Ground-State Roughness of the Disordered Substrate and Flux Line in d=2

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using $d=2$ systems up to size $420^2$, with a minimum of $2 \times 10^3$ realizations at each size, we find very strong evidence for a $\ln^2(L)$ super-rough state at low temperatures.Comment: 10 pages, 3 PS figures, to appear in PR

Charge-Induced Fragmentation of Sodium Clusters

The fission of highly charged sodium clusters with fissilities X>1 is studied by {\em ab initio} molecular dynamics. Na_{24}^{4+} is found to undergo predominantly sequential Na_{3}^{+} emission on a time scale of 1 ps, while Na_{24}^{Q+} (5 \leq Q \leq 8) undergoes multifragmentation on a time scale \geq 0.1 ps, with Na^{+} increasingly the dominant fragment as Q increases. All singly-charged fragments Na_{n}^{+} up to size n=6 are observed. The observed fragment spectrum is, within statistical error, independent of the temperature T of the parent cluster for T \leq 1500 K. These findings are consistent with and explain recent trends observed experimentally.Comment: To appear in Physical Review Letter

Rearrangement of cluster structure during fission processes

Results of molecular dynamics simulations of fission reactions $Na_{10}^{2+} \to Na_7^+ + Na_3^+$ and $Na_{18}^{2+} \to 2 Na_9^+$ are presented. Dependence of the fission barriers on isomer structure of the parent cluster is analyzed. It is demonstrated that the energy necessary for removing homothetic groups of atoms from the parent cluster is largely independent of the isomer form of the parent cluster. Importance of rearrangement of the cluster structure during the fission process is elucidated. This rearrangement may include transition to another isomer state of the parent cluster before actual separation of the daughter fragments begins and/or forming a "neck" between the separating fragments

Engineering Planar Separator Algorithms

We consider classical linear-time planar separator algorithms, determining for a given planar graph a small subset of the nodes whose removal separates the graph into two components of similar size. These algorithms are based upon Planar Separator Theorems, which guarantee separators of size asymptotically in the square root of the number of nodes n and remaining components of size less than 2n/3. In this work, we present a comprehensive experimental study of the algorithms applied to a large variety of graphs, where the main goal is to find separators that do not only satisfy upper bounds but also possess other desirable qualities with respect to separator size and component balance. We propose the usage of fundamental cycles, whose size is at most twice the diameter of the graph, as planar separators: For graphs of small diameter the guaranteed bound is better than the bounds of the classical algorithms, and it turns out that this simple strategy almost always outperforms the other algorithms, even for graphs with large diameter

Dissociation of vertical semiconductor diatomic artificial molecules

We investigate the dissociation of few-electron circular vertical semiconductor double quantum dot artificial molecules at 0 T as a function of interdot distance. Slight mismatch introduced in the fabrication of the artificial molecules from nominally identical constituent quantum wells induces localization by offsetting the energy levels in the quantum dots by up to 2 meV, and this plays a crucial role in the appearance of the addition energy spectra as a function of coupling strength particularly in the weak coupling limit.Comment: Accepted for publication in Phys. Rev. Let

Evolution of electronic and ionic structure of Mg-clusters with the growth cluster size

The optimized structure and electronic properties of neutral and singly charged magnesium clusters have been investigated using ab initio theoretical methods based on density-functional theory and systematic post-Hartree-Fock many-body perturbation theory accounting for all electrons in the system. We have systematically calculated the optimized geometries of neutral and singly charged magnesium clusters consisting of up to 21 atoms, electronic shell closures, binding energies per atom, ionization potentials and the gap between the highest occupied and the lowest unoccupied molecular orbitals. We have investigated the transition to the hcp structure and metallic evolution of the magnesium clusters, as well as the stability of linear chains and rings of magnesium atoms. The results obtained are compared with the available experimental data and the results of other theoretical works.Comment: 30 pages, 10 figures, 3 table

Rough droplet model for spherical metal clusters

We study the thermally activated oscillations, or capillary waves, of a neutral metal cluster within the liquid drop model. These deformations correspond to a surface roughness which we characterize by a single parameter $\Delta$. We derive a simple analytic approximate expression determining $\Delta$ as a function of temperature and cluster size. We then estimate the induced effects on shell structure by means of a periodic orbit analysis and compare with recent data for shell energy of sodium clusters in the size range $50 < N < 250$. A small surface roughness $\Delta\simeq 0.6$ \AA~ is seen to give a reasonable account of the decrease of amplitude of the shell structure observed in experiment. Moreover -- contrary to usual Jahn-Teller type of deformations -- roughness correctly reproduces the shape of the shell energy in the domain of sizes considered in experiment.Comment: 20 pages, 4 figures, important modifications of the presentation, to appear in Phys. Rev.