Anomalous quantum reflection of Bose-Einstein condensates from a silicon surface: the role of dynamical excitations

We investigate the effect of inter-atomic interactions on the quantum-mechanical reflection of Bose-Einstein condensates from regions of rapid potential variation. The reflection process depends critically on the density and incident velocity of the condensate. For low densities and high velocities, the atom cloud has almost the same form before and after reflection. Conversely, at high densities and low velocities, the reflection process generates solitons and vortex rings that fragment the condensate. We show that this fragmentation can explain the anomalously low reflection probabilities recently measured for low-velocity condensates incident on a silicon surface.Comment: 5 figures, 5 pages, references correcte

The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

Saddles in the energy landscape: extensivity and thermodynamic formalism

We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system size, as well as several approximations for the properties of low-order saddles (i.e., those with only a few unstable directions). We then cast the canonical partition function in a saddle-explicit form and develop, for the first time, a rigorous energy landscape approach capable of reproducing trends observed in simulations, in particular the temperature dependence of the energy and fractional order of sampled saddles.Comment: 4 pages, 1 figur

Local cloning of entangled states

We investigate the conditions under which a set \SC of pure bipartite quantum states on a $D\times D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in \SC must be full Schmidt rank and equally entangled under the $G$-concurrence measure, and (ii) the set \SC can be extended to a larger clonable set generated by a finite group $G$ of order $|G|=N$, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides $D$ exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all $D$; and (ii) local cloning of entangled qubit states with non-vanishing entanglement. In both of these cases, a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary "shift" operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in D=3 we show that a maximally entangled resource is again necessary and sufficient, while for higher dimensional systems, we find that the resource state must be strictly more entangled than the states in \SC. All of our necessary conditions for separable operations are also necessary conditions for LOCC, since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.Comment: REVTEX 15 pages, 1 figure, minor modifications. Same as the published version. Any comments are welcome

A λ = 1.3 Millimeter Aperture Synthesis Molecular Line Survey of Orion Kleinmann-Low

We present a 1".3 spatial resolution interferometric spectral line survey of the core of the Orion molecular cloud, obtained with the OVRO millimeter array. Covering 4 GHz bandwidth in total, the survey contains ~100 emission lines from 18 chemical species. The spatial distributions of a number of molecules point to source I near the IRc2 complex as the dominant energy source in the region but do not rule out the presence of additional lower luminosity objects. At arcsecond resolution, the offsets between dust emission and various molecular tracers suggest that the spectacular "hot core" emission in the Orion core arises via the heating and ablation of material from the surfaces of very high density clumps located ≳500 AU from source I and traced by the dust emission. We find no evidence for a strong internal heating source within the hot core condensation(s)

Cross-Correlation Studies between CMB Temperature Anisotropies and 21 cm Fluctuations

During the transition from a neutral to a fully reionized universe, scattering of cosmic microwave background (CMB) photons via free-electrons leads to a new anisotropy contribution to the temperature distribution. If the reionization process is inhomogeneous and patchy, the era of reionization is also visible via brightness temperature fluctuations in the redshifted 21 cm line emission from neutral Hydrogen. Since regions containing electrons and neutral Hydrogen are expected to trace the same underlying density field, the two are (anti) correlated and this is expected to be reflected in the anisotropy maps via a correlation between arcminute-scale CMB temperature and the 21 cm background. In terms of the angular cross-power spectrum, unfortunately, this correlation is insignificant due to a geometric cancellation associated with second order CMB anisotropies. The same cross-correlation between ionized and neutral regions, however, can be studied using a bispectrum involving large scale velocity field of ionized regions from the Doppler effect, arcminute scale CMB anisotropies during reionization, and the 21 cm background. While the geometric cancellation is partly avoided, the signal-to-noise ratio related to this bispectrum is reduced due to the large cosmic variance related to velocity fluctuations traced by the Doppler effect. Unless the velocity field during reionization can be independently established, it is unlikely that the correlation information related to the relative distribution of ionized electrons and regions containing neutral Hydrogen can be obtained with a combined study involving CMB and 21 cm fluctuations.Comment: 10 pages, 3 figure

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

Quantum Numbers for Excitations of Bose-Einstein Condensates in 1D Optical Lattices

The excitation spectrum and the band structure of a Bose-Einstein condensate in a periodic potential are investigated. Analyses within full 3D systems, finite 1D systems, and ideal periodic 1D systems are compared. We find two branches of excitations in the spectra of the finite 1D model. The band structures for the first and (part of) the second band are compared between a finite 1D and the fully periodic 1D systems, utilizing a new definition of a effective wavenumber and a phase-slip number. The upper and lower edges of the first gap coincide well between the two cases. The remaining difference is explained by the existence of the two branches due to the finite-size effect.Comment: 5 pages, 9 figure

On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble

We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte-Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom--in which all potential energies, volumes, and numbers of particles are equally probable--we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.Comment: 21 pages, 4 figure