In search of multipolar order on the Penrose tiling

Based on Monte Carlo calculations, multipolar ordering on the Penrose tiling, relevant for two-dimensional molecular adsorbates on quasicrystalline surfaces and for nanomagnetic arrays, has been analyzed. These initial investigations are restricted to multipolar rotors of rank one through four - described by spherical harmonics Ylm with l=1...4 and restricted to m=0 - positioned on the vertices of the rhombic Penrose tiling. At first sight, the ground states of odd-parity multipoles seem to exhibit long-range multipolar order, indicated by the appearance of a superstructure in the form of the decagonal Hexagon-Boat-Star tiling, in agreement with previous investigations of dipolar systems. Yet careful analysis establishes that long-range multipolar order is absent in all cases investigated here, and only short-range order exists. This result should be taken as a warning for any future analysis of order in either real or simulated arrangements of multipoles on quasiperiodic templates

Cascade Encryption Revisited

The security of cascade blockcipher encryption is an important and well-studied problem in theoretical cryptography with practical implications. It is well-known that double encryption improves the security only marginally, leaving triple encryption as the shortest reasonable cascade. In a recent paper, Bellare and Rogaway showed that in the ideal cipher model, triple encryption is significantly more secure than single and double encryption, stating the security of longer cascades as an open question. In this paper, we propose a new lemma on the indistinguishability of systems extending Maurer\u27s theory of random systems. In addition to being of independent interest, it allows us to compactly rephrase Bellare and Rogaway\u27s proof strategy in this framework, thus making the argument more abstract and hence easy to follow. As a result, this allows us to address the security of longer cascades as well as some errors in their paper. Our result implies that for blockciphers with smaller key space than message space (e.g. DES), longer cascades improve the security of the encryption up to a certain limit. This partially answers the open question mentioned above

Towards magnetic slowing of atoms and molecules

We outline a method to slow paramagnetic atoms or molecules using pulsed magnetic fields. We also discuss the possibility of producing trapped particles by adiabatic deceleration of a magnetic trap. We present numerical simulation results for the slowing and trapping of molecular oxygen

Comment on ``Antiferromagnetic Potts Models''

We show that the Wang-Swendsen-Koteck\'y algorithm for antiferromagnetic $q$-state Potts models is nonergodic at zero temperature for $q=3$ on periodic $3m \times 3n$ lattices where $m,n$ are relatively prime. For $q \ge 4$ and/or other lattice sizes or boundary conditions, the ergodicity at zero temperature is an open question

Unsplittable coverings in the plane

A system of sets forms an {\em $m$-fold covering} of a set $X$ if every point of $X$ belongs to at least $m$ of its members. A $1$-fold covering is called a {\em covering}. The problem of splitting multiple coverings into several coverings was motivated by classical density estimates for {\em sphere packings} as well as by the {\em planar sensor cover problem}. It has been the prevailing conjecture for 35 years (settled in many special cases) that for every plane convex body $C$, there exists a constant $m=m(C)$ such that every $m$-fold covering of the plane with translates of $C$ splits into $2$ coverings. In the present paper, it is proved that this conjecture is false for the unit disk. The proof can be generalized to construct, for every $m$, an unsplittable $m$-fold covering of the plane with translates of any open convex body $C$ which has a smooth boundary with everywhere {\em positive curvature}. Somewhat surprisingly, {\em unbounded} open convex sets $C$ do not misbehave, they satisfy the conjecture: every $3$-fold covering of any region of the plane by translates of such a set $C$ splits into two coverings. To establish this result, we prove a general coloring theorem for hypergraphs of a special type: {\em shift-chains}. We also show that there is a constant $c>0$ such that, for any positive integer $m$, every $m$-fold covering of a region with unit disks splits into two coverings, provided that every point is covered by {\em at most} $c2^{m/2}$ sets

Localized helium excitations in 4He_N-benzene clusters

We compute ground and excited state properties of small helium clusters 4He_N containing a single benzene impurity molecule. Ground-state structures and energies are obtained for N=1,2,3,14 from importance-sampled, rigid-body diffusion Monte Carlo (DMC). Excited state energies due to helium vibrational motion near the molecule surface are evaluated using the projection operator, imaginary time spectral evolution (POITSE) method. We find excitation energies of up to ~23 K above the ground state. These states all possess vibrational character of helium atoms in a highly anisotropic potential due to the aromatic molecule, and can be categorized in terms of localized and collective vibrational modes. These results appear to provide precursors for a transition from localized to collective helium excitations at molecular nanosubstrates of increasing size. We discuss the implications of these results for analysis of anomalous spectral features in recent spectroscopic studies of large aromatic molecules in helium clusters.Comment: 15 pages, 5 figures, submitted to Phys. Rev.