Quantum Phase Transitions in Bosonic Heteronuclear Pairing Hamiltonians

We explore the phase diagram of two-component bosons with Feshbach resonant pairing interactions in an optical lattice. It has been shown in previous work to exhibit a rich variety of phases and phase transitions, including a paradigmatic Ising quantum phase transition within the second Mott lobe. We discuss the evolution of the phase diagram with system parameters and relate this to the predictions of Landau theory. We extend our exact diagonalization studies of the one-dimensional bosonic Hamiltonian and confirm additional Ising critical exponents for the longitudinal and transverse magnetic susceptibilities within the second Mott lobe. The numerical results for the ground state energy and transverse magnetization are in good agreement with exact solutions of the Ising model in the thermodynamic limit. We also provide details of the low-energy spectrum, as well as density fluctuations and superfluid fractions in the grand canonical ensemble.Comment: 11 pages, 14 figures. To appear in Phys. Rev.

Polaritons and Pairing Phenomena in Bose--Hubbard Mixtures

Motivated by recent experiments on cold atomic gases in ultra high finesse optical cavities, we consider the problem of a two-band Bose--Hubbard model coupled to quantum light. Photoexcitation promotes carriers between the bands and we study the non-trivial interplay between Mott insulating behavior and superfluidity. The model displays a global U(1) X U(1) symmetry which supports the coexistence of Mott insulating and superfluid phases, and yields a rich phase diagram with multicritical points. This symmetry property is shared by several other problems of current experimental interest, including two-component Bose gases in optical lattices, and the bosonic BEC-BCS crossover problem for atom-molecule mixtures induced by a Feshbach resonance. We corroborate our findings by numerical simulations.Comment: 4 pages, 3 figure

Smoking and COVID Living Review (v11): a bayesian analysis

Aims: To estimate the association of smoking status with rates of i) infection, ii) hospitalisation, iii) disease severity, and iv) mortality from SARS-CoV-2/COVID-19 disease. Design: Living rapid review of observational and experimental studies with random-effects hierarchical Bayesian meta-analyses. Published articles and pre-prints were identified via MEDLINE and medRxiv. Setting: Community or hospital. No restrictions on location. Participants: Adults who received a SARS-CoV-2 test or a COVID-19 diagnosis. Measurements: Outcomes were SARS-CoV-2 infection, hospitalisation, disease severity and mortality stratified by smoking status. Study quality was assessed (i.e. ‘good’, ‘fair’ and ‘poor’). Findings: v11 (searches up to 2021-02-16) included 405 studies with 62 ‘good’ and ‘fair’ quality studies included in unadjusted meta-analyses. 121 studies (29.9%) reported current, former and never smoking status with the remainder using broader categories. Recorded smoking prevalence among people with COVID-19 was generally lower than national prevalence. Current compared with never smokers were at reduced risk of SARS-CoV-2 infection (RR = 0.71, 95% Credible Interval (CrI) = 0.61-0.82, τ = 0.34). Data for former smokers were inconclusive (RR = 1.03, 95% CrI = 0.95-1.11, τ = 0.17) but favoured there being no important association (4% probability of RR ≥1.1). Former compared with never smokers were at increased risk of hospitalisation (RR = 1.19, CrI = 1.1-1.29, τ = 0.13), greater disease severity (RR = 1.8, CrI = 1.27-2.55, τ = 0.46) and mortality (RR = 1.56, CrI = 1.23-2, τ = 0.43). Data for current smokers on hospitalisation, disease severity and mortality were inconclusive (RR = 1.1, 95% CrI = 0.99-1.21, τ = 0.15; RR 1.26, 95% CrI = 0.92-1.73, τ = 0.32; RR = 1.12, 95% CrI = 0.84-1.47, τ = 0.42, respectively) but favoured there being no important associations with hospitalisation and mortality (49% and 56% probability of RR ≥1.1, respectively) and a small but important association with disease severity (83% probability of RR ≥1.1). Conclusions: Compared with never smokers, current smokers appear to be at reduced risk of SARS-CoV-2 infection while former smokers appear to be at increased risk of hospitalisation, greater disease severity and mortality from COVID-19. However, it is uncertain whether these associations are causal

Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians

We explore the Mott insulating state of single-band bosonic pairing Hamiltonians using analytical approaches and large scale density matrix renormalization group calculations. We focus on the second Mott lobe which exhibits a magnetic quantum phase transition in the Ising universality class. We use this feature to discuss the behavior of a range of physical observables within the framework of the 1D quantum Ising model and the strongly anisotropic Heisenberg model. This includes the properties of local expectation values and correlation functions both at and away from criticality. Depending on the microscopic interactions it is possible to achieve either antiferromagnetic or ferromagnetic exchange interactions and we highlight the possibility of observing the E8 mass spectrum for the critical Ising model in a longitudinal magnetic field.Comment: 14 pages, 15 figure

A characterization of quadric constant mean curvature hypersurfaces of spheres

Let $\phi:M\to\mathbb{S}^{n+1}\subset\mathbb{R}^{n+2}$ be an immersion of a complete $n$-dimensional oriented manifold. For any $v\in\mathbb{R}^{n+2}$, let us denote by $\ell_v:M\to\mathbb{R}$ the function given by $\ell_v(x)=\phi(x),v$ and by $f_v:M\to\mathbb{R}$, the function given by $f_v(x)=\nu(x),v$, where $\nu:M\to\mathbb{S}^{n}$ is a Gauss map. We will prove that if $M$ has constant mean curvature, and, for some $v\ne{\bf 0}$ and some real number $\lambda$, we have that $\ell_v=\lambda f_v$, then, $\phi(M)$ is either a totally umbilical sphere or a Clifford hypersurface. As an application, we will use this result to prove that the weak stability index of any compact constant mean curvature hypersurface $M^n$ in $\mathbb{S}^{n+1}$ which is neither totally umbilical nor a Clifford hypersurface and has constant scalar curvature is greater than or equal to $2n+4$.Comment: Final version (February 2008). To appear in the Journal of Geometric Analysi

PTSD Symptoms and Alcohol-Related Problems among Veterans: Temporal Associations and Vulnerability

Posttraumatic stress disorder (PTSD) is associated with elevated risk of both alcohol use disorder (AUD) and related conduct problems, which are associated with behavioral and emotional dysregulation. We conducted an intensive longitudinal burst design study with 10 weeks of experience sampling over the course of 1.5 years with 250 veterans of recent conflicts. We tested time-series models of daily associations between posttraumatic stress symptoms (PTSS), alcohol dependence syndrome, and conduct problems. Exacerbations of PTSS predicted higher dependence syndrome and conduct problems the next day. This effect was significant after controlling for both concurrent (i.e., same-day) associations between drinking and the outcomes as well as the strength of associations between the outcomes from one day to the next (i.e., autoregression). Affect lability and disinhibition were hypothesized vulnerability factors increasing the strength of within-person predictors of dependence syndrome and conduct problems. Lability and disinhibition were associated with greater dependence syndrome symptoms and conduct problems over the follow-up period. Consistent with expectation, lability rather than disinhibition increased the association between drinking and dependence syndrome as well as the strength of association between dependence syndrome symptoms from one day to the next. Moderating effects of disinhibition in the conduct problems model were not significant. Importantly, results indicated reciprocal associations over time. Lability potentiated the association between dependence syndrome symptoms and next-day PTSS, whereas disinhibition potentiated the association between conduct problems and next-day PTSS. Results demonstrate complex dynamic associations between PTSS, AUD symptoms, and conduct problems over time indicative of broad regulatory impairments

Highly charged ion X-rays from Electron-Cyclotron Resonance Ion Sources

Radiation from the highly-charged ions contained in the plasma of Electron-Cyclotron Resonance Ion Sources constitutes a very bright source of X-rays. Because the ions have a relatively low kinetic energy ($\approx 1$ eV) transitions can be very narrow, containing only small Doppler broadening. We describe preliminary accurate measurements of two and three-electron ions with Z=16--18. We show how these measurement can test sensitively many-body relativistic calculations or can be used as X-ray standards for precise measurements of X-ray transitions in exotic atoms

Manifestation of Quantum Chaos in Electronic Band Structures

We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the {\it ab initio} band structure of silicon and the tight-binding spectrum of the alloy $Al_xGa_{1-x}As$, and show that some of their statistical properties obey the universal predictions of quantum chaos derived from the theory of random matrices. Also, the Bloch momenta are interpreted as external, tunable, parameters, acting on the reduced (unit cell) Hamiltonian, in close analogy to Aharonov-Bohm fluxes threading a torus. They are used in the investigation of the parametric autocorrelator of crystal velocities. We find that our results are in good agreement with the universal curves recently proposed by Simons and coworkers.Comment: 15 pages with 6 Postscript figures included, RevTex-3, CMT-ERM/940

Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

A Brownian Motion Model of Parametric Correlations in Ballistic Cavities

A Brownian motion model is proposed to study parametric correlations in the transmission eigenvalues of open ballistic cavities. We find interesting universal properties when the eigenvalues are rescaled at the hard edge of the spectrum. We derive a formula for the power spectrum of the fluctuations of transport observables as a response to an external adiabatic perturbation. Our formula correctly recovers the Lorentzian-squared behaviour obtained by semiclassical approaches for the correlation function of conductance fluctuations.Comment: 19 pages, written in RevTe