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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

THE PHASE COHERENCE OF INTERSTELLAR DENSITY FLUCTUATIONS

Studies of MHD turbulence often investigate the Fourier power spectrum to provide information on the nature of the turbulence cascade. However, the Fourier power spectrum only contains the Fourier amplitudes and rejects all information regarding the Fourier phases. Here, we investigate the utility of two statistical diagnostics for recovering information on Fourier phases in ISM column density maps: the averaged amplitudes of the bispectrum and the phase coherence index (PCI), a new phase technique for the ISM. We create three-dimensional density and two-dimensional column density maps using a set of simulations of isothermal ideal MHD turbulence with a wide range of sonic and Alfvénic Mach numbers. We find that the bispectrum averaged along different angles with respect to either the k {sub 1} or k {sub 2} axis is primarily sensitive to the sonic Mach number while averaging the bispectral amplitudes over different annuli is sensitive to both the sonic and Alfvénic Mach numbers. The PCI of density suggests that the most correlated phases occur in supersonic sub-Alfvénic turbulence and near the shock scale. This suggests that nonlinear interactions with correlated phases are strongest in shock-dominated regions, in agreement with findings from the solar wind. Our results suggest that the phase information contained in the bispectrum and PCI can be used to find the turbulence parameters in column density maps.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

HOW THE DENSITY ENVIRONMENT CHANGES THE INFLUENCE OF THE DARK MATTER–BARYON STREAMING VELOCITY ON COSMOLOGICAL STRUCTURE FORMATION

We study the dynamical effect of the relative velocity between dark matter and baryonic fluids, which remained supersonic after the epoch of recombination. The impact of this supersonic motion on the formation of cosmological structures was first formulated by Tseliakhovich and Hirata, in terms of the linear theory of small-scale fluctuations coupled to large-scale, relative velocities in mean-density regions. In their formalism, they limited the large-scale density environment to be that of the global mean density. We improve on their formulation by allowing variation in the density environment as well as the relative velocities. This leads to a new type of coupling between large-scale and small-scale modes. We find that the small-scale fluctuation grows in a biased way: faster in the overdense environment and slower in the underdense environment. We also find that the net effect on the global power spectrum of the density fluctuation is to boost its overall amplitude from the prediction by Tseliakhovich and Hirata. Correspondingly, the conditional mass function of cosmological halos and the halo bias parameter are both affected in a similar way. The discrepancy between our prediction and that of Tseliakhovich and Hirata is significant, and therefore, the related cosmology and high-redshift astrophysics should be revisited. The mathematical formalism of this study can be used for generating cosmological initial conditions of small-scale perturbations in generic, overdense (underdense) background patches.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Insights from Synthetic Star-forming Regions. II. Verifying Dust Surface Density, Dust Temperature, and Gas Mass Measurements With Modified Blackbody Fitting

We use a large data set of realistic synthetic observations (produced in Paper I of this series) to assess how observational techniques affect the measurement physical properties of star-forming regions. In this part of the series (Paper II), we explore the reliability of the measured total gas mass, dust surface density and dust temperature maps derived from modified blackbody fitting of synthetic Herschel observations. We find from our pixel-by-pixel analysis of the measured dust surface density and dust temperature a worrisome error spread especially close to star formation sites and low-density regions, where for those “contaminated” pixels the surface densities can be under/overestimated by up to three orders of magnitude. In light of this, we recommend to treat the pixel-based results from this technique with caution in regions with active star formation. In regions of high background typical in the inner Galactic plane, we are not able to recover reliable surface density maps of individual synthetic regions, since low-mass regions are lost in the far-infrared background. When measuring the total gas mass of regions in moderate background, we find that modified blackbody fitting works well (absolute error: + 9%; −13%) up to 10 kpc distance (errors increase with distance). Commonly, the initial images are convolved to the largest common beam-size, which smears contaminated pixels over large areas. The resulting information loss makes this commonly used technique less verifiable as now χ {sup 2} values cannot be used as a quality indicator of a fitted pixel. Our control measurements of the total gas mass (without the step of convolution to the largest common beam size) produce similar results (absolute error: +20%; −7%) while having much lower median errors especially for the high-mass stellar feedback phase. In upcoming papers (Paper III; Paper IV) of this series we test the reliability of measured star formation rate with direct and indirect techniques.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2012

Reliability of High I/O High Density CCGA Interconnect Electronic Packages under Extreme Thermal Environment

This paper provides the experimental test results of advanced CCGA packages tested in extreme temperature thermal environments. Standard optical inspection and x-ray non-destructive inspection tools were used to assess the reliability of high density CCGA packages for deep space extreme temperature missions. Ceramic column grid array (CCGA) packages have been increasing in use based on their advantages such as high interconnect density, very good thermal and electrical performances, compatibility with standard surface-mount packaging assembly processes, and so on. CCGA packages are used in space applications such as in logic and microprocessor functions, telecommunications, payload electronics, and flight avionics. As these packages tend to have less solder joint strain relief than leaded packages or more strain relief over lead-less chip carrier packages, the reliability of CCGA packages is very important for short-term and long-term deep space missions. We have employed high density CCGA 1152 and 1272 daisy chained electronic packages in this preliminary reliability study. Each package is divided into several daisy-chained sections. The physical dimensions of CCGA1152 package is 35 mm x 35 mm with a 34 x 34 array of columns with a 1 mm pitch. The dimension of the CCGA1272 package is 37.5 mm x 37.5 mm with a 36 x 36 array with a 1 mm pitch. The columns are made up of 80% Pb/20%Sn material. CCGA interconnect electronic package printed wiring polyimide boards have been assembled and inspected using non-destructive x-ray imaging techniques. The assembled CCGA boards were subjected to extreme temperature thermal atmospheric cycling to assess their reliability for future deep space missions. The resistance of daisy-chained interconnect sections were monitored continuously during thermal cycling. This paper provides the experimental test results of advanced CCGA packages tested in extreme temperature thermal environments. Standard optical inspection and x-ray non-destructive inspection tools were used to assess the reliability of high density CCGA packages for deep space extreme temperature missions. Keywords: Extreme temperatures, High density CCGA qualification, CCGA reliability, solder joint failures, optical inspection, and x-ray inspection.

high density CCGA qualifications↗
NASA NTRS2014

Core and Wing Densities of Asymmetric Coronal Spectral Profiles: Implications for the Mass Supply of the Solar Corona

Recent solar spectroscopic observations have shown that coronal spectral lines can exhibit asymmetric profiles, with enhanced emissions at their blue wings. These asymmetries correspond to rapidly upflowing plasmas at speeds exceeding approximately equal to 50 km per sec. Here, we perform a study of the density of the rapidly upflowing material and compare it with that of the line core that corresponds to the bulk of the plasma. For this task, we use spectroscopic observations of several active regions taken by the Extreme Ultraviolet Imaging Spectrometer of the Hinode mission. The density sensitive ratio of the Fe(sub XIV) lines at 264.78 and 274.20 Angstroms is used to determine wing and core densities.We compute the ratio of the blue wing density to the core density and find that most values are of order unity. This is consistent with the predictions for coronal nanoflares if most of the observed coronal mass is supplied by chromospheric evaporation driven by the nanoflares. However, much larger blue wing-to-core density ratios are predicted if most of the coronal mass is supplied by heated material ejected with type II spicules. Our measurements do not rule out a spicule origin for the blue wing emission, but they argue against spicules being a primary source of the hot plasma in the corona. We note that only about 40% of the pixels where line blends could be safely ignored have blue wing asymmetries in both Fe(sub XIV) lines. Anticipated sub-arcsecond spatial resolution spectroscopic observations in future missions could shed more light on the origin of blue, red, and mixed asymmetries.

coronal spectral profiles↗
NASA NTRSDate not supplied

Urban Air Mobility Airspace Dynamic Density

Airspace safety must be assured for Urban Air Mobility (UAM) to become reality. Emerging operations need to safely integrate with existing and future air traffic. UAM is anticipated to evolve in stages. Early stages, characterized by low-density operations, may be accommodated by traditional air traffic management approaches. However, to enable the scale of UAM operations necessary to reach ubiquitous integration into daily life, new paradigms that utilize collaborative and automated systems are being considered. Correspondingly, traditional approaches for determining a safe number of simultaneous operations in an airspace must be adapted to suit evolving traffic management paradigms. In this paper, we examine dynamic density as an approach to determine when an airspace is excessively populated, and safety may become compromised. We review previous work on dynamic density as it relates to air traffic controller workload and propose factors that may be more fitting for UAMs. Rather than considering controller workload, we propose factors that suggest increased likelihood of loss of separation and may lead to conflicts that require tactical avoidance maneuvers. In addition to monitoring dynamic density for tactical decision making, we endeavor to predict airspace dynamic density with adequate look-ahead to allow for strategic route selection.

UAM↗
NASA NTRSDate not supplied

Urban Air Mobility Airspace Dynamic Density

Effective flight planning requires information about a variety of potential threats, such as adverse weather or airspace restrictions, and about alternatives available if unforeseen events occur. Expected traffic along the route of flight is also essential to a safe outcome so that, for example, adequate fuel/energy supply can be loaded prior to flight. A dynamic density (DD) metric is introduced for the emerging urban air mobility (UAM) concept to predict airspace congestion that may lead to loss of separation between aircraft or less efficient operations. Using inspiration from dynamic density metric research for traditional air traffic management and a two-way highway analogy, we develop a dynamic density metric for a portion of airspace (aUAM corridor) that aggregates the impact from five factors: aircraft density, density of populous clusters, mean number of aircraft in populous clusters, mean distance between aircraft, and minimum distance between aircraft. This works describes our methodology, rationale, use cases, and visualization techniques to efficiently present the DD metric to an operator for informed decision making. We also present an approach for validating the metric. However, validation remains part of future work.

UAM↗
DOE OSTI2018

Acoustic Techniques for UF6 Density and Mass Flow Measurements

A key enabling capability for enrichment plant safeguards is high-accuracy, non-invasive, unattended measurement of UF6 gas density and mass flow rate. Acoustic techniques are currently used to non-invasively monitor gas flow in industrial applications; however, the operating pressures at gaseous centrifuge enrichment plants (GCEPs) are roughly two orders magnitude below the capabilities of commercial instrumentation. Pacific Northwest National Laboratory is refining acoustic techniques for estimating density and mass flow rate of UF6 gas in scenarios typical of gaseous centrifuge enrichment plants, with the goal of achieving 1% measurement uncertainty. Proof-of-concept laboratory measurements of UF6 have demonstrated signature sensitivity to gas density at pressures equivalent to 10-50 Torr of UF6, typical pressures for GCEP unit header pipes. This sensitivity was clearly observable above background acoustic interference. Current efforts involve developing a test bed for conducting acoustic measurements on flowing surrogate gas, air and SF6, at representative flow rates and pressures to ascertain the viability of conducting gas flow measurements under these conditions. Density and flow measurements will be conducted to support the evaluation. If successful, the approach could enable an unattended, non-invasive approach to measure UF6 density and mass flow in unit header pipes of GCEPs.

International safeguards instrumentation, acoustic↗
DOE OSTI2022

Experimental Steps toward a Density Law for Chlorine-Crediting Criticality Models of Aqueous Plutonium solutions

Criticality accident prevention is an essential safety consideration for all operations involving fissionable and fissile materials. Predictive criticality calculations using advanced neutron transport codes, such as Monte Carlo N-Particle Transport (MCNP), are invaluable tools for designing and implementing operational limits. While indispensable, these tools are limited by the quality and accuracy of the inputs that the user provides to define the modeled system. Parameters such as atomic composition, shape, and material density must be accurately defined to obtain a meaningful result. In the case of material property details for a plutonium model, accurate material characterization data is sometimes sparse. Thus limitations in calculation accuracy can be reduced by improving our knowledge of material properties in the targeted fissile systems. One of the biggest remaining challenges to accurately defining fissile systems is the description of aqueous fissile solutions. Even simple properties, such as density, are not well-known for fissile solutions relevant to nuclear energy and security. Described here are initial efforts undertaken to improve criticality calculation inputs for fissile plutonium chloride solutions in water. This effort is focused on experimentally determining accurate solution characteristics for ternary plutonium chloride/hydrochloric acid/water systems, by measurement of water activity and solution density. The effect of inputting experimental densities for these solutions into MCNP criticality calculations is compared to the traditional approach of modeling an idealized (and fictitious) plutonium-water mixture. Expansion of these efforts to a working density law for aqueous plutonium chloride solutions is also discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

CHARGED POINT DEFECTS AND DEFECT COMPLEXES IN PHOSPHORENE AND STRUCTURAL PREDICTION OF TAU-11, A DENSITY FUNCTIONAL THEORY APPROACH

With the advent of powerful computers, first principle calculations have become a robust and reliable tool to complement experiments in the study of materials. First principle calculations such as density functional theory can be used to guide experiments to save time and effort when it comes to new and advanced materials discovery. Study of charge defects in materials and crystal structure prediction are such areas in which density functional theory calculations facilitate the prediction of defect formation energy, charge transition levels and elemental site occupations. Experimentally, studying charge defects requires inferring results from various techniques. Likewise, determining site occupancies for similar elements using experimental techniques is challenging and sometimes impossible. In this work, we study the charged intrinsic and extrinsic defects and defect complexes in phosphorene and determine the site occupancies of Al, Fe and Si in the τ11 phase using density functional theory. In the defect work, we calculate the defect formation energy, charge transition level, binding energies and Stokes shift for vacancy, dopant substitution and dopant-vacancy defect complexes in phosphorene. We found that vacancy defect in phosphorene becomes negatively charged in n-type doping and may passivate the dopants and reduce carrier concentration and mobility. For non-metal dopants in phosphorene, we predict that O, S and Si prefer to form dopant-vacancy complexes removing the vacancy defect states from the band gap. Mn dopant-vacancy defect complex exhibits possibility of switching between two magnetic spin states. Lastly, using density functional theory, we complement the results from neutron powder diffraction to determine the site occupancies of Al and Si in τ11 phase which was used to determine the alloying element to develop a high temperature and low density alloy.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A New Mechanistic Model of Nucleation Site Density

The two-fluid model, which is a macroscopic formulation of nucleate boiling systems, still makes use of experimental data or empirical correlations for closure models. The use of empirical correlations outside the range of conditions where they have been developed is questionable, which limits the application of the two-fluid model in the design of new boiling systems. This paper proposes a mechanistic model of nucleation site density, which, along with bubble departure frequency and bubble departure diameter, are key factors in the accurate prediction of evaporation heat flux and vapor generation rate on the heated surface in the two-fluid model formulation. Nucleation originates from cavities on boiling surface. Griffith and Wallis proposed that a nucleation site becomes active when vapor is entrapped inside the cavity and the mouth radius is larger than the minimum cavity size corresponding to the wall superheat. Yang and Kim obtained the probability density function of the cavity mouth radius and the half cone angle through a statistical treatment based on the measured cavities by a scanning electron microscope and a differential interference contrast microscope. Hibiki and Ishii modified the distribution profiles of the size and cone angle of cavities present on the heater surface and proposed a new model which is valid over rather wide range of flow conditions. The existing nucleation site density models are not physically consistent at onset of nucleation, where no boiling occurs even though the models predict a high nucleation site density. The new model developed in this paper took into account the non-uniform temperature in liquid near the wall, which allows one to physically impart the onset of nucleation into the nucleation site density model. The new model was parametrically tested and showed physical consistency at the region near onset of nucleate boiling. The new model was also validated against selected experimental data and good agreement was reached.

42 ENGINEERING↗
DOE OSTI2024

Evaluation of Thermal Scattering Law for U 3 Si 2 Using Temperature-Dependent Phonon Density of States

The thermal scattering law for uranium silicide, a candidate material for high-density nuclear fuel, was evaluated from the temperature-dependent phonon density of states obtained using the quasi-harmonic approximation. For uranium silicide model systems of various volumes near the equilibrium volume, Hellmann-Feynman forces were calculated by performing ab initio lattice dynamics simulations based on density functional theory. Subsequently, the quasi-harmonic approximation was applied by interpolating the results of the harmonic approximation for each volume system. As a sensitivity test, the phonon density of states was calculated for the structures with temperature-dependent volumes at 298 K and 1000 K, obtained by the quasi-harmonic approximation, and the corresponding thermal neutron scattering cross section was evaluated. The temperature-dependent volume and heat capacity of uranium silicide obtained by the quasi-harmonic approximation showed reasonable agreement with experimental data while lattice thermal expansion showed deviation from experimental observations. Thermal scattering cross sections evaluated from 0 K and temperature-dependent phonon density of states exhibited differences of up to 4.1% at 1000 K. This study examines the impact of temperature on the thermal scattering law, employing ab initio lattice dynamics simulations through the quasi-harmonic approximation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory

Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to leading order (–0.221 Z 5/3 and –0.021 Z ln Z respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to E x (N,Z) ≈ –0.354 N 2/3 Z (as known before only for Z >> N >> 1) and E c ≈ –0.02 N ln N . These asymptotic estimates are most correct for atomic ions with large N and Z >> N, but we find that they are qualitatively and semi- quantitatively correct even for small N and for N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely-predictive approximate density functionals should be designed to recover the correct asymptotics. Here, it is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Investigation of the Electron Density Variation During the 21 August 2017 Solar Eclipse

Abstract This paper presents a comparison of modeled and measured electron densities for the 21 August 2017 solar eclipse across the USA. The location of the instrument was (43.81°N, 247.32°E) where the maximum obscuration of 99.6% occurred at 17.53 hr UT on 21 August. The solar apparent time was 9.96 hr, and the duration of the eclipse was 2.7 hr. It was found that if it is assumed that there are no chromosphere emissions at totality, ~30% coronal emission remaining at totality gave the best fit to the electron density variation at 150 km. The 30% coronal emission estimate has uncertainties associated with respect to uncertainties in the solar spectrum, the measured electron density, and the amount of chromosphere emissions remaining at totality. The agreement between the modeled and measured electron densities is excellent at 150 km with the assumed 30% coronal emission at totality. At other altitudes, the agreement is very good, but the altitude profile would be improved if the model peak electron density ( N m F 2 ) decayed more slowly to better match the data. The minimum N m F 2 in the model occurs ~10 min after totality when it decreases to 0.55 from its noneclipse value. The minimum of the N m F 2 data occurs between 6 and 10 min after totality but is ~15% larger. The total electron content decreases to 0.65 of its preeclipse value. These relative changes agree well with those predicted by others prior to the eclipse.

Reinisch, B. W.↗
DOE OSTI2018

Dense Graphene Monolith for High Volumetric Energy Density Li-S Batteries

Despite the outstanding gravimetric performance of lithium-sulfur (Li-S) batteries, their practical volumetric energy density is normally lower than that of lithium-ion batteries, mainly due to the low density of nanostructured sulfur as well as the porous carbon hosts. Here, a novel approach is developed to fabricate high-density graphene bulk materials with ink-bottle-like mesopores by phosphoric acid (H 3 PO 4 ) activation. These pores can effectively confine the polysulfides due to their unique structure with a wide body and narrow neck, which shows only a 0.05% capacity fade per cycle for 500 cycles (75% capacity retention) for accommodating polysulfides. With a density of 1.16 g cm -3 , a hybrid cathode containing 54 wt% sulfur delivers a high volumetric capacity of 653 mA h cm -3 . As a result, a device-level volumetric energy density as high as 408 W h L -1 is achieved with a cathode thickness of 100 mu m. This is a periodic yet practical advance to improve the volumetric performance of Li-S batteries from a device perspective. Furthermore, this work suggests a design principle for the real use Li-S batteries although there is a long way ahead to bridge the gap between Li-S batteries and Li-ion batteries in volumetric performance.

25 ENERGY STORAGE↗
DOE OSTI2022

Density Dependence in Three Snake River Sockeye Salmon Nursery Lakes in Central Idaho

Abstract Snake River Sockeye Salmon Oncorhynchus nerka, listed as an endangered species in 1991, currently inhabit three nursery lakes (Redfish, Pettit, and Alturas lakes) in the Sawtooth Valley, Idaho. Conspecific kokanee (lacustrine Sockeye Salmon) are also present in the lakes. Snake River Sockeye Salmon recovery efforts, initially focused on genetic conservation, are now attempting to rebuild naturally spawning populations using hatchery supplementation. However, in Sockeye Salmon nursery lakes, density dependence is frequently observed when elevated O. nerka abundance leads to declines in zooplankton biomass, body size, and shifts in community composition. In turn, these changes lead to reductions in juvenile O. nerka growth rates, survival, and adult returns. We examined a long-term data set of O. nerka population metrics and associated zooplankton community metrics. We found evidence of density dependence within and among nursery lakes. We detected differences in zooplankton biomass, lengths of preferred zooplankton prey (Daphnia spp. and cyclopoid copepods), parr growth rates, and age-1 smolt size among the three lakes. We found negative relationships between O. nerka density and zooplankton biomass and size. We identified positive relationships between zooplankton biomass and two response variables: smolt size at migration and growth rates of hatchery parr. The relationships were generally similar among lakes. Variable outcomes were a result of differences in O. nerka density (or zooplankton biomass), controlled primarily by the relative proportion of spawning and rearing habitat in each lake. Understanding unique lake habitats, ecological interactions, and the role of density dependence is germane to management of Snake River Sockeye Salmon populations.

Griswold, Robert G.↗
DOE OSTI2024

Spatial patterns in occupancy and density of larval lampreys in freshwater habitats restored to a Stage 0 condition

Abstract We examined occupancy and density of larval lampreys ( Entosphenus tridentatus and Lampetra spp.) in two rivers in Oregon (USA) restored to a Stage 0 condition 1–5 years prior, using a multiscale occupancy model and a zero‐inflated Poisson mixture model. We sampled lampreys using backpack electrofishing in randomly distributed, paired, 1‐m 2 quadrats and recorded environmental data. Probabilities of occupancy and density were higher when water velocity was low, the substrate was noncompacted, and sediment was dominated by fines (<4 mm). At mean water depth (0.34 m) and velocity (0.09 m/s), estimated densities in occupied quadrats were 4.8 lampreys/m 2 (95%: 3.4–6.9) when the substrate was compacted, and fines were not dominant, and 21.1 lampreys/m 2 (95%: 17.7–25.3) when the substrate was noncompacted and fines were dominant. Probabilities of detecting occupancy in a 1‐m 2 quadrat sampled by backpack electrofishing were 0.76 (95%: 0.64–0.87) when captured after visual observation and 0.80 (95%: 0.71–0.88) with blind sweeps (i.e., constantly moving the net regardless of observation). The probability of capturing a single lamprey in a quadrat sampled by blind sweeps was 0.32 (95%: 0.27–0.37). Sampling in paired 1‐m 2 quadrats facilitated concurrent examination of patterns in occupancy and density while accounting for capture probability, which could aid temporal monitoring of restored habitats. To the best of our knowledge, this is the first study to document occupancy and estimate densities of larval lampreys in habitats that underwent valley floor restoration to Stage 0. We observed both lamprey genera within 5 years of restoration. Aquatic restoration that increases low‐velocity, noncompacted, fine sediment habitats could benefit lampreys.

Harris, Julianne E.↗
DOE OSTI2023

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

We consider U(1)-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in d > 2 spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3 and 4, at leading order in the 1/N expansion. We derive these results by computing analytically the zero-temperature, finite-μ one-loop effective potential, paying special attention to subtle points related to the iε terms. We check our results against the one-loop low-energy effective action for the superfluid phonons in λΦ 4 theory in d = 4 previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-n operator for the λΦ 6 conformal superfluid in d = 3, at leading order in 1/n, reproducing a numerical result of Badel et al. For a λΦ 4 superfluid in d = 4, we also reproduce the Lee-Huang-Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗