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At least 163 records · Page 9

Twenty Years of Progress, Challenges, and Opportunities in Measuring and Understanding Soil Respiration

Abstract Soil respiration (Rs), the soil‐to‐atmosphere flux of CO 2 , is a dominant but uncertain part of the carbon cycle, even after decades of study. This review focuses on progress in understanding Rs from laboratory incubations to global estimates. We survey key developments of in situ ecosystem‐scale Rs observations and manipulations, synthesize Rs meta‐analyses and global flux estimates, and discuss the most compelling challenges and opportunities for the future. Increasingly sophisticated lab experiments have yielded insights into the interaction among heterotrophic respiration, substrate supply, and enzymatic kinetics, and extended incubation‐based analyses across space and time. Observational and manipulative field‐based experiments have used improved measurement approaches to deepen our understanding of the integrated effects of environmental change and disturbance on Rs. Freely‐available observational databases have enabled meta‐analyses and studies probing the magnitude of, and constraints on, the global Rs flux. Key challenges for the field include expanding Rs measurements, experiments, and opportunities to under‐represented communities and ecosystems; reconciling independent estimates of global respiration fluxes and trends; testing and leveraging the power of machine learning and process‐based models, both independently and in conjunction with each other; and continuing the field's tradition of using novel experiments to explore diverse mechanisms and ecosystems.

54 ENVIRONMENTAL SCIENCES↗

New Perspective on Phase Space Density Analysis for Outer Radiation Belt Enhancements: The Influence of MeV Electron Injections

Observation of growing phase space density (PSD) peak in the outer electron radiation belt has been considered evidence for local wave-driven acceleration as a primary cause of radiation belt enhancement. However, recent studies showed that strong substorm-associated MeV electron injections can also cause significant radiation belt enhancements on fast timescales (~10s min). Such rapid enhancements pose challenges for determining true spatial PSD profiles. To address this, we conduct a detailed spatiotemporal analysis of electron flux and PSD during an enhancement event, using Van Allen Probes data. Our analysis reveals rapid and intermittent flux enhancements. During these rapid enhancements, inbound spacecraft observed false PSD peaks, due to spacecraft's relatively slow movement. However, we identify time intervals of stable fluxes between enhancements, enabling us to determine quasi-stationary PSD profiles with no noticeable peaks. This study provides new insights into accurate PSD analysis, critical for understanding the mechanisms underlying radiation belt enhancements.

79 ASTRONOMY AND ASTROPHYSICS↗

The gravitational index of 5d black holes and black strings

The supersymmetric index of 5d black strings and spinning black holes in M-theory is related to that of 4d black holes in type IIA supergravity when both theories are compactified on the same Calabi-Yau threefold. We find the finite-temperature saddles for the 5d gravitational supersymmetric index by uplifting the recently found attractor saddles of the corresponding 4d index. We study uplifts for two types of geometries: 5d black holes and 5d black strings. For 5d black holes, the uplift guarantees that the index of 4d and 5d black holes match. For 5d black strings, the saddle reproduces the microscopic index at leading order in G N , even without the conventional decoupling limit taken in AdS/CFT. In particular, when the temperature is set to be finite in the 5d flat space region, the black string index is computed from an asymptotically flat solution where the AdS throat is absent. Further, as the temperature is lowered and eventually becomes infinitesimally small in the flat space region, the solution admits a novel decoupling limit in which the AdS 3 throat takes the form of a finite-temperature BTZ black hole that is known to compute the index in AdS 3 /CFT 2 . This represents the first step towards understanding holography for supersymmetric observables in flat space, away from the decoupling limit.

AdS-CFT correspondence↗

Controlling light emission by engineering atomic geometries in silicon photonics

By engineering atomic geometries composed of nearly 1000 atomic segments embedded in micro-resonators, we observe Bragg resonances induced by the atomic lattice at the telecommunication wavelength. The geometrical arrangement of erbium atoms into a lattice inside a silicon nitride (SiN) microring resonator reduces the scattering loss at a wavelength commensurate with the lattice. We confirm dependency of light emission to the atomic positions and lattice spacing and also observe Fano interference between resonant modes in the system.

42 ENGINEERING↗

Abundances of CNO elements in z ∼ 0.3–0.4 Lyman continuum leaking galaxies

We present observations with the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope (HST) of 11 Lyman continuum (LyC) leaking galaxies at redshifts, z , in the range 0.29–0.43, with oxygen abundances 12+log(O/H) = 7.64–8.16, stellar masses M ⋆ ∼ 10 7.8 –10 9.8 M ⊙ , and O 32 = [O III ] λ5007/[O II ] λ3727 of ∼ 5–20 aiming to detect the C III ] λ1908 emission line. We combine these observations with the optical Sloan Digital Sky Survey (SDSS) spectra for the determination of carbon, nitrogen, and oxygen abundances. Our sample was supplemented by 31 galaxies from the literature, for which carbon, nitrogen, and oxygen abundances can be derived from the HST and SDSS spectra. These additional galaxies, however, do not have LyC observations. We find that log(C/O) for the entire sample at 12+log(O/H) < 8.1 does not depend on metallicity, with a small dispersion of ∼0.13 dex around the average value of ∼−0.75 dex. On the other hand, the log(N/O) in galaxies at z > 0.1, including LyC leakers, is systematically higher compared to the rest of the sample with lower metallicity. We find that log(C/O) slightly decreases with increasing M ⋆ from ∼ −0.65 at M ⋆ = 10 6 M ⊙ to ∼ −0.80 at M ⋆ = 10 9 –10 10 M ⊙ , whereas log(N/O) is considerably enhanced at M ⋆ > 10 8 M ⊙ . The origin of these trends remains basically unknown. A possible solution would be to assume that the upper mass limit of the stellar initial mass function in more massive galaxies is higher. This would result in a higher production of oxygen and a larger fraction of massive stars with stellar wind polluting the interstellar medium with nitrogen.

79 ASTRONOMY AND ASTROPHYSICS↗

Predictions for a Low-mass Cutoff for the Primordial Black Hole Mass Spectrum

In this note, we outline how a modest violation in the conservation of mass during the merger of two PBHs affects the PBH mass spectrum that we previously obtained using a Boltzmann equation model for the evolution of the mass spectrum with no mass loss. We find that if the initial cosmological redshift is of the order of 10 12 , then the fraction of primordial holes with masses greater than 10 3 solar masses appears to be close to what is required to provide the seeds for galaxies. In addition, we note that as a result of rapid collisions and strong coupling to electromagnetic radiation for temperatures > GeV, there will be an effective low-mass cutoff in the mass spectrum for PBH masses less than a certain PBH mass less than 0.1M ⊙ . We also point out that this cutoff in the mass spectrum below ~ 0.1M ⊙ can be confirmed by combining future microlensing observations from the Roman Space Telescope and the Vera C. Rubin Observatory with astrometric observations.

79 ASTRONOMY AND ASTROPHYSICS↗

In-situ heating-and-electron tomography for materials research: from 3D ( In-situ 2D) to 4D ( In-situ 3D)

In-situ observation has expanded the application of transmission electron microscopy (TEM) and has made a significant contribution to materials research and development for energy, biomedical, quantum, etc. Recent technological developments related to in-situ TEM have empowered the incorporation of three-dimensional observation, which was previously considered incompatible. In this review article, we take up heating as the most commonly used external stimulus for in-situ TEM observation and overview recent in-situ TEM studies. Then, we focus on the electron tomography (ET) and in-situ heating combined observation by introducing the authors’ recent research as an example. Assuming that in-situ heating observation is expanded from two dimensions to three dimensions using a conventional TEM apparatus and a commercially available in-situ heating specimen holder, the following in-situ heating-and-ET observation procedure is proposed: (i) use a rapid heating-and-cooling function of a micro-electro-mechanical system holder; (ii) heat and cool the specimen intermittently and (iii) acquire a tilt-series dataset when the specimen heating is stopped. This procedure is not too technically challenging and can have a wide range of applications. Essential technical points for a successful 4D (space and time) observation will be discussed through reviewing the authors’ example application.

36 MATERIALS SCIENCE↗

The Global Dynamical Atlas of the Milky Way Mergers: Constraints from Gaia EDR3–based Orbits of Globular Clusters, Stellar Streams, and Satellite Galaxies

The Milky Way halo was predominantly formed by the merging of numerous progenitor galaxies. However, our knowledge of this process is still incomplete, especially in regard to the total number of mergers, their global dynamical properties and their contribution to the stellar population of the Galactic halo. Here, we uncover the Milky Way mergers by detecting groupings of globular clusters, stellar streams, and satellite galaxies in action (J) space. While actions fully characterize the orbits, we additionally use the redundant information on their energy (E) to enhance the contrast between the groupings. For this endeavor, we use Gaia EDR3–based measurements of 170 globular clusters, 41 streams, and 46 satellites to derive their J and E. To detect groups, we use the ENLINK software, coupled with a statistical procedure that accounts for the observed phase-space uncertainties of these objects. We detect a total of N = 6 groups, including the previously known mergers Sagittarius, Cetus, Gaia–Sausage/Enceladus, LMS-1/Wukong, Arjuna/Sequoia/I'itoi, and one new merger that we call Pontus. All of these mergers, together, comprise 62 objects (≈25% of our sample). We discuss their members, orbital properties, and metallicity distributions. We find that the three most-metal-poor streams of our galaxy—"C-19" ([Fe/H] = –3.4 dex), "Sylgr" ([Fe/H] = –2.9 dex), and "Phoenix" ([Fe/H] = –2.7 dex)—are associated with LMS-1/Wukong, showing it to be the most-metal-poor merger. The global dynamical atlas of Milky Way mergers that we present here provides a present-day reference for galaxy formation models.

79 ASTRONOMY AND ASTROPHYSICS↗

Grid Spacing Sensitivities of Simulated Mid-Latitude and Tropical Mesoscale Convective Systems in the Convective Gray Zone

The main objective of this study is to observationally constrain processes in tropical and midlatitude mesoscale convective systems (MCSs), and to use these constraints for model evaluation. To accomplish this, we leverage MCS observations collected at the U.S. DOE Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site in Oklahoma and ARM's mobile GoAmazon2014/15 site in Manaus, Brazil (MAO). We simulate 13 and 11 of these observed MCSs at the SGP and MAO site, respectively, using the Weather Research and Forecasting model at 12-, 4-, 2-, and 1-km horizontal grid spacing. Observations from radiosondes, surface meteorology, and radar wind profilers are used to characterize MCS properties, such as MCS timing and location, cold pools, and convective drafts, and evaluate these simulations. SGP cases are found in better agreement with observations than MAO cases, and when simulated at 2 km, outperform simulations at 1 km regarding the timing of MCS overpass and the accuracy of surface variable trends. MAO simulations suggest a consistent improvement in model accuracy with increasing model resolution in depicting the downdraft structure, the timing of MCSs, and the surface variables changes, except for the latter two metrics at 2 km. Deficiencies are still evident at km-scales, suggesting the need for higher resolution to simulate tropical MCSs. Overall, location-dependent improvements in MCS representation are obtained with the increasing model resolution, prompting the evaluation of sub-km scale simulations.

54 ENVIRONMENTAL SCIENCES↗

CHESS 2025: Spectrometer orthorectified at-sensor radiance from NEON AOP imaging spectroscopy surveys

This dataset provides Level 1 (L1) orthorectified at-sensor radiance derived from measurements collected by the Imaging Spectrometer-1 (NIS-1) onboard the NEON (National Ecological Observatory Network) Airborne Observation Platform (AOP) for the 2025 Colorado Headwaters Ecological Spectroscopy Study (CHESS). NIS-1 captures light reflected from the Earth’s surface in 426 discrete wavelength bands as raw digital numbers (DNs; Level 0). These data are then calibrated to physical units (uW/cm²·sr·nm) following the processing steps described in the NEON Imaging Spectrometer Level 1B Calibrated Radiance Algorithm Theoretical Basis Document (ATBD; Gallery 2022). The data delivered here are the primary inputs for the surface reflectance product in “Custom surface reflectance, shade masks, and equivalent water thickness maps for the Colorado Headwaters Ecological Spectroscopy Study” (Carroll et al. 2026). For intertemporal comparison, the radiance data here are most directly relatable to the v2 radiance data in “NEON AOP Imaging Spectroscopy Survey of Upper East River Colorado Watersheds: Raw-Space Radiance and Observational Variable Dataset” (Goulden et al. 2018), to which the same processing methodology was applied. Together, the radiance and reflectance data enable users to exploit the unique reflection signatures of different surface objects for land cover classification, foliar trait mapping, plant vigor assessment, water content estimation, trace-element identification, and other scientific applications. The data were acquired over three study domains in the Upper Gunnison river basin: the upper East River watershed (CRBU); Almont Triangle and Taylor Canyon (ALMO); and Upper Taylor River watershed (UPTA) between 2025-06-13 and 2025-07-15. Within each domain, data are delivered by flightline as orthorectified and calibrated hyperspectral rasters in Hierarchical Data Format version 5 (HDF5) format, with radiance values provided in uW/cm²·sr·nm on a fixed, uniform Universal Transverse Mercator (UTM) grid at 1 meter spatial resolution. The radiance rasters include all 426 NIS-1 spectral bands, along with associated quality-assurance (QA) and diagnostic and ancillary layers needed for atmospheric correction workflows. Orthorectified radiance is produced from pushbroom spectrometer observations by applying NEON’s radiometric calibration (including bad pixel masking, dark subtract, dark pedestal shift correction, electronic panel ghost correction, grating ghost correction, deblur correction and flat-fielding) and spectral calibration (using spectral response function band centers and full-width at half-maximum intensity), followed by geolocation and regridding to the fixed grid. CHESS Project Description: The Colorado Headwaters Ecological Spectroscopy Study (CHESS) comprised a multi-week airborne remote sensing and field observation campaign in the Upper Gunnison Basin, Colorado, conducted in June and July of 2025. Airborne remote sensing was conducted by the National Ecological Observatory Network Airborne Observation Platform (NEON AOP), concurrent with a field campaign run by the Rocky Mountain Biological Laboratory (RMBL), the Lawrence Berkeley National Laboratory (LBNL) and SLAC National Accelerator Laboratory Watershed Function Science Focus Area (SFA), and NASA-JPL (Jet Propulsion Laboratory) Earth Surface Mineral Dust Source Investigation (EMIT) program. Between June 10 and July 18, 2025, the NEON AOP flight team collected high-resolution aerial imaging spectroscopy and Light Detection and Ranging (LiDAR) data over three domains: the Upper East River (CRBU), Almont Triangle (ALMO), and the Upper Taylor Basin (UPTA). In coordination with the flights, a field campaign acquired ground-truth observations, including observations of vegetation composition, foliar traits, forest demography, and subsurface properties in 18 core sampling areas within the domains. Additional surface water observations were taken at over 380 point locations. All CHESS campaign datasets can be found within the CHESS ESS-DIVE data portal: https://data.ess-dive.lbl.gov/portals/chess. Funding Acknowledgement: Field and remote-sensing data acquisition was performed under a grant from the National Aeronautics and Space Administration (80NSSC24K1005). This work was also supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

2018 NEON and 2025 CHESS Campaigns↗

Input-response space-filling designs

Traditional space-filling designs are a convenient way to explore throughout an input space of flexible dimension and have design points close to any region where future predictions might be of interest. In some applications, there may be a model connecting the input factors to the response(s), which provides an opportunity to consider the spacing not only in the input space but also in the response space. In this paper, we present an approach for leveraging current understanding of the relationship between inputs and responses to generate designs that allow the experimenter to flexibly balance the spacing in these two regions to find an appropriate design for the experimental goals. Applications where good spacing of the observed response values include calibration problems where the goal is to demonstrate the adequacy of the model across the range of the responses, sensitivity studies where the outputs from a submodel may be used as inputs for subsequent models, and inverse problems where the outputs of a process will be used in the inverse prediction for the unknown inputs. Here, we use the multi-objective optimization method of Pareto fronts to generate multiple non-dominated designs with different emphases on the input and response space-filling criteria from which the experimenter can choose. The methods are illustrated through several examples and a chemical engineering case study.

42 ENGINEERING↗

Characterization of high-frequency waves in the Martian magnetosphere

Context.Various high-frequency waves in the vicinity of upper-hybrid and Langmuir frequencies are commonly observed in different space plasma environments. Such waves and fluctuations have been reported in the magnetosphere of the Earth, a planet with an intrinsic strong magnetic field. Mars has no intrinsic magnetic field and, instead, it possesses a weak induced magnetosphere, which is highly dynamic due to direct exposure to the solar wind. In the present paper, we investigate the presence of high-frequency plasma waves in the Martian plasma environment by making use of the high-resolution electric field data from the Mars Atmosphere and Volatile Evolution missioN (MAVEN) spacecraft. Aims.This study aims to provide conclusive observational evidence of the occurrence of high-frequency plasma waves around the electron plasma frequency in the Martian magnetosphere. We observe two distinct wave modes with frequency below and above the electron plasma frequency. The characteristics of these high-frequency waves are quantified and presented here. We discuss the generation of possible wave modes by taking into account the ambient plasma parameters in the region of observation. Methods.We have made use of the medium frequency (100 Hz–32 kHz) burst mode-calibrated electric field data from the Langmuir Probe and Waves instrument on board NASA’s MAVEN mission. Due to the weak magnetic field strength, the electron gyro-frequency is much lower than the electron plasma frequency, which implies that the upper-hybrid and Langmuir waves have comparable frequencies. A total of 19 wave events with wave activities around electron plasma frequency were identified by examining high-resolution spectrograms of the electric field. Results.These waves were observed around 5 LT when MAVEN crossed the magnetopause boundary and entered the magnetosheath region. These waves are either a broadband- or narrowband-type with distinguishable features in the frequency domain. The narrowband-type waves have spectral peak above the electron plasma frequency. However, in the case of broadband-type waves, the spectral peak always occurred below the electron plasma frequency. The broadband waves consistently show a periodic modulation of 8–14 ms. Conclusions.The high-frequency narrowband-type waves observed above the electron plasma frequency are believed to be associated with upper-hybrid or Langmuir waves. However, the physical mechanism responsible for the generation of broadband-type waves and the associated 8–14 ms modulation remain unexplained and further investigation is required.

Astronomy & Astrophysics↗

SPT-CL J2215−3537: A Massive Starburst at the Center of the Most Distant Relaxed Galaxy Cluster

Abstract We present the discovery of the most distant, dynamically relaxed cool core cluster, SPT-CL J2215−3537 (SPT2215), and its central brightest cluster galaxy (BCG) at z = 1.16. Using new X-ray observations, we demonstrate that SPT2215 harbors a strong cool core with a central cooling time of 200 Myr (at 10 kpc) and a maximal intracluster medium cooling rate of 1900 ± 400 M ⊙ yr −1 . This prodigious cooling may be responsible for fueling the extended, star-forming filaments observed in Hubble Space Telescope imaging. Based on new spectrophotometric data, we detect bright [O ii ] emission in the BCG, implying an unobscured star formation rate (SFR) of 320 − 140 + 230 M ⊙ yr −1 . The detection of a weak radio source (2.0 ± 0.8 mJy at 0.8 GHz) suggests ongoing feedback from an active galactic nucleus (AGN), though the implied jet power is less than half the cooling luminosity of the hot gas, consistent with cooling overpowering heating. The extreme cooling and SFR of SPT2215 are rare among known cool core clusters, and it is even more remarkable that we observe these at such high redshift, when most clusters are still dynamically disturbed. The high mass of this cluster, coupled with the fact that it is dynamically relaxed with a highly isolated BCG, suggests that it is an exceptionally rare system that must have formed very rapidly in the early universe. Combined with the high SFR, SPT2215 may be a high- z analog of the Phoenix cluster, potentially providing insight into the limits of AGN feedback and star formation in the most massive galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

Snowmass2021 Cosmic Frontier White Paper: Cosmological Simulations for Dark Matter Physics

Over the past several decades, unexpected astronomical discoveries have been fueling a new wave of particle model building and are inspiring the next generation of ever-more-sophisticated simulations to reveal the nature of Dark Matter (DM). This coincides with the advent of new observing facilities coming online, including JWST, the Rubin Observatory, the Nancy Grace Roman Space Telescope, and CMB-S4. The time is now to build a novel simulation program to interpret observations so that we can identify novel signatures of DM microphysics across a large dynamic range of length scales and cosmic time. This white paper identifies the key elements that are needed for such a simulation program. We identify areas of growth on both the particle theory side as well as the simulation algorithm and implementation side, so that we can robustly simulate the cosmic evolution of DM for well-motivated models. We recommend that simulations include a fully calibrated and well-tested treatment of baryonic physics, and that outputs should connect with observations in the space of observables. We identify the tools and methods currently available to make predictions and the path forward for building more of these tools. A strong cosmic DM simulation program is key to translating cosmological observations to robust constraints on DM fundamental physics, and provides a connection to lab-based probes of DM physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Contrastive Machine Learning with Gamma Spectroscopy Data Augmentations for Detecting Shielded Radiological Material Transfers

Data analysis techniques can be powerful tools for rapidly analyzing data and extracting information that can be used in a latent space for categorizing observations between classes of data. Machine learning models that exploit learned data relationships can address a variety of nuclear nonproliferation challenges like the detection and tracking of shielded radiological material transfers. The high resource cost of manually labeling radiation spectra is a hindrance to the rapid analysis of data collected from persistent monitoring and to the adoption of supervised machine learning methods that require large volumes of curated training data. Instead, contrastive self-supervised learning on unlabeled spectra can enhance models that are built on limited labeled radiation datasets. This work demonstrates that contrastive machine learning is an effective technique for leveraging unlabeled data in detecting and characterizing nuclear material transfers demonstrated on radiation measurements collected at an Oak Ridge National Laboratory testbed, where sodium iodide detectors measure gamma radiation emitted by material transfers between the High Flux Isotope Reactor and the Radiochemical Engineering Development Center. Label-invariant data augmentations tailored for gamma radiation detection physics are used on unlabeled spectra to contrastively train an encoder, learning a complex, embedded state space with self-supervision. A linear classifier is then trained on a limited set of labeled data to distinguish transfer spectra between byproducts and tracked nuclear material using representations from the contrastively trained encoder. The optimized hyperparameter model achieves a balanced accuracy score of 80.30%. Any given model—that is, a trained encoder and classifier—shows preferential treatment for specific subclasses of transfer types. Regardless of the classifier complexity, a supervised classifier using contrastively trained representations achieves higher accuracy than using spectra when trained and tested on limited labeled data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Testing gravitational physics by combining DESI DR1 and weak lensing datasets using the E_G estimator

The action of gravitational physics across space-time creates observable signatures in the behaviour of light and matter. We perform combined-probe studies using data from the Baryon Oscillation Spectroscopic Survey (BOSS) and Dark Energy Spectroscopic Instrument survey Data Release 1 (DESI-DR1), in combination with three existing weak lensing surveys, the Kilo-Degree Survey (KiDS), the Dark Energy Survey (DES), and the Hyper Suprime-Cam Survey (HSC), to test and constrain General Relativity (GR) in the context of the standard model of cosmology (LCDM). We focus on measuring the gravitational estimator statistic, E_G, which describes the relative amplitudes of weak gravitational lensing and galaxy velocities induced by a common set of overdensities. By comparing our amplitude measurements with their predicted scale- and redshift-dependence within the GR+LCDM model, we demonstrate that our results are consistent with the predictions of the Planck cosmology. The redshift span of the DESI dataset allows us to perform these E_G measurements at the highest redshifts achieved to date, z ~ 1.

cosmology↗

Accelerating multicanonical sampling with irreversibility

Flat-histogram Monte Carlo simulations are well-established, robust methods to perform random walks in a physical observable or parameter space, making them suitable for finding ground states or studying phase transitions in complex systems in statistical physics. However, their efficiency can be limited by the time to attain the desired flat distribution, which is generally unknown prior to the simulations. In particular, they might suffer from slowing down towards the end of a simulation due to the diffusive nature of random walks. In this work we apply irreversibility to the multicanonical Monte Carlo method via the lifting approach to alleviate this behavior. We achieve a 2–4 times speedup in ground-state search for a two-dimensional (2D) Ising model, and up to an order of magnitude of speedup for finding the ground-state energy in an Edwards–Anderson spin glass, compared to traditional multicanonical sampling. In conclusion, the round-trip times between ground states show a narrower distribution and are significantly shorter compared to the reversible counterpart, suggesting that a lower convergence time with a smaller time variance is feasible.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗