 18 pages, 16 figures, accepted MNRA

Spatially heterogeneous dynamics in granular compaction

We prove the emergence of spatially correlated dynamics in slowly compacting dense granular media by analyzing analytically and numerically multi-point correlation functions in a simple particle model characterized by slow non-equilibrium dynamics. We show that the logarithmically slow dynamics at large times is accompanied by spatially extended dynamic structures that resemble the ones observed in glass-forming liquids and dense colloidal suspensions. This suggests that dynamic heterogeneity is another key common feature present in very different jamming materials.Comment: 4 pages, 3 figure