Tensor Coordinates in Noncommutative Mechanics

A consistent classical mechanics formulation is presented in such a way that, under quantization, it gives a noncommutative quantum theory with interesting new features. The Dirac formalism for constrained Hamiltonian systems is strongly used, and the object of noncommutativity ${\mathbf \theta}^{ij}$ plays a fundamental rule as an independent quantity. The presented classical theory, as its quantum counterpart, is naturally invariant under the rotation group $SO(D)$.Comment: 12 pages, Late

Kappa-deformed Snyder spacetime

We present Lie-algebraic deformations of Minkowski space with undeformed Poincare algebra. These deformations interpolate between Snyder and kappa-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and kappa-Minkowski in Maggiore-type realizations are discussed. Our construction leads to a new class of deformed special relativity theories.Comment: 12 pages, no figures, LaTeX2e class file, accepted for publication in Modern Physics Letters

Noncommutative Complex Scalar Field and Casimir Effect

A noncommutative complex scalar field, satisfying the deformed canonical commutation relations proposed by Carmona et al. [27]-[31], is constructed. Using these noncommutative deformed canonical commutation relations, a model describing the dynamics of the noncommutative complex scalar field is proposed. The noncommutative field equations are solved, and the vacuum energy is calculated to the second order in the parameter of noncommutativity. As an application to this model, the Casimir effect, due to the zero point fluctuations of the noncommutative complex scalar field, is considered. It turns out that in spite of its smallness, the noncommutativity gives rise to a repulsive force at the microscopic level, leading to a modifed Casimr potential with a minimum at the point amin= racine(5/84){\pi}{\theta}.Comment: Revtex style, 28 page

Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra

We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. By introducing modules, it is shown that although deformed and undeformed structures are not isomorphic at the level of vector spaces, they are however isomorphic at the level of Hopf algebraic action on corresponding modules. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from $\kappa$-deformed Snyder to Snyder space is constructed. Deformed Leibniz rule, the Hopf structure and star product are found. Special cases, particularly Snyder and $\kappa$-Minkowski in Maggiore-type realizations are discussed. The same generalized Hopf algebraic structures are as well considered in the case of an arbitrary allowable kind of realisation and results are given perturbatively up to second order in deformation parameters.Comment: 38 pages, LaTeX2e class fil

Family Connect: Keeping families informed during the COVID-19 pandemic

Family Connect programs to enhance communication with families and care partners who were unable to visit their inpatient loved ones during the COVID-19 crisis. While they differed in composition, the Family Connect programs at both institutions leveraged providers who had decreased clinical activity during the pandemic. The Family Connect team became integrated with the team. At both institutions, Family Connect teams perform virtual chart review, discuss patient status and care plan with the primary provider and communicate with the patient’s designated family member or care partner daily. Conversations are documented in the electronic medical record (EMR), which allows for metric tracking and clear communication to all team members. All Family Connect providers undergo a comprehensive training program focused on workflow, communication, and EMR training. Family Connect can be tailored to the needs of specific health systems based on patient volume and staffing. The NYULH Family Connect model incorporated medical student mentorship, on-site nurse liaisons to assist patients with virtual visits with families, and a 24/7 call center for family support. The YNHHS model was separate from the YNHHS COVID-19 call center and utilized attending and trainee physicians. The program is highly portable and can be easily reinitiated if needed. Experience Framework This article is associated with the Patient, Family & Community Engagement lens of The Beryl Institute Experience Framework. (http://bit.ly/ExperienceFramework) Access other PXJ articles related to this lens. Access other resources related to this lens

The ecological diversity of vegetation within Urban Parks in the Dabrowski Basin (southern Poland)

The aim of this work is to present the diversity of flora in terms of ecological requirements. The research was conducted in the area of two urban parks in the area of two cities in southern Poland: Bedzin and Czeladz. These parks were established in different historical periods, and were planned (and are managed) differently. The results of the investigation have shown that the occurrence of 192 vascular species has been observed in the Gora Zamkowa (Castle Hill) Park, while in the Grabek park, 334 such species are known to exist. Such disparity is the result of the occurrence of micro-habitats and of the differences between the ways the two parks are managed. It is also due to these parks’ different functions. In the first case, the park area is protected by law. In the latter case, human activity has created a new ecological niche for organisms with a high degree of ecological tolerance. Based on the ecological values, the following groups of plants were distinguished: saxifrages grasslands, xerothermic grasslands, beech forests, alder forests and artificial planted trees. Analysis has shown that urban parks are potential places for growth various type of vegetation and also for increasing biodiversity, and can constitute particularly important hotspots for biodiversity in the cityscape, even if their primary role is recreational. As the study shows, the environment of a highly urbanized and industrialized region can also have a positive influence on ecological and floristic diversity

Formulation, Interpretation and Application of non-Commutative Quantum Mechanics

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non commutativity are identified.Comment: 11 page

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

We present a numerical study of the coupled time-dependent Gross-Pitaevskii equation, which describes the Bose-Einstein condensate of several types of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. The same approach is used to study both stationary and time-evolution problems. We consider up to four types of atoms in the study of stationary problems. We consider the time-evolution problems where the frequencies of the traps or the atomic scattering lengths are suddenly changed in a stable preformed condensate. We also study the effect of periodically varying these frequencies or scattering lengths on a preformed condensate. These changes introduce oscillations in the condensate which are studied in detail. Good convergence is obtained in all cases studied.Comment: 9 pages, 10 figures, accepted in Physical Review

Including debris cover effects in a distributed model of glacier ablation

Distributed glacier melt models generally assume that the glacier surface consists of bare exposed ice and snow. In reality, many glaciers are wholly or partially covered in layers of debris that tend to suppress ablation rates. In this paper, an existing physically based point model for the ablation of debris-covered ice is incorporated in a distributed melt model and applied to Haut Glacier d’Arolla, Switzerland, which has three large patches of debris cover on its surface. The model is based on a 10 m resolution digital elevation model (DEM) of the area; each glacier pixel in the DEM is defined as either bare or debris-covered ice, and may be covered in snow that must be melted off before ice ablation is assumed to occur. Each debris-covered pixel is assigned a debris thickness value using probability distributions based on over 1000 manual thickness measurements. Locally observed meteorological data are used to run energy balance calculations in every pixel, using an approach suitable for snow, bare ice or debris-covered ice as appropriate. The use of the debris model significantly reduces the total ablation in the debris-covered areas, however the precise reduction is sensitive to the temperature extrapolation used in the model distribution because air near the debris surface tends to be slightly warmer than over bare ice. Overall results suggest that the debris patches, which cover 10% of the glacierized area, reduce total runoff from the glacierized part of the basin by up to 7%