Snyder Model Research Articles

One-dimensional Dirac oscillator with generalized Snyder model in a thermal bath

One-dimensional Dirac oscillator with generalized Snyder model in a thermal bath

Diffeomorphisms of the energy-momentum space: Perturbative QED

A perturbative formulation of quantum electrodynamics is given in terms of geometrical invariants of the energy-momentum space, whose geometry is taken to be one of a constant curvature. The construction is relevant for different classes of noncommutativity: the Snyder model and the so called GUP models. For the Snyder model it is shown that all the amplitudes are finite at every order of the perturbation expansion.

Yang Model Revisited

A long time ago, C.N. Yang proposed a generalization of the Snyder model to the case of a curved background spacetime, based on an algebra isomorphic to o(1, 5) which includes, as subalgebras both the Snyder and the de Sitter algebras. His proposal can, therefore, be interpreted as a model of noncommutative curved spacetime, and could be useful for relating physics on very small and very large scales. We review this model and some recent progress concerning its generalizations and its interpretation in the framework of Hopf algebras. We also report some possibilities to relate it to more phenomenological aspects.

Quasinormal Frequencies of Fields with Various Spin in the Quantum Oppenheimer–Snyder Model of Black Holes

AbstractA recent development involves an intriguing model of a quantum‐corrected black hole, established through the application of the quantum Oppenheimer–Snyder model within loop quantum cosmology [Lewandowski et al., Phys. Rev. Lett. (2023) 130, 101501]. Employing both time‐domain integration and the Wentzel–Kramers–Brillouin (WKB) approach, the quasinormal frequencies for scalar, electromagnetic, and neutrino perturbations in these quantum‐corrected black holes are computed. This analysis reveals that while the real oscillation frequencies undergo only minor adjustments due to the quantum parameter, the damping rate experiences a significant decrease as a result of its influence. The author also deduced the analytic formula for quasinormal frequencies in the eikonal limit and showed that the correspondence between the null geodesics and eikonal quasinormal modes holds in this case.

Quantum Oppenheimer–Snyder–Swiss Cheese model

The quantum Oppenheimer–Snyder (qOS) model in loop quantum cosmology is combined with the quantum Swiss Cheese (qSC) model. While in the qOS model, the interior Ashtekar–Pawlowski–Singh (APS) semiclassical metric is joined to an exterior static spherically symmetric metric, in the qSC model an exterior APS metric is joined to an interior spherically symmetric metric. The qOS model represents a deformed Schwarzschild black hole containing a collapsing APS ball. On the other hand, the qSC describes a deformed Schwarzschild black hole surrounded by a quantum-modified Friedmann–Robertson–Walker universe i.e., APS metric. In this Letter, we apply the concept of the Thin-Shell Wormhole (TSW) to combine the two individual models in a single model that is called the quantum Oppenheimer–Snyder–Swiss Cheese (qOSSC) model. Unlike qOS and qSC, in which the interior and exterior metrics are glued smoothly without an energy–momentum tensor on the interface hypersurface, in the qOSSC model there exists an exotic surface fluid on the throat which satisfies a dark energy equation of state. The dynamic of the throat is investigated, and the universe may bounce from the minimum radius without forming a black hole.

Non-singular gravitational collapse through modified Heisenberg algebra

We study the effects of cut-off physics, in the form of a modified algebra inspired by Polymer Quantum Mechanics and by the Generalized Uncertainty Principle representation, on the collapse of a spherical dust cloud. We analyze both the Newtonian formulation, originally developed by Hunter, and the general relativistic formulation, that is the Oppenheimer–Snyder model; in both frameworks we find that the collapse is stabilized to an asymptotically static state above the horizon, and the singularity is removed. In the Newtonian case, by requiring the Newtonian approximation to be valid, we find lower bounds of the order of unity (in Planck units) for the deformation parameter of the modified algebra. We then study the behaviour of small perturbations on the non-singular collapsing backgrounds, and find that for certain range of the parameters (the polytropic index for the Newtonian case and the sound velocity in the relativistic setting) the collapse is stable to perturbations of all scales, and the non-singular super-Schwarzschild configurations have physical meaning.

Hope and dementia.

Dementia is a terminal and progressive condition which often brings with it a loss of hope, and feelings of hopelessness in those living with the condition and their family carers. Community nurses are in a unique position of being able to interact with people with dementia and their family carers in their own homes, or the care settings in which they reside, and in some case, will be the only professionals with regular contact with the family. Therefore, they have the opportunity to increase feelings of hope in those they work with. This article will discuss the concept of hope as it relates to dementia. It goes on to give an overview of Snyder's model of hope, which presents hope as a cognitive state, and therefore presents the opportunity for professionals to increase feelings of hope. An overview of the research evidence around hope-based interventions is then given, with the ideas applied to community nursing practice using a case study. This article aims to add some hope-based interventions to the toolkit of community nurses as they work with people and families affected by dementia.

Thermal properties of a one-dimensional dirac oscillator in a homogeneous electric field with generalized snyder model: path integral treatment

Thermal properties of a one-dimensional dirac oscillator in a homogeneous electric field with generalized snyder model: path integral treatment

Quantum system ascribed to the Oppenheimer–Snyder model of massive stars

We quantize the Oppenheimer–Snyder model of black holes using the integral quantization method. We treat spatial and temporal coordinates on the same footing at both the classical and quantum levels. Our quantization resolves or smears the singularities of the classical curvature invariants. Quantum trajectories with bounces can replace singular classical trajectories. The considered quantum black hole may have finite bouncing time. As a by-product, we obtain the resolution of the gravitational singularity of the Schwarzschild black hole at the quantum level.

Hope during somber times: a defining moment.

In addition to the diverse educational materials the National Cancer Institute provides to patients, caregivers, and health-care professionals, the NCI maintains an online dictionary that provides concise definitions of terms used in modern oncology. The dictionary is regarded as a valuable data reserve because it is updated frequently and employs language that facilitates comprehension among lay users and professionals alike. In this commentary, we call attention to the absence of the word hope as an entry in this important digital resource. Moreover, we propose not only including the concept of hope in this vital reference text but also basing its meaning on C. R. Snyder's model of "hope theory," which stresses the importance of 3 entities: goals, pathways thinking, and agency. Finally, we argue that hope can be taught as a skill to relevant stakeholders (eg, patients, caregivers, and health-care professionals) through brief workshops that have recently been expanded from in-person encounters to virtual platforms revolving around a user-friendly mobile app called "Hopetimize."

Estimation of reference evapotranspiration using some class-A pan evaporimeter pan coefficient estimation models in Mediterranean-Southeastern Anatolian transitional zone conditions of Turkey.

Reference evapotranspiration (ETo), which is used as the basic data in many studies within the scope of hydrology, meteorology, irrigation and soil sciences, can be estimated by using the evaporation (Epan) measured from the class-A pan evaporimeter. However, this method requires reliable pan coefficients (Kp). Many empirical models are used to estimate Kp coefficients. The reliability of these models varies depending on climatic and environmental conditions. Therefore, they need to be tested in the local conditions where they will be used. In this study, conducted in Kahramanmaraş, which has a semi-arid Mediterranean climate in Turkey during the July-October periods of 2020 and 2021, aimed to determine the usability levels of six Kp models in estimating daily and monthly average ETo. The Kp coefficients estimated by the models were multiplied with the daily Epan values, and the daily average ETo values were estimated on the basis of the model. The daily Epan values were measured using an ultrasonic sensor sensitive to the water surface placed on the class-A pan evaporimeter. The ultrasonic sensor was managed by a programmable logic controller (PLC). To enable the sensor to be managed by PLC, a software was prepared using the CODESYS programming language and uploaded to the PLC. The daily average ETo values determined by the FAO-56 Penman-Monteith equation were accepted as actual values. The ETo values estimated by the Kp models were compared with the actual ETo values using the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE) and determination coefficient (R2) statistical approaches. The Wahed & Snyder outperformed the other models in estimating daily (MAE = 0.78 mm day-1, MAPE = 14.40%, RMSE = 0.97 mm day-1, R2 = 0.82) and monthly (MAE = 0.32 mm day-1, MAPE = 5.88%, RMSE = 0.32 mm day-1, R2 = 0.99) average ETo. FAO-56 showed the nearest performance to Wahed & Snyder. The Snyder model presented the worst performance in estimating daily (MAE = 2.09 mm day-1, MAPE = 37.53%, RMSE = 2.36 mm day-1, R2 = 0.82) and monthly (MAE = 1.83 mm day-1, MAPE = 31.82%, RMSE = 1.87 mm day-1, R2 = 0.99) average ETo. It has been concluded that none of the six Kp models can be used to estimate the daily ETo in Kahramanmaraş located in the Mediterranean-Southeastern Anatolian transitional zone, and only Wahed & Snyder and FAO-56 can be used to estimate the monthly ETo without calibration.

Constraining Snyder and GUP models with low-mass stars

We investigate the application of an equation of state that incorporates corrections derived from the Snyder model (and the Generalized Uncertainty Principle) to describe the behaviour of matter in a low-mass star. Remarkably, the resulting equations exhibit striking similarities to those arising from modified Einstein gravity theories. By modeling matter with realistic considerations, we are able to more effectively constrain the theory parameters, surpassing the limitations of existing astrophysical bounds. The bound we obtain is β0≤4.5×1047\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta _0 \\le 4.5 \ imes 10^{47}$$\\end{document}. We underline the significance of realistic matter modeling in order to enhance our understanding of effects arising in quantum gravity phenomenology and implications of quantum gravitational corrections in astrophysical systems.

PREDICTION OF RUNOFF BY SYNTHETIC UNIT HYDROGRAPH METHODS FOR THE DESIGN STORMS IN WARANA RIVER BASIN, MAHARASHTRA, INDIA

The authors' goal was to calculate average representative unit hydrographs (UHs) from a few isolated storms for the upper Warana River basin in Maharashtra, India. Based on the approaches used by Snyder, the Soil Conservation Service (SCS), the Central Water Commission (CWC), and Common, synthetic unit hydrographs were created. This study was utilised to choose appropriate correlation coefficients for Synthetic Unit Hydrograph (SUH) evaluation for the ungauged basins with identical hydrological conditions. The outcomes were then analyzed with those attained using other techniques and with the actual UH. In order to calibrate and validate the effectiveness of Snyder's model, the authors employed it on the sub-basins of the Warana river basin. The hydrograph's shape resembled the observed UH produced by the other methods, according to the results, and the peak discharge calculated using Snyder's technique had the lowest percentage error (0.26%)

A comparative assessment and geospatial simulation of three hydrological models in urban basins

Abstract The risk of flooding is a destructive natural hazard, and it is increasing due to heavy rainfall and anthropogenic factors. Hydrologic–hydraulic models serve as valuable tools for flood forecasting and predicting future flow patterns. These models evaluate and simplify processes in ungauged basins. In this study, three hydrologic models (soil conservation service [SCS], Snyder, and Temez) were used to calculate synthetic unit hydrographs for the Humaya and Tamazula River (H-T-R) basin. Additionally, the flows derived from the three models were simulated in Hydrological Engineering Center River Analysis System for various return periods (2, 5, 10, 25, 50, and 100 years). The accuracy of the models SCS, Snyder, and Temez was evaluated using the root-mean-square error (1162.44, 144.76, and 2890.6); Nash–Sutcliffe efficiency (−51.12, 0.19, and −312.28); R 2 (0.97, 0.94, and 0.94), and kappa index (0.8534, 0.9895, and 0.7155), respectively. The data used in this study were obtained from a hydrometric station located on the Culiacan River. The main findings indicate that the Snyder model demonstrated a better predictive capability compared to the Temez and SCS models, albeit with a tendency to overestimate. Simulated flood depths are deeper in the upstream areas, particularly upstream from the Musala Island bifurcation on the Tamazula River, with values of 11.82 m for SCS, 9.76 m for Snyder, and 13.5 m for Temez. The simulation revealed potential overflow zones along the Tamazula River, particularly at the channel bifurcation and near the confluence with the Humaya River, during the 100 year return period simulation.

Realizations of the Extended Snyder Model

We present the exact realization of the extended Snyder model. Using similarity transformations, we construct realizations of the original Snyder and the extended Snyder models. Finally, we present the exact new realization of the $\kappa$-deformed extended Snyder model.

Fermi equation of state with finite temperature corrections in quantum space-times approach: Snyder model vs GUP case

We investigate the impact of the deformed phase space associated with the quantum Snyder space on microphysical systems. The general Fermi–Dirac equation of state and specific corrections to it are derived. We put emphasis on non-relativistic degenerate Fermi gas as well as on the temperature-finite corrections to it. Considering the most general one-parameter family of deformed phase spaces associated with the Snyder model allows us to study whether the modifications arising in physical effects depend on the choice of realization. It turns out that we can distinguish three different cases with radically different physical consequences.

Quantum Mechanics of the Extended Snyder Model

We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by D spatial coordinates and D(D−1)/2 tensorial degrees of freedom, together with their conjugated momenta. The coordinates obey nontrivial commutation relations and generate a noncommutative geometry, which admits nicer properties than the usual realization of the model, in particular giving rise to an associative star product. The spectrum of the harmonic oscillator is studied through the introduction of creation and annihilation operators. Some physical consequences of the introduction of the additional degrees of freedom are discussed.

Noncommutative Yang model and its generalizations

Long time ago, Yang [Phys. Rev. 72, 874 (1947)] proposed a model of noncommutative spacetime that generalized the Snyder model to a curved background. In this paper, we review his proposal and the generalizations that have been suggested during the years. In particular, we discuss the most general algebras that contain as subalgebras both de Sitter and Snyder algebras, preserving Lorentz invariance, and are generated by a two-parameter deformation of the canonical Heisenberg algebra. We also define their realizations on quantum phase space, giving explicit examples, both exact and in terms of a perturbative expansion in deformation parameters.

κ-Galilean and κ-Carrollian noncommutative spaces of worldlines

The noncommutative spacetimes associated to the κ-Poincaré relativistic symmetries and their “non-relativistic” (Galilei) and “ultra-relativistic” (Carroll) limits are indistinguishable, since their coordinates satisfy the same algebra. In this work, we show that the three quantum kinematical models can be differentiated when looking at the associated spaces of time-like worldlines. Specifically, we construct the noncommutative spaces of time-like geodesics with κ-Galilei and κ-Carroll symmetries as contractions of the corresponding κ-Poincaré space and we show that these three spaces are defined by different algebras. In particular, the κ-Galilei space of worldlines resembles the so-called Euclidean Snyder model, while the κ-Carroll space turns out to be commutative. Furthermore, we identify the map between quantum spaces of geodesics and the corresponding noncommutative spacetimes, which requires to extend the space of geodesics by adding the noncommutative time coordinate.

Generalized quantum phase spaces for the κ-deformed extended Snyder model

We describe, in an algebraic way, the κ-deformed extended Snyder models, that depend on three parameters β,κ and λ, which in a suitable algebra basis are described by the de Sitter algebras o(1,N). The commutation relations of the algebra contain a parameter λ, which is used for the calculations of perturbative expansions. For such κ-deformed extended Snyder models we consider the Heisenberg double with dual generalized momenta sector, and provide the respective generalized quantum phase space depending on three parameters mentioned above. Further, we study for these models an alternative Heisenberg double, with the algebra of functions on de Sitter group. In both cases we calculate the formulae for the cross commutation relations between generalized coordinate and momenta sectors, at linear order in λ. We demonstrate that in the commutators of quantum space-time coordinates and momenta of the quantum-deformed Heisenberg algebra the terms generated by κ-deformation are dominating over β-dependent ones for small values of λ.