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At least 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Structural basis for adenylation and thioester bond formation in the ubiquitin E1

The ubiquitin (Ub) and Ub-like (Ubl) protein-conjugation cascade is initiated by E1 enzymes that catalyze Ub/Ubl activation through C-terminal adenylation, thioester bond formation with an E1 catalytic cysteine, and thioester bond transfer to Ub/Ubl E2 conjugating enzymes. Each of these reactions is accompanied by conformational changes of the E1 domain that contains the catalytic cysteine (Cys domain). Open conformations of the Cys domain are associated with adenylation and thioester transfer to E2s, while a closed conformation is associated with pyrophosphate release and thioester bond formation. Several structures are available for Ub E1s, but none has been reported in the open state before pyrophosphate release or in the closed state. Here, we describe the structures of Schizosaccharomyces pombe Ub E1 in these two states, captured using semisynthetic Ub probes. In the first, with a Ub-adenylate mimetic (Ub-AMSN) bound, the E1 is in an open conformation before release of pyrophosphate. In the second, with a Ub-vinylsulfonamide (Ub-AVSN) bound covalently to the catalytic cysteine, the E1 is in a closed conformation required for thioester bond formation. These structures provide further insight into Ub E1 adenylation and thioester bond formation. Conformational changes that accompany Cys-domain rotation are conserved for SUMO and Ub E1s, but changes in Ub E1 involve additional surfaces as mutational and biochemical analysis of residues within these surfaces alter Ub E1 activities.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Augmenting a Simulation Campaign for Hybrid Computer Model and Field Data Experiments

The Kennedy and O’Hagan (KOH) calibration framework uses coupled Gaussian processes (GPs) to meta-model an expensive simulator (first GP), tune its “knobs” (calibration inputs) to best match observations from a real physical/field experiment and correct for any modeling bias (second GP) when predicting under new field conditions (design inputs). There are well-established methods for placement of design inputs for data-efficient planning of a simulation campaign in isolation, that is, without field data: space-filling, or via criterion like minimum integrated mean-squared prediction error (IMSPE). Analogues within the coupled GP KOH framework are mostly absent from the literature. Here, in this study, we derive a closed form IMSPE criterion for sequentially acquiring new simulator data for KOH. We illustrate how acquisitions space-fill in design space, but concentrate in calibration space. Closed form IMSPE precipitates a closed-form gradient for efficient numerical optimization. We demonstrate that our KOH-IMSPE strategy leads to a more efficient simulation campaign on benchmark problems, and conclude with a showcase on an application to equilibrium concentrations of rare earth elements for a liquid–liquid extraction reaction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Deferred Verification: The Role of New Verification Technologies and Approaches

Researchers at UNIDIR have recently proposed a fundamentally new approach to nuclear arms control verification, dubbed "deferred verification." The concept forgoes inspections at sensitive nuclear sites and inspections of nuclear materials or components in classified form. To implement this concept, a state first divides its territory into a closed segment and an open segment. The total fissile material inventory in the closed segment, which includes the weapon complex, is known and declared with very high accuracy. Essentially no inspections take place in the closed segment. Yet, inspectors have access to the open segment, which includes in particular the civilian nuclear sector. The fissile material inventory in the open segment is known with less accuracy, but uncertainties can be reduced over time using methods of nuclear archaeology. Deferred verification relies primarily on established safeguards techniques and avoids many unresolved verification challenges, including for example the need for information barriers for warhead confirmation measurements. At the same time, deferred verification faces some unique challenges. In this work, we explore some of these challenges and offer possible solutions while maintaining the strengths of the concept; to do so, we examine possible noncompliance strategies in which a state would seek to withhold a higher-than-declared inventory.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2022

Topological magnetic hysteresis in single crystals of CeAgSb 2 ferromagnet

Closed-topology magnetic domains are usually observed in thin films and in an applied magnetic field. In this work, we report the observation of rectangular cross-section tubular ferromagnetic domains in thick single crystals of CeAgSb 2 in zero applied field. Relatively low exchange energy, small net magnetic moment, and anisotropic in-plane crystal electric fields lower the domain wall energy and allow for the formation of the closed-topology patterns. The tubular domain structure irreversibly transforms into a dendritic pattern upon cycling the magnetic field. This transition between closed and open topologies results in a ‘topological magnetic hysteresis’— the actual hysteresis in magnetization, not due to the imperfections and pinning, but due to the difference in the pattern morphology. Similar physics was suggested before in pure type-I superconductors and is believed to be a generic feature of other nonlinear single (present case), or two-phase (type-I superconductor) systems where the effects similar to demagnetization (shape-dependent macroscopic variation of properties) lead to pattern formation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Effect of resistivity on poloidal asymmetries in electron density in the edge and scrape off layer in 3D full-F gyro-fluid simulations with FELTOR

In this contribution, we analyze the poloidal asymmetries in electron density in the edge and scrape-off layer (SOL) in a COMPASS-sized, diverted tokamak with the 3D full-F, isothermal, electromagnetic, and gyro-fluid model FELTOR. The study is performed for different simulations that span over 2 orders of magnitude in resistivity. The poloidal asymmetries of density are evaluated in the edge and the SOL relative to the outer midplane (OMP), where the highest densities are usually found. In the closed magnetic surfaces, the relative poloidal asymmetry with respect to the OMP is not larger than 20% independently of the plasma resistivity. For the open field lines in the SOL, the relative density asymmetry can range from 55% for the highest resistivity to around 40% for the lowest. The lowest densities inside the separatrix are found between the inner midplane and the top of the magnetic configuration, away from the X-point. In the SOL it is usually close to the X-point in the high field side. The observations in the closed field lines are consistent with ballooning transport but in the SOL oppose experimental evidence for high-density plasmas. In conclusion, this indicates the necessity for more complex physics to reproduce the experimental observations in the SOL for higher density plasmas, such as neutral-plasma dynamics and realistic divertor conditions.

3D full-f gyrofluid↗
DOE OSTI2019

Comprehensive magnetohydrodynamic hybrid simulations of Alfvén eigenmode bursts and fast-ion losses in the Large Helical Device

Comprehensive magnetohydrodynamic (MHD) hybrid simulations with neutral beam injection and collisions were conducted to investigate the Alfvén eigenmode (AE) bursts and the fast-ion losses in the large helical device (LHD) for the realistic conditions close to the experiments. In this study, it is found in the simulation of the slowing-down time scale that the AE bursts take place repetitively accompanied by fast-ion redistribution and losses leading to lower saturation levels of stored fast-ion energy than those in a classical calculation where the MHD perturbations are neglected. The fast-ion loss rate caused by the AE burst has the quadratic dependence on AE amplitude, which was observed in the LHD experiment. The majority of the lost fast ions are counter-passing particles whose velocity and pitch-angle are close to those of the beam injection. The second component of the lost fast ions is transit particles whose velocity is close to thermal velocity. The loss of the counter-passing particles occurs mainly during the AE bursts, while the transit particles are lost both during the AE bursts and the quiescent periods with larger loss rate than that in the classical calculation. The initial location of the lost counter-injected particles spreads from the plasma edge to the plasma center, while only the particles initially located in the peripheral region are lost for the co-injected beam.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Runaway electron deconfinement in SPARC and DIII-D by a passive 3D coil

The operation of a 3D coil—passively driven by the current quench (CQ) loop voltage—for the deconfinement of runaway electrons (REs) is modeled for disruption scenarios in the SPARC and DIII-D tokamaks. Nonlinear magnetohydrodynamic (MHD) modeling is carried out with the NIMROD code including time-dependent magnetic field boundary conditions to simulate the effect of the coil. Further modeling in some cases uses the ASCOT5 code to calculate advection and diffusion coefficients for REs based on the NIMROD-calculated fields, and the DREAM code to compute the runaway evolution in the presence of these transport coefficients. Compared with similar modeling in Tinguely et al (2021 Nucl. Fusion 61 124003), considerably more conservative assumptions are made with the ASCOT5 results, zeroing low levels of transport, particularly in regions in which closed flux surfaces have reformed. Of three coil geometries considered in SPARC, only the n = 1 coil is found to have sufficient resonant components to suppress the runaway current growth. Without the new conservative transport assumptions, full suppression of the RE current is maintained when the thermal quench MHD is included in the simulation or when the RE current is limited to 250kA, but when transport in closed flux regions is fully suppressed, these scenarios allow RE beams on the order of 1–2 MA to appear. Additional modeling is performed to consider the effects of the close ideal wall. In DIII-D, the CQ is modeled for both limited and diverted equilibrium shapes. In the limited shape, the onset of stochasticity is found to be insensitive to the coil current amplitude and governed largely by the evolution of the safety-factor profile. In both devices, prediction of the q-profile evolution is seen to be critical to predicting the later time effects of the coil.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

The case for digital twins in metal additive manufacturing

The digital twin (DT) is a relatively new concept that is finding increased acceptance in industry. A DT is generally considered as comprising a physical entity, its virtual replica, and two-way digital data communications in-between. Its primary purpose is to leverage the process intelligence captured within digital models—or usually their faster-solving surrogates—towards generating increased value from the physical entities. The surrogate models are created using machine learning based on data obtained from the field, experiments and digital models, which may be physics-based or statistics-based. Anomaly detection and correction, and diagnostic closed-loop process control are examples of how a process DT can be deployed. In the manufacturing industry, its use can achieve improvements in product quality and process productivity. Metal additive manufacturing (AM) stands to gain tremendously from the use of DTs. This is because the AM process is inherently chaotic, resulting in poor repeatability. However, a DT acting in a supervisory role can inject certainty into the process by actively keeping it within bounds through real-time control commands. Closed-loop feedforward control is achieved by observing the process through sensors that monitor critical parameters and, if there are any deviations from their respective optimal ranges, suitable corrective actions are triggered. The type of corrective action (e.g. a change in laser power or a modification to the scanning speed) and its magnitude are determined by interrogating the surrogate models. Because of their artificial intelligence (AI)-endowed predictive capabilities, which allow them to foresee a future state of the physical twin (e.g. the AM process), DTs proactively take context-sensitive preventative steps, whereas traditional closed-loop feedback control is usually reactive. Apart from assisting a build process in real-time, a DT can help with planning the build of a part by pinpointing the optimum processing window relevant to the desired outcome. Again, the surrogate models are consulted to obtain the required information. In this article, we explain how the application of DTs to the metal AM process can significantly widen its application space by making the process more repeatable (through quality assurance) and cheaper (by getting builds right the first time).

36 MATERIALS SCIENCE↗
DOE OSTI2022

Investigating the limits of superconductivity in UTe 2

Abstract Spin-triplet bulk superconductors are a promising route to topological superconductivity, and UTe 2 is a recently discovered contender. The superconducting properties of UTe 2 , however, vary substantially as a function of the synthetic route, and even nonsuperconducting single crystals have been reported. To understand the driving mechanism suppressing superconductivity, we investigate UTe 2 single crystals grown close to the nonsuperconducting boundary (growth temperature ∼710 ∘ C) through a combination of thermodynamic and x-ray diffraction measurements. Specific heat measurements reveal a sharp decrease in the superconducting volume and a concomitant increase in the residual specific heat coefficient close to the nonsuperconducting boundary. Notably, these crystals are inhomogeneous and show an apparent double transition in specific heat measurements, similar to samples grown at much higher temperatures (∼1000 ∘ C). Our single crystal x-ray diffraction measurements reveal that there are two important tuning parameters: uranium vacancies and the atomic displacement along the c axis, which shows a twofold increase in samples with a reduced superconducting volume. Our results highlight the key role of local disorder along the uranium-uranium dimers and suggest that the apparent double superconducting transition is more likely to emerge close to the superconducting limits of UTe 2 .

Weiland, A. (ORCID:0000000171983559)↗
DOE OSTI2020

Giant Planet Scatterings and Collisions: Hydrodynamics, Merger-Ejection Branching Ratio, and Properties of the Remnants

Planetary systems with sufficiently small orbital spacings can experience planetary mergers and ejections. The branching ratio of mergers vs ejections depends sensitively on the treatment of planetary close encounters. Previous works have adopted a simple “sticky-sphere” prescription, whose validity is questionable. We apply both smoothed particle hydrodynamics and N-body integrations to investigate the fluid effects in close encounters between gas giants and the long-term evolution of closely-packed planetary systems. Focusing on parabolic encounters between Jupiter-like planets with MJ and 2MJ, we find that quick mergers occur when the impact parameter rp (the pericenter separation between the planets) is less than 2RJ, and the merger conserved at least 97% of the initial mass. Strong tidal effects can affect the “binary-planet” orbit when rp is between 2RJ and 4RJ. We quantify these effects using a set of fitting formulae that can be implemented in N-body codes. We run a suite of N-body simulations with and without the formulae for systems of two giant planets initially in unstable, nearly circular and nearly coplanar orbits. The fluid (tidal) effects significantly increase the branching ratio of planetary mergers relative to ejections by doubling the effective collision radius. While the fluid effects do not change the distributions of semi-major axis and eccentricity of each type of remnant planets (mergers vs surviving planets in ejections), the overall orbital properties of planet scattering remnants are strongly affected due to the branching ratio change. We also find that the merger products have broad distributions of spin magnitudes and obliquities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Stellar multiplicity and stellar rotation: insights from APOGEE

ABSTRACT We measure rotational broadening in spectra taken by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey to characterize the relationship between stellar multiplicity and rotation. We create a sample of 2786 giants and 24 496 dwarfs with stellar parameters and multiple radial velocities from the APOGEE pipeline, projected rotation speeds vsin i determined from our own pipeline, and distances, masses, and ages measured by Sanders & Das. We use the statistical distribution of the maximum shift in the radial velocities, ΔRVmax, as a proxy for the close binary fraction to explore the interplay between stellar evolution, rotation, and multiplicity. Assuming that the minimum orbital period allowed is the critical period for Roche Lobe overflow and rotational synchronization, we calculate theoretical upper limits on expected vsin i and ΔRVmax values. These expectations agree with the positive correlation between the maximum ΔRVmax and vsin i values observed in our sample as a function of log(g). We find that the fast rotators in our sample have a high occurrence of short-period [log(P/d) ≲ 4] companions. We also find that old, rapidly rotating main-sequence stars have larger completeness-corrected close binary fractions than their younger peers. Furthermore, rapidly rotating stars with large ΔRVmax consistently show differences of 1–10 Gyr between the predicted gyrochronological and measured isochronal ages. These results point towards a link between rapid rotation and close binarity through tidal interactions. We conclude that stellar rotation is strongly correlated with stellar multiplicity in the field, and caution should be taken in the application of gyrochronology relations to cool stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Bioapatite in shark centra studied by wide-angle and by small-angle X-ray scattering

Members of subclass Elasmobranchii possess cartilage skeletons; the centra of many species are mineralized with a bioapatite, but virtually nothing is known about the mineral's organization. This study employed high-energy, small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS, i.e. X-ray diffraction) to investigate the bioapatite crystallography within blocks cut from centra of four species (two carcharhiniform families, one lamniform family and 1-ID of the Advanced Photon Source). All species' crystallographic quantities closely matched and indicated a bioapatite closely related to that in bone. The centra's lattice parameters a and c were somewhat smaller and somewhat larger, respectively, than in bone. Nanocrystallite sizes (WAXS peak widths) in shark centra were larger than typical of bone, and little microstrain was observed. Compared with bone, shark centra exhibited SAXS D-period peaks with larger D magnitudes, and D-period arcs with narrower azimuthal widths. The shark mineral phase, therefore, is closely related to that in bone but does possess real differences which probably affect mechanical property and which are worth further study.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Exact spectral gaps of random one-dimensional quantum circuits

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. Here, by focusing on the second moment of one-dimensional unitary circuits where nearest-neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Towards a Deeper Fundamental Understanding of (Al,Sc)N Ferroelectric Nitrides

Density functional theory (DFT) calculations, within the virtual crystal alloy approximation, are performed, along with the development of a Landau-type model employing a symmetry-allowed analytical expression of the internal energy and having parameters determined from first principles, to investigate properties and energetics of Al1-xScxN ferroelectric nitrides in their hexagonal forms. These DFT computations and this model predict the existence of two different types of minima, namely, the fourfold-coordinated wurtzite (WZ) polar structure and a five-fold coordinated paraelectric hexagonal phase (denoted as H5), for any Sc composition up to 40%. The H5 minimum progressively becomes the lowest-energy state within hexagonal symmetry as the Sc concentration increases from 0 to 0.4. Furthermore, the model points to several key findings. Examples include the crucial role of the coupling between polarization and strains to create the WZ minimum, in addition to polar and elastic energies, and that the origin of the H5 state overcoming the WZ phase as the global minimum within hexagonal symmetry when increasing the Sc composition mostly lies in the compositional dependency of only two parameters-one linked to the polarization and another one being purely elastic in nature. Other examples are that forcing Al1-xScxN systems to have no or a weak change in lattice parameters when heating them allows us to reproduce their finite-temperature polar properties well and that a value of the axial ratio close to that of the ideal WZ structure implies a large polarization at low temperatures but not necessarily at high temperatures because of the ordered-disordered character of the temperature-induced formation of the WZ state. Such findings should allow for a better fundamental understanding of (Al,Sc)N ferroelectric nitrides, which may be used to design efficient devices having, e.g., low operating voltages.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Higher-dimensional generalizations of Berry curvature

A family of finite-dimensional quantum systems with a nondegenerate ground state gives rise to a closed two-form on the parameter space, the curvature of the Berry connection. Its integral over a surface detects the presence of degeneracy points inside the volume enclosed by the surface. In this work, we seek generalizations of the Berry curvature to gapped many-body systems in $\textit{D}$ spatial dimensions which can detect gapless or degenerate points in the phase diagram of a system. Field theory predicts that in spatial dimension $\textit{D}$ the analog of the Berry curvature is a closed ($\textit{D}$ + 2) -form on the parameter space (the Wess-Zumino-Witten form). We construct such closed forms for arbitrary families of gapped interacting lattice systems in all dimensions. We show that whenever the integral of the Wess-Zumino-Witten form over a ($\textit{D}$ + 2)-dimensional surface in the parameter space is nonzero, there must be gapless edge modes for at least one value of the parameters. These edge modes arise even when the bulk system is in a trivial phase for all values of the parameters and are protected by the nontrivial topology of the phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Hot-lines topology and the fate of the spin resonance mode in three-dimensional unconventional superconductors

In the quasi-two-dimensional (quasi-2D) copper- and iron-based superconductors, the onset of superconductivity is accompanied by a prominent peak in the magnetic spectrum at momenta close to the wave-vector of the nearby antiferromagnetic state. Such a peak is well described in terms of a spin resonance mode, i.e., a spin-1 exciton theoretically predicted for quasi-2D superconductors with a sign-changing gap. The same theories, however, indicate that such a resonance mode should be absent in a three-dimensional (3D) system with a spherical Fermi surface. This raises the question of the fate of the spin resonance mode in layered unconventional superconductors that are not strongly anisotropic, such as certain heavy-fermion compounds and potentially the newly discovered nickelate superconductor NdNiO 2 . Here, we use the random phase approximation to calculate the dynamical spin susceptibility of 3D superconductors with a d x 2 –y 2 -wave gap symmetry and corrugated cylindrical-like Fermi surfaces. By varying the out-of-plane hopping anisotropy t z /t, we demonstrate that the appearance of a spin resonance mode is determined by the topology of the hot lines, i.e., lines on the Fermi surface that are connected by the magnetic wave vector. For an in-plane antiferromagnetic wave vector, the hot lines undergo a topological transition from open lines to closed loops at a critical t z /t value. The closed hot lines cross the nodal superconducting lines, making the spin resonance mode overdamped and incoherent. In contrast, for an out-of-plane antiferromagnetic wave vector, the hot lines remain open and the spin resonance mode remains sharp. We discuss the experimental implications of our results for the out-of-plane dispersion of the spin resonance mode and, more generally, for inelastic neutron scattering experiments on unconventional superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Structures of elemental potassium at terapascal pressures

Here we investigate the pressure-temperature phase diagram of elemental potassium (K) up to multiterapascal (TPa) pressures using ab initio random structure searching (AIRSS), discovering eight structural phase transitions beyond the already known double hexagonal close-packed (dhcp) structure. Starting at 1.15 TPa, K transitions from the dhcp structure and passes through a variety of close-packed hexagonal and trigonal phases (dhcp → P6 3 /mmc → P3m1 → P$\bar{6}m2$), which differ only in their stacking sequence along the c axis. At 2.55 TPa, K adopts the hexagonal close-packed (hcp) structure, and at 7.21 TPa transitions into a complex orthorhombic phase of Fddd symmetry with 64 atoms in its (conventional) unit cell, before assuming an Ibam structure at 8.60 TPa, and, eventually, the face centered cubic (fcc) structure at 23.6 TPa, which persists well into the petapascal (PPa) regime. Further, we calculate the full pressure-temperature dependence of the melting line of K through extensive molecular dynamics simulations. We study the evolution of the bonding topology of K with pressure, finding that K passes through two quasi-molecular phases featuring diatomic pairs (the Fddd and Ibam structures), before ultimately becoming a high pressure electride (HPE) in the fcc phase. The electron-phonon and superconducting properties of K at these extreme pressures are also investigated, where we find the critical temperature T c rises to a maximum of between 7.65 K and 15.70 K in the hcp phase, before eventually decreasing to essentially zero in the fcc phase. Our results fully elucidate the structural and electronic behavior of K under the most extreme conditions, and provide new case studies for multi-TPa dynamic compression experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Zero-pairing and zero-temperature limits of finite-temperature Hartree-Fock-Bogoliubov theory

Recently, variational Hartree-Fock-Bogoliubov (HFB) mean-field equations were shown to possess a mathematically well-defined zero-pairing limit, independently of the closed- or open-shell character of the system under consideration. This limit is non-trivial for open-shell systems such that HFB theory does {\it not} reduce to the Hartree-Fock (HF) formalism in all cases. The present work extends this analysis to finite-temperature HFB (FTHFB) theory by investigating the behavior of this more general formalism in the combined zero-temperature and zero-pairing limits. The zero-pairing and zero-temperature limits of the FTHFB statistical density operator constrained to carry an arbitrary (integer) number of particles A on average is worked out analytically and realized numerically using a two-nucleon interaction. While the FTHFB density operator reduces to the projector corresponding to a pure HF Slater determinant for closed-shell nuclei, the FTHFB formalism does not reduce to the HF theory in all cases in the zero-temperature and zero-pairing limits, i.e. for open-shell nuclei. However, the fact that a nucleus can be of open-shell character in these joint limits is necessarily the result of some symmetry restrictions. Whenever it is the case, the non-trivial description obtained for open-shell systems is shown to depend on the order with which both limits are taken, i.e. the two limits do not commute for these systems. When the zero-temperature limit is performed first, the FTHFB density operator is demoted to a projector corresponding to a pure state made out of a linear combination of a finite number of Slater determinants with different (even) numbers of particles. When the zero-pairing limit is performed first, the FTHFB density operator remains a statistical mixture of a finite number of Slater determinants with both even and odd particle numbers. While the entropy (pairing density) is zero in the first (second) case, it does not vanish in the second (first) case in spite of the temperature (pairing) tending towards zero. The difference between both limits can have striking consequences for the (thermal) expectation values of observables. For instance, the particle-number variance does not vanish in either case and has limiting values that differ by a factor of two in both cases. In conclusion, while in the textbook situation associated with closed-shell nuclei Hartree-Fock-Bogoliubov (finite-temperature Hartree-Fock) theory reduces to Hartree-Fock theory in the zero-pairing (zero-temperature) limit, the present analysis demonstrates that a non trivial and unexpected limit is obtained for this formalism in open-shell systems. This result sheds a new light on certain aspects of this otherwise very well-studied many-body formalism.

20 ≤ A ≤ 38↗