Spectral Gap and Edge Excitations of dd-dimensional PVBS models on half-spaces

We analyze a class of quantum spin models defined on half-spaces in the $d$-dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector $m\in\mathbb{R}^d$. The family of models was previously introduced as the single species Product Vacua with Boundary States (PVBS) model, which is a spin-$1/2$ model with a XXZ-type nearest neighbor interactions depending on parameters $\lambda_j\in (0,\infty)$, one for each coordinate direction. For any given values of the parameters, we prove an upper bound for the spectral gap above the unique ground state of these models, which vanishes for exactly one direction of the normal vector $m$. For all other choices of $m$ we derive a positive lower bound of the spectral gap, except for the case $\lambda_1 =\cdots =\lambda_d=1$, which is known to have gapless excitations in the bulk

Product Vacua and Boundary State Models in d Dimensions

We introduce and analyze a class of quantum spin models defined on d-dimensional lattices Lambda subset of Z^d, which we call `Product Vacua with Boundary States' (PVBS). We characterize their ground state spaces on arbitrary finite volumes and study the thermodynamic limit. Using the martingale method, we prove that the models have a gapped excitation spectrum on Z^d except for critical values of the parameters. For special values of the parameters we show that the excitation spectrum is gapless. We demonstrate the sensitivity of the spectrum to the existence and orientation of boundaries. This sensitivity can be explained by the presence or absence of edge excitations. In particular, we study a PVBS models on a slanted half-plane and show that it has gapless edge states but a gapped excitation spectrum in the bulk

Decreasing Post-Operative Ventilator Time in the Cardiovascular Surgical Patient: A Nursing Education Quality Initiative

Extended mechanical ventilation times after open heart surgery can contribute to complications prolonging recovery and length of stay, as well as increasing mortality. Standardized staff education of immediate post-open-heart recovery and ventilator weaning protocols, combined with the use of ABCDE and VAP bundles can reduce these complications. At Hospital X during summer of 2022, the average length of time patients remained mechanically ventilated after open heart surgery increased. After an initial needs survey was distributed to nursing staff, a set of novel QR codes was created to simplify and centralize training for staff in the ICU to facilitate early extubation and mobility, as well as increase adherence to standards of care. As a result, average post operative ventilator times showed a downward trend and staff reported increased confidence in their skills. In addition, QR codes have led to an electronic resource of protocols that could be updated as needed. Use of QR codes can be extended to other areas of education and patient care

Stability of the bulk gap for frustration-free topologically ordered quantum lattice systems

We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system Hamiltonians uniform in the system size. To obtain this result, we adapt the Bravyi-Hastings-Michalakis strategy to the GNS representation of the infinite-system ground state.Comment: Minor edit

Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the Bravyi-Hastings-Michalakis (BHM) strategy that under a condition of Local Topological Quantum Order, the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work we expand the class of frustration-free quantum spin models that can be handled to include models with more general boundary conditions, and models with discrete symmetry breaking. Detailed estimates allow us to formulate sufficient conditions for the validity of positive lower bounds for the gap that are uniform in the system size and that are explicit to some degree. We provide a survey of the BHM strategy following the approach of Michalakis and Zwolak, with alterations introduced to accommodate more general than just periodic boundary conditions and more general lattices. We express the fundamental condition known as LTQO by means of the notion of indistinguishability radius, which we introduce. Using the uniform finite-volume results we then proceed to study the thermodynamic limit. We first study the case of a unique limiting ground state and then also consider models with spontaneous breaking of a discrete symmetry. In the latter case, LTQO cannot hold for all local observables. However, for perturbations that preserve the symmetry, we show stability of the gap and the structure of the broken symmetry phases. We prove that the GNS Hamiltonian associated with each pure state has a non-zero spectral gap above the ground state.Comment: Turned off `showkeys' :) and minor edit

Drugs and the internet.

Key findings: The number of retailers on the Silk Road increased (from 282 at time 1 to 374 at the last time point), while the number of retailers on the surface web remained relatively stable (92 at time 1 and 101 at the last time point). The increase on the Silk Road is largely driven by international rather than domestic retailers. • On the Silk Road, cannabis and EPS were sold by the largest number of retailers consistently across all time points, followed by MDMA (3,4-methylenedioxy-Nmethylamphetamine) and pharmaceuticals (primarily benzodiazepines and sildenafil). • The type of EPS available from surface web retailers differed substantially from the EPS available from those selling on the Silk Road. EPS sold on the Silk Road more closely mirrored those most commonly used by EDRS participants (i.e. people who regularly use psychostimulants) including drugs from the 2C-x and NBOMe categories, followed by DMT (dimethyltryptamine), Mephedrone and Methylone. • Average prices of methamphetamine, cocaine and ecstasy being sold on the Silk Road remained stable across the time period. Average domestic prices for common quantities of these substances were comparable to prices paid for these same quantities by 2012 EDRS participants. Average international prices for these substances were substantially lower