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Temporal, Spatial, and Temperature Controls on Organic Carbon Mineralization and Methanogenesis in Arctic High-Centered Polygon Soils

Warming temperatures in continuous permafrost zones of the Arctic will alter both hydrological and geochemical soil conditions, which are strongly linked with heterotrophic microbial carbon (C) cycling. Heterogeneous permafrost landscapes are often dominated by polygonal features formed by expanding ice wedges: water accumulates in low centered polygons (LCPs), and water drains outward to surrounding troughs in high centered polygons (HCPs). These geospatial differences in hydrology cause gradients in biogeochemistry, soil C storage potential, and thermal properties. Presently, data quantifying carbon dioxide (CO 2 ) and methane (CH 4 ) release from HCP soils are needed to support modeling and evaluation of warming-induced CO 2 and CH 4 fluxes from tundra soils. This study quantifies the distribution of microbial CO 2 and CH 4 release in HCPs over a range of temperatures and draws comparisons to previous LCP studies. Arctic tundra soils were initially characterized for geochemical and hydraulic properties. Laboratory incubations at −2, +4, and +8°C were used to quantify temporal trends in CO 2 and CH 4 production from homogenized active layer organic and mineral soils in HCP centers and troughs, and methanogen abundance was estimated from mcrA gene measurements. Results showed that soil water availability, organic C, and redox conditions influence temporal dynamics and magnitude of gas production from HCP active layer soils during warming. At early incubation times (2–9 days), higher CO 2 emissions were observed from HCP trough soils than from HCP center soils, but increased CO 2 production occurred in center soils at later times (>20 days). HCP center soils did not support methanogenesis, but CH 4 -producing trough soils did indicate methanogen presence. Consistent with previous LCP studies, HCP organic soils showed increased CO 2 and CH 4 production with elevated water content, but HCP trough mineral soils produced more CH 4 than LCP mineral soils. HCP mineral soils also released substantial CO 2 but did not show a strong trend in CO 2 and CH 4 release with water content. Knowledge of temporal and spatial variability in microbial C mineralization rates of Arctic soils in response to warming are key to constraining uncertainties in predictive climate models.

59 BASIC BIOLOGICAL SCIENCES↗

Frost Table Elevation across a Low-Centered and a High-Centered Polygon, Mapped using Ground Penetrating Radar, Utqiagvik (Barrow), Alaska, 2015

Ground Penetrating Radar, active layer thickness point measurements, and ground elevation surveys were conducted on a low-centered and a high-centered polygon in Utqiagvik (Barrow), AK (on October 2nd, 2015) to map frost table topography and evaluate its influence on hydrological flow. Data were collected to improve our understanding of the topography of the permafrost table across polygons which may have a major influence on hydrology. This dataset includes 2 zip files containing the raw data, 2 csv files of processed data, and a pdf user guide.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

Iron and Phosphorus Geochemistry in High-Centered and Low-Centered Polygon Soils from the Barrow Environmental Observatory, Utqiagvik, Alaska, 2015

This dataset provides chemical characterization of soil cores obtained in triplicate from center and trough positions of a high-centered polygon and center, ridge, and trough positions of a low-centered polygon in the NGEE Arctic research area within the Barrow Environmental Observatory, Utqiagvik, Alaska. Photographs of the 15 collected cores are provided. Cores were collected to thaw depth in early October 2015 and subsequently divided into subsamples for analysis, which included bulk soil horizons (organic or mineral) and finer scale depth increments (minimum 4 cm thickness per increment). Bulk horizons and depth increments were characterized using sequential chemical extractions for Fe and P and with Fe K-edge x-ray absorption spectroscopy. Additional soil parameters such as loss-on-ignition, gravimetric water content, and carbon and nitrogen concentrations were also quantified for bulk horizons. This dataset includes four csv files, one pdf user guide, and one zip folder of *.jpg photos.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method (FEM) for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. We numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular and square meshes where the method coincides with the P 1 - P 0 Scott-Vogelius scheme, which is well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗

Impact of Salinity on Ground Ice Distribution Across an Arctic Coastal Polygonal Tundra Environment

The heterogeneous distribution of ground ice in the Arctic is a key driver of uneven ground subsidence as permafrost thaws, significantly impacting infrastructure and surface/subsurface hydrology. These topographic and hydrological changes contribute to major uncertainties in energy and carbon fluxes and storage in a warming Arctic. This study aims to improve our understanding of the controls on ground ice and organic matter distribution within the top 3 m of permafrost in coastal polygonal tundra near Utqiagvik, Alaska. To this end, we apply a neural network approach to bulk density distributions derived from nondestructive X-ray tomography of soil cores, trained with laboratory analyses, to improve the resolution and spatial coverage of estimates of dry bulk density, ice content, and organic matter content. In addition, we use capacitively coupled geophysical imaging to map soil electrical conductivity and salinity variations. The results show that sedimentary deposits from ocean transgressions, along with subsequent ice wedge polygon geomorphological processes, jointly influence the distribution of ice content at various scales. The impact of the latter decreases with depth, whereas the influence of salinity and sedimentary history increases. Although the controls on the distribution of soil organic matter content (g/cm 3 ) remain unclear, the pronounced heterogeneity in bulk density strongly influences its calculation from laboratory mass fraction measurements (g/g). From a methodological perspective, the interdependencies among soil components and the need for increased data coverage underscore the value of high-resolution density measurements, such as using X-ray tomography. Overall, this study emphasizes the importance of considering salinity constraints on ice content distribution in coastal permafrost regions. The results are expected to aid in the development of data products and process representations in geomorphological and ecosystem models.

Dafflon, Baptiste [Lawrence Berkeley National Labo↗

Feedbacks Between Surface Deformation and Permafrost Degradation in Ice Wedge Polygons, Arctic Coastal Plain, Alaska

In the past three decades, an abrupt, pan-Arctic acceleration of ice wedge melting has transformed tundra landscapes, spurring the formation of hummock-like features known as high-centered polygons (HCPs). This rapid geomorphic transition profoundly alters regional hydrology and influences surface emissions of CO 2 and CH 4 . In Arctic Alaska, most recent instances of ice wedge degradation have arrested within 15–20 years of inception, stabilizing HCP microtopography. However, feedbacks between ground surface deformation and permafrost stability are incompletely understood, limiting our capacity to predict trajectories of landscape evolution in a still warmer future. In this work, we use field data from a site near Prudhoe Bay, Alaska, to develop a modeling-based framework for assessing the strength of positive (i.e., exacerbating) feedbacks on ice wedge degradation, focusing on the importance of heterogeneity in surface drainage and microtopographic conditions. Our simulations suggest that, when troughs are narrow, positive feedbacks on ice wedge melting (associated with thermokarst pool formation) are relatively weak. Positive feedbacks are markedly stronger beneath wide troughs, such as those that form above older, larger ice wedges. Seasonal thaw abruptly accelerates once a talik begins to form beneath wide and deep thermokarst pools. Once a talik initiates, winter severity and snowpack thickness increase in importance as predictors of thaw intensity in summer. Our results indicate that meter-scale heterogeneity in polygonal microtopography potentially exerts strong, nonlinear controls on thermokarst trajectories. These findings are useful for predicting future thermokarst dynamics and for interpreting the results from coarser-resolution land surface models operating at greater spatial and temporal scales.

54 ENVIRONMENTAL SCIENCES↗

Iron and iron-bound phosphate accumulate in surface soils of ice-wedge polygons in arctic tundra

Phosphorus (P) is a limiting or co-limiting nutrient to plants and microorganisms in diverse ecosystems that include the arctic tundra. Certain soil minerals can adsorb or co-precipitate with phosphate, and this mineral-bound P provides a potentially large P reservoir in soils. Iron (Fe) oxyhydroxides have a high capacity to adsorb phosphate; however, the ability of Fe oxyhydroxides to adsorb phosphate and limit P bioavailability in organic tundra soils is not known. In this study, we examined the depth distribution of soil Fe and P species in the active layer (<30 cm) of low-centered and high-centered ice-wedge polygons at the Barrow Environmental Observatory on the Alaska North Slope. Soil reservoirs of Fe and P in bulk horizons and in narrower depth increments were characterized using sequential chemical extractions and synchrotron-based X-ray absorption spectroscopy (XAS). Organic horizons across all polygon features ( e.g. , trough, ridge, and center) were enriched in extractable Fe and P relative to mineral horizons. Soil Fe was dominated by organic-bound Fe and short-range ordered Fe oxyhydroxides, while soil P was primarily associated with oxides and organic matter in organic horizons but apatite and/or calcareous minerals in mineral horizons. Iron oxyhydroxides and Fe-bound inorganic P (P i ) were most enriched at the soil surface and decreased gradually with depth, and Fe-bound P i was >4× greater than water-soluble P i . These results demonstrate that Fe-bound P i is a large and ecologically important reservoir of phosphate. We contend that Fe oxyhydroxides and other minerals may regulate P i solubility under fluctuating redox conditions in organic surface soils on the arctic tundra.

54 ENVIRONMENTAL SCIENCES↗

Saturated random packing built of arbitrary polygons under random sequential adsorption protocol

Random packings and their properties are a popular and active field of research. Numerical algorithms that can efficiently generate them are useful tools in their study. This paper focuses on random packings produced according to the random sequential adsorption (RSA) protocol. Developing the idea presented by G. Zhang, where saturated random packings built of regular polygons were studied, we create an algorithm that generates strictly saturated packings built of any polygons. Then, the algorithm was used to determine the packing fractions for arbitrary triangles. In this work, the highest mean packing density, 0.552 814 ± 0.000 063, was observed for triangles of side lengths 0.63 : 1 : 1. Additionally, microstructural properties of such packings, kinetics of their growth, as well as distributions of saturated packing fractions and the number of RSA iterations needed to reach saturation were analyzed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Permafrost Thaw, Uneven Subsidence and Projected Drying of Ice-wedge Polygon Tundra: Modeling Archive

This dataset is a model archive of the paper Permafrost Thaw, Uneven Subsidence and Projected Drying of Ice-wedge Polygon Tundra (in prep) to support a modeling study investigating how projected increases in Arctic temperature and precipitation will jointly influence hydrologic conditions in ice-rich tundra landscapes. With this dataset, this study is to address the research question: Will Arctic tundra landscapes become wetter or drier with increasing precipitation and temperature in the future when thaw-induced ground subsidence and associated microtopographic evolution are represented? The simulations focus on ice-wedge polygon tundra, a widespread form of ice-rich permafrost terrain that is highly sensitive to thaw-driven landscape change. This dataset contains model input and output data for four study watersheds in Alaska: Anaktuvuk, Utqiagvik (formerly Barrow), Brooks Foothills, and Prudhoe Bay. Simulations were performed using the Advanced Terrestrial Simulator (ATS, v1.5), a physics-rich integrated surface–subsurface hydrologic model. For each watershed, ten modeling cases were performed representing two landscape evolution conditions (with subsidence and without subsidence) combined with five climate forcing scenarios derived from Shared Socioeconomic Pathways (SSP5, SSP5 with precipitation trend, SSP2, SSP2 with precipitation trend, and SSP2 with double precipitation trend). Particularly, for each watershed under the forcing SSP2 with precipitation trend, there are two additional simulations considering spatially heterogeneous subsidence distributions: one assumes randomly distributed scaling and the other includes elevation dependent distribution scaling. These simulations span 1980–2099 and include spin-up runs (1980–2009) followed by transient projections (2010–2099). To facilitate reproducibility of simulations, all datasets are organized by watershed. For each study watershed, the dataset contains: (1) Pre-partitioned mesh files for 32-core modeling (.par.32.XX), located in EACH_WATERSHED/mesh/basin; and also a non-partitioned mesh file (.exo) located in EACH_WATERSHED/mesh; (2) Climate forcings corresponding to the five SSP scenarios (.h5), located in EACH_WATERSHED/data; (3) Final states (.h5) from column spin-up modeling used to initialize historical watershed-scale spin-up runs from 1980 to 2009, located in EACH_WATERSHED/PreSpinupHistorical; (4) Final states (.h5) of historical watershed-scale spin-up runs from 1980 to 2009 used to initialize projection runs, located in EACH_WATERSHED/Spinup_daymetERA5; (5) ATS modeling input files (.xml), located in EACH_WATERSHED/EACH_SIMULATION_SCENARIO/inputfiles; (6) ATS modeling output files (.dat), located in in EACH_WATERSHED/EACH_SIMULATION_SCENARIO/combined_obs; (7) For the Brooks Foothills watershed, additional spatial model outputs are provided (.h5) for selected years (2033 and 2093) used to generate spatial figures in this study, located in Brooksfoothills/EACH_SIMULATION_SCENARIO/results-WITH/WITHOUT_SUBSIDENCE-year2033/2093. All data files with suffix .h5 can be accessible through Python h5py, and all data files with suffix of .dat can be imported by Python pandas. Mesh file with .exo can be visualized through Paraview or read by Python netCDF. The Next-Generation Ecosystem Experiments in the Arctic (NGEE Arctic) project is a research effort to reduce uncertainty in the Department of Energy’s Energy Exascale Earth System Model (E3SM) by developing a predictive understanding of Arctic tundra ecosystems underlain by permafrost and to quantify feedbacks from the Arctic tundra to the Earth system. NGEE Arctic is supported by the Department of Energy's Office of Biological and Environmental Research. Over Phases 1–3, observations made by the NGEE Arctic team across a gradient of permafrost landscapes in Arctic Alaska improved the representation of tundra processes in the land surface component of E3SM (the E3SM Land Model, ELM). Model improvements emphasized unique aspects of permafrost environments and explored reductions in model complexity while retaining predictive power. The Arctic-informed ELM developed by NGEE Arctic has been used to make novel predictions on processes ranging from permafrost thaw to soil biogeochemical cycling to Earth system feedbacks associated with the unique characteristics of tundra plants. In Phase 4, the NGEE Arctic team is evaluating our new predictive understanding under novel conditions across the Arctic domain. In collaboration with partners at long-term pan-Arctic research sites we are examining whether an Arctic-informed ELM can faithfully simulate interactions among surface and subsurface processes at site, regional, and pan-Arctic scales. In turn, we are using variety of tools to dynamically extend and evaluate ELM inference, with an emphasis on data synthesis and pan-Arctic model evaluation, reintegration of code with an evolving E3SM, scaling across heterogeneous Arctic landscapes, and the appropriate representation of the impacts of increasingly frequent Arctic disturbances.

EARTH SCIENCE > ATMOSPHERE > PRECIPITATION↗

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. Finally, we numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the $\mathbb{P}_1$ – $\mathbb{P}_0$ Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗

NGEE Arctic Tram: Radiation and Environmental Measurements over Low- and High-Centered Polygon Vegetation Communities, Barrow, Alaska, 2014-2017

These data were generated from an observational platform (Tram), an automated cart carrying a suite of radiation and remote sensing instruments running on 68 meters of elevated track 1 to 1.5 meters above the surface of the vegetation communities of low- and high-centered polygon ground. The Tram is in the footprint of the NGEE Arctic/AmeriFlux eddy covariance flux tower (US-NGB) at the Barrow Environmental Observatory, Barrow, Alaska, and operated before, during, and after the growing seasons of 2014-2017. Dataset includes one user guide (*.pdf) with final and raw *.csv data files. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

Conservative high-order data transfer method on generalized polygonal meshes

A conservative data transfer (remap) between two meshes is an important step of arbitrary Lagrangian-Eulerian (ALE) hydrodynamics simulations. High-order numerical methods for ALE simulations require both high-order (curvilinear) meshes and high-order remap algorithms. Here we develop a conservative and bounds-preserving method for accurate remapping of discrete fields on generalized polygonal meshes with curvilinear edges. The properties of the proposed method are studied theoretically and numerically for various (smooth and non-smooth) mesh deformations and discrete fields that represent smooth and discontinuous functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Open and Close-Packed, Shape-Engineered Polygonal Nanoparticle Metamolecules with Tailorable Fano Resonances

In this study, a top-down lithographic patterning and deposition process is reported for producing nanoparticles (NPs) with well-defined sizes, shapes, and compositions that are often not accessible by wet-chemical synthetic methods. These NPs are ligated and harvested from the substrate surface to prepare colloidal NP dispersions. Using a template-assisted assembly technique, fabricated NPs are driven by capillary forces to assemble into size- and shape-engineered templates and organize into open or close-packed multi-NP structures or NP metamolecules. The sizes and shapes of the NPs and of the templates control the NP number, coordination, interparticle gap size, disorder, and location of defects such as voids in the NP metamolecules. The plasmonic resonances of polygonal-shaped Au NPs are exploited to correlate the structure and optical properties of assembled NP metamolecules. Comparing open and close-packed architectures highlights that introduction of a center NP to form close-packed assemblies supports collective interactions, altering magnetic optical modes and multipolar interactions in Fano resonances. Decreasing the distance between NPs strengthens the plasmonic coupling, and the structural symmetries of the NP metamolecules determine the orientation-dependent scattering response.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

A high-resolution pseudo-polygon discrete element model for regional sea ice

Here, this work presents a pseudo-polygon discrete element model for high-resolution sea ice simulations. A scale-invariant bonded particle contact model is proposed to model joints between sea ice floes based on the smeared fracture model and a lattice spring beam model, and the Mohr–Coulomb failure criterion is implemented to represent the shearing failure mechanism of sea ice packings under complex loadings. All mechanical parameters of the bond model can be directly determined from laboratory tests. Validations of the proposed model are made by investigations of mechanical response and failure criteria of field sea ice sheets. Compared with the field observations of sea ice from satellite radar and in situ stress sensors, the proposed model is capable of reproducing the typical constitutive behavior and the Coulomb friction envelope of field sea ice. Finally, the proposed discrete element sea ice model is used to study the effect of loading rates on mechanical behavior including failure strength of regional sea ice.

54 ENVIRONMENTAL SCIENCES↗

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

In this work, we propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Georectified polygon database of ground-mounted large-scale solar photovoltaic sites in the United States.

Over 4,400 large-scale solar photovoltaic (LSPV) facilities operate in the United States as of December 2021, representing more than 60 gigawatts of electric energy capacity. Of these, over 3,900 are ground-mounted LSPV facilities with capacities of 1 megawatt direct current (MW dc ) or more. Ground-mounted LSPV installations continue increasing, with more than 400 projects appearing online in 2021 alone; however, a comprehensive, publicly available georectified dataset including spatial footprints of these facilities is lacking. The United States Large-Scale Solar Photovoltaic Database (USPVDB) was developed to fill this gap. Using US Energy Information Administration (EIA) data, locations of 3,699 LSPV facilities were verified using high-resolution aerial imagery, polygons were digitized around panel arrays, and attributes were appended. Quality assurance and control were achieved via team peer review and comparison to other US PV datasets. Data are publicly available via an interactive web application and multiple downloadable formats, including: comma-separated value (CSV), application programming interface (API), and GIS shapefile and GeoJSON.

14 SOLAR ENERGY↗

Laser field control of subradiant states of a system of several atoms in a configuration close to a regular polygon

Some collective excitations of an ensemble of closely spaced (two-level) atoms can be characterised by extremely low rates of radiation decay, which is of considerable interest for storing quantum information. Such (dark) states are realised, for example, in planar geometry when atoms are located at the nodes of a regular polygon. However, the decay rate of such excitations increases markedly when the geometry deviates from ideal. Using the example of small deformation of a square in a rhombus, we show that an increase in the decay rate of the dark state due to symmetry breaking can be compensated for by adjusting the transition frequency of some atoms exposed to external laser radiation. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗