Dense packing on uniform lattices

We study the Hard Core Model on the graphs ${\rm {\bf \scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\scriptstyle \{0,1\}^{{\rm {\bf G}}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cellular automaton that generates the legal configurations. Its rule involves a parameter which can be naturally characterized as packing pressure. It can have a critical value but from packing point of view just as interesting are the noncritical cases. These phenomena are related to the exponential size of the set of densest packings and more specifically whether these packings are maximally symmetric, simple laminated or essentially random packings.Comment: 18 page

L1551NE - Discovery of a Binary Companion

L1551NE is a very young (class 0 or I) low-mass protostar located close to the well-studied L1551 IRS5. We present here evidence, from 1.3mm continuum interferometric observations at ~1'' resolution, for a binary companion to L1551NE. The companion, whose 1.3mm flux density is ~1/3 that of the primary component, is located 1.43'' (~230 A.U. at 160pc) to the southeast. The millimeterwave emission from the primary component may have been just barely resolved, with deconvolved size ~0.82"x0.70" (~131x112 A.U.). The companion emission was unresolved (<100 A.U.). The pair is embedded within a flattened circum-binary envelope of size ~5.4'' x 2.3'' (~860 x 370 A.U.). The masses of the three components (i.e. from the cicumstellar material of the primary star and its companion, and the envelope) are approximately 0.044, 0.014 and 0.023 Mo respectively.Comment: 8 pages, 1 figur

Thermal state entanglement in harmonic lattices

We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons. Further sites are shown to be entangled only due to boundary effects. Other forms of entanglement are addressed in the second part of the paper by using the energy as witness of entanglement. We close with a comprehensive diagram showing the different phases of entanglement versus complete separability and propose techniques to swap and tune entanglement experimentally.Comment: 9 pages, 4 figure

Phase Diagram of the Dissipative Hofstadter Model

The dissipative quantum mechanics of a charged particle in a uniform magnetic field and periodic potential has delocalization critical points which correspond to backgrounds for the open string. We study the phase diagram of this system (in the magnetic field/dissipation constant plane) and find a fractal structure which, in the limit of zero dissipation, matches the fractal energy level structure of the pure quantum mechanical version of this problem (Hofstadter model).Comment: 23 page

Wannier-Stark ladders in one-dimensional elastic systems

The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and viceversa.Comment: 10 pages, 6 figures, accepted in Phys. Rev. Let

On the Green's Function of the almost-Mathieu Operator

The square tight-binding model in a magnetic field leads to the almost-Mathieu operator which, for rational fields, reduces to a $q\times q$ matrix depending on the components $\mu$, $\nu$ of the wave vector in the magnetic Brillouinzone. We calculate the corresponding Green's function without explicit knowledge of eigenvalues and eigenfunctions and obtain analytical expressions for the diagonal and the first off-diagonal elements; the results which are consistent with the zero magnetic field case can be used to calculate several quantities of physical interest (e. g. the density of states over the entire spectrum, impurity levels in a magnetic field).Comment: 9 pages, 3 figures corrected some minor errors and typo

The detection of the J = 3-2 lines of HCN, HNC, and HCO^+ in the Orion molecular cloud

We report the first measurements of the 1.1 mm (J = 3-2) lines of HCN, HNC, and HCO^+ in the Orion molecular cloud. The low-intensity broad velocity wings seen in the (1-0) lines of HCN and HCO^+ are greatly enhanced in the HCN (3-2) line but not in HCO^+ (3-2). No broad wings are seen in the HNC (3-2) line. The HCN observations suggest molecular hydrogen densities ~ 10^6 cm^(-3) in the broad wing source, and the differences between the lines of HCN and HCO^+ suggest that the lines may be formed in different regions within the source

Off Resonant Pumping for Transition from Continuous to Discrete Spectrum and Quantum Revivals in Systems in Coherent States

We show that in parametrically driven systems and, more generally, in systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the non-linear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomena as an optical analog of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions.Comment: 5 pages, 4 figures, submitted to Jnl. of Optics

Conductivity of 2D lattice electrons in an incommensurate magnetic field

We consider conductivities of two-dimensional lattice electrons in a magnetic field. We focus on systems where the flux per plaquette $\phi$ is irrational (incommensurate flux). To realize the system with the incommensurate flux, we consider a series of systems with commensurate fluxes which converge to the irrational value. We have calculated a real part of the longitudinal conductivity $\sigma_{xx}(\omega)$. Using a scaling analysis, we have found $\Re\sigma_{xx}(\omega)$ behaves as $1/\omega ^{\gamma}$ \,$(\gamma =0.55)$ when $\phi =\tau,(\tau =\frac{\sqrt{5}-1}{2})$ and the Fermi energy is near zero. This behavior is closely related to the known scaling behavior of the spectrum.Comment: 16 pages, postscript files are available on reques

Critical Theories of the Dissipative Hofstadter Model

It has recently been shown that the dissipative Hofstadter model (dissipative quantum mechanics of an electron subject to uniform magnetic field and periodic potential in two dimensions) exhibits critical behavior on a network of lines in the dissipation/magnetic field plane. Apart from their obvious condensed matter interest, the corresponding critical theories represent non-trivial solutions of open string field theory, and a detailed account of their properties would be interesting from several points of view. A subject of particular interest is the dependence of physical quantities on the magnetic field since it, much like $\theta_{\rm QCD}$, serves only to give relative phases to different sectors of the partition sum. In this paper we report the results of an initial investigation of the free energy, $N$-point functions and boundary state of this type of critical theory. Although our primary goal is the study of the magnetic field dependence of these quantities, we will present some new results which bear on the zero magnetic field case as well.Comment: 42 pages (25 reduced