Cold atoms in real-space optical lattices

Cold atoms in optical lattices are described in {\it real space} by multi-orbital mean-field Ans\"atze. In this work we consider four typical systems: (i) spinless identical bosons, (ii) spinor identical bosons (iii), Bose-Bose mixtures, and (iv) Bose-Fermi mixtures and derive in each case the corresponding multi-orbital mean-field energy-functional and working equations. The notions of {\it dressed} Wannier functions and Wannier spinors are introduced and the equations defining them are presented and discussed. The dressed Wannier functions are the set of orthogonal, translationally-equivalent orbitals which minimizes the energy of the Hamiltonian including boson-boson (particle-particle) interactions. Illustrative examples of dressed Wannier functions are provided for spinless bosonic atoms and mixtures in one-dimensional optical lattices.Comment: 27 pages, 4 figures; [version minus figures published

On-top fragmentation stabilizes atom-rich attractive Bose-Einstein condensates

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number $N_{\mathrm{cr}}^{\mathrm{GP}}$ of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above $N_{\mathrm{cr}}^{\mathrm{GP}}$. The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.Comment: 12 pages, 4 figure

Confidential genetic testing and electronic health records: A survey of current practices among Huntington disease testing centers

BACKGROUND: Clinical care teams providing presymptomatic genetic testing often employ advanced confidentiality practices for documentation and result storage. However, patient requests for increased confidentiality may be in conflict with the legal obligations of medical providers to document patient care activities in the electronic health record (EHR). Huntington disease presents a representative case study for investigating the ways centers currently balance the requirements of EHRs with the privacy demands of patients seeking presymptomatic genetic testing. METHODS: We surveyed 23 HD centers (53% response rate) regarding their use of the EHR for presymptomatic HD testing. RESULTS: Our survey revealed that clinical care teams and laboratories have each developed their own practices, which are cumbersome and often include EHR avoidance. We found that a majority of HD care teams record appointments in the EHR (91%), often using vague notes. Approximately half of the care teams (52%) keep presymptomatic results of out of the EHR. CONCLUSION: As genetic knowledge grows, linking more genes to late-onset conditions, institutions will benefit from having professional recommendations to guide development of policies for EHR documentation of presymptomatic genetic results. Policies must be sensitive to the ethical differences and patient demands for presymptomatic genetic testing compared to those undergoing confirmatory genetic testing

Minimal ureagenesis is necessary for survival in the murine model of hyperargininemia treated by AAV-based gene therapy.

Hyperammonemia is less severe in arginase 1 deficiency compared with other urea cycle defects. Affected patients manifest hyperargininemia and infrequent episodes of hyperammonemia. Patients typically suffer from neurological impairment with cortical and pyramidal tract deterioration, spasticity, loss of ambulation, seizures and intellectual disability; death is less common than with other urea cycle disorders. In a mouse model of arginase I deficiency, the onset of symptoms begins with weight loss and gait instability, which progresses toward development of tail tremor with seizure-like activity; death typically occurs at about 2 weeks of life. Adeno-associated viral vector gene replacement strategies result in long-term survival of mice with this disorder. With neonatal administration of vector, the viral copy number in the liver greatly declines with hepatocyte proliferation in the first 5 weeks of life. Although the animals do survive, it is not known from a functional standpoint how well the urea cycle is functioning in the adult animals that receive adeno-associated virus. In these studies, we administered [1-13C] acetate to both littermate controls and adeno-associated virus-treated arginase 1 knockout animals and examined flux through the urea cycle. Circulating ammonia levels were mildly elevated in treated animals. Arginine and glutamine also had perturbations. Assessment 30 min after acetate administration demonstrated that ureagenesis was present in the treated knockout liver at levels as low at 3.3% of control animals. These studies demonstrate that only minimal levels of hepatic arginase activity are necessary for survival and ureagenesis in arginase-deficient mice and that this level of activity results in control of circulating ammonia. These results may have implications for potential therapy in humans with arginase deficiency

Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass

In 2015, Mantoulidis and Schoen constructed $3$-dimensional asymptotically Euclidean manifolds with non-negative scalar curvature whose ADM mass can be made arbitrarily close to the optimal value of the Riemannian Penrose Inequality, while the intrinsic geometry of the outermost minimal surface can be "far away" from being round. The resulting manifolds, called \emph{extensions}, are geometrically not "close" to a spatial Schwarzschild manifold. This suggests instability of the Riemannian Penrose Inequality. Their construction was later adapted to $n+1$ dimensions by Cabrera Pacheco and Miao, suggesting instability of the higher dimensional Riemannian Penrose Inequality. In recent papers by Alaee, Cabrera Pacheco, and Cederbaum and by Cabrera Pacheco, Cederbaum, and McCormick, a similar construction was performed for asymptotically Euclidean, electrically charged Riemannian manifolds and for asymptotically hyperbolic Riemannian manifolds, respectively, obtaining $3$-dimensional extensions that suggest instability of the Riemannian Penrose Inequality with electric charge and of the conjectured asymptotically hyperbolic Riemannian Penrose Inequality in $3$ dimensions. This paper combines and generalizes all the aforementioned results by constructing suitable asymptotically hyperbolic or asymptotically Euclidean extensions with electric charge in $n+1$ dimensions for $n\geq2$. Besides suggesting instability of a naturally conjecturally generalized Riemannian Penrose Inequality, the constructed extensions give insights into an ad hoc generalized notion of Bartnik mass, similar to the Bartnik mass estimate for minimal surfaces proven by Mantoulidis and Schoen via their extensions, and unifying the Bartnik mass estimates in the various scenarios mentioned above

Ab initio Green's function formalism for band structures

Using the Green's function formalism, an ab initio theory for band structures of crystals is derived starting from the Hartree-Fock approximation. It is based on the algebraic diagrammatic construction scheme for the self-energy which is formulated for crystal orbitals (CO-ADC). In this approach, the poles of the Green's function are determined by solving a suitable Hermitian eigenvalue problem. The method is not only applicable to the outer valence and conduction bands, it is also stable for inner valence bands where strong electron correlations are effective. The key to the proposed scheme is to evaluate the self-energy in terms of Wannier orbitals before transforming it to a crystal momentum representation. Exploiting the fact that electron correlations are mainly local, one can truncate the lattice summations by an appropriate configuration selection scheme. This yields a flat configuration space; i.e., its size scales only linearly with the number of atoms per unit cell for large systems and, under certain conditions, the computational effort to determine band structures also scales linearly. As a first application of the new formalism, a lithium fluoride crystal has been chosen. A minimal basis set description is studied, and a satisfactory agreement with previous theoretical and experimental results for the fundamental band gap and the width of the F 2p valence band complex is obtained.Comment: 20 pages, 3 figures, 1 table, RevTeX4, new section on lithium fluorid

Mass, angular-momentum, and charge inequalities for axisymmetric initial data

We present the key elements of the proof of an upper bound for angular-momentum and charge in terms of the mass for electro-vacuum asymptotically flat axisymmetric initial data sets with simply connected orbit space

Dynamic interference of photoelectrons produced by high-frequency laser pulses

The ionization of an atom by a high-frequency intense laser pulse, where the energy of a single-photon is sufficient to ionize the system, is investigated from first principles. It is shown that as a consequence of an AC Stark effect in the continuum, the energy of the photoelectron follows the envelope of the laser pulse. This is demonstrated to result in strong dynamic interference of the photoelectrons of the same kinetic energy emitted at different times. Numerically exact computations on the hydrogen atom demonstrate that the dynamic interference spectacularly modifies the photoionization process and is prominently manifested in the photoelectron spectrum by the appearance of a distinct multi-peak pattern. The general theory is shown to be well approximated by explicit analytical expressions which allow for a transparent understanding of the discovered phenomena and for making predictions on the dependence of the measured spectrum on the properties of the pulse.Comment: 5 figure