Structure Factors for Hot Neutron Matter from Ab Initio Lattice Simulations with High-Fidelity Chiral Interactions.

We present the first ab initio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this Letter, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It solves the problem of exponential scaling of computational effort when using perturbation theory for higher-body operators and higher-order corrections. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. The ab initio lattice results are in good agreement with virial expansion calculations at low densities but are more reliable at higher densities. Random phase approximation codes used to estimate neutrino opacity in core-collapse supernovae simulations can now be calibrated with ab initio lattice calculations.

Wavefunction matching for solving quantum many-body problems.

Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions1-3 to quantum chemistry4-6 and from atomic and molecular systems7-9 to nuclear physics10-14. One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations15,16 of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions17,18 and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations19,20.

Emergent geometry and duality in the carbon nucleus.

The carbon atom provides the backbone for the complex organic chemistry composing the building blocks of life. The physics of the carbon nucleus in its predominant isotope, 12C, is similarly full of multifaceted complexity. Here we provide a model-independent density map of the geometry of the nuclear states of 12C using the ab initio framework of nuclear lattice effective field theory. We find that the well-known but enigmatic Hoyle state is composed of a "bent-arm" or obtuse triangular arrangement of alpha clusters. We identify all of the low-lying nuclear states of 12C as having an intrinsic shape composed of three alpha clusters forming either an equilateral triangle or an obtuse triangle. The states with the equilateral triangle formation also have a dual description in terms of particle-hole excitations in the mean-field picture.

Perturbative Quantum Monte Carlo Method for Nuclear Physics.

While first order perturbation theory is routinely used in quantum Monte Carlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. We demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to ^{16}O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second-order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.

Hidden Spin-Isospin Exchange Symmetry.

The strong interactions among nucleons have an approximate spin-isospin exchange symmetry that arises from the properties of quantum chromodynamics in the limit of many colors, N_{c}. However this large-N_{c} symmetry is well hidden and reveals itself only when averaging over intrinsic spin orientations. Furthermore, the symmetry is obscured unless the momentum resolution scale is close to an optimal scale that we call Λ_{large-N_{c}}. We show that the large-N_{c} derivation requires a momentum resolution scale of Λ_{large-N_{c}}∼500 MeV. We derive a set of spin-isospin exchange sum rules and discuss implications for the spectrum of ^{30}P and applications to nuclear forces, nuclear structure calculations, and three-nucleon interactions.

Ab Initio Nuclear Thermodynamics.

We propose a new Monte Carlo method called the pinhole trace algorithm for ab initio calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first ab initio study of the density and temperature dependence of nuclear clustering.

Ab initio Calculations of the Isotopic Dependence of Nuclear Clustering.

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (^{4}He nuclei) within the interior of a larger nucleus. In this Letter, we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in ^{12}C, ^{14}C, and ^{16}C. The structural similarities among the carbon isotopes suggest that ^{14}C and ^{16}C have excitations analogous to the well-known Hoyle state resonance in ^{12}C.

Nuclear Binding Near a Quantum Phase Transition.

How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and neutrons, we discover a first-order transition at zero temperature from a Bose-condensed gas of alpha particles (^{4}He nuclei) to a nuclear liquid. Whether one has an alpha-particle gas or nuclear liquid is determined by the strength of the alpha-alpha interactions, and we show that the alpha-alpha interactions depend on the strength and locality of the nucleon-nucleon interactions. This insight should be useful in improving calculations of nuclear structure and important astrophysical reactions involving alpha capture on nuclei. Our findings also provide a tool to probe the structure of alpha cluster states such as the Hoyle state responsible for the production of carbon in red giant stars and point to a connection between nuclear states and the universal physics of bosons at large scattering length.

Pseudospin symmetry in single particle resonant states.

The pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the small component of the Dirac spinor. The origin of PSS in single particle bound states in atomic nuclei has been revealed and studied extensively. By examining the zeros of Jost functions corresponding to the small components of Dirac wave functions and phase shifts of continuum states, we show that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. The exact conservation and the breaking of the PSS are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials.

[Effect of polymeric aluminum-iron on EPS and bio-flocculation in A2/O system].

Polymeric aluminum-iron (PAFC) was added at the end of aeration tank to enhance phosphorus removal, so that the phosphorus concentration in the effluent could meet the calss A standard in municipal sewage treatment plant pollutant discharge standard (GB 18918-2002). The characteristics of extracellular polymer substances (EPS) and bio-flocculation for the activated sludge in the A2/O system were analyzed in the experiment. The results showed that, the gross of EPS varied little with the increase in PAFC dosage, while, the ratio of albumen to polysaccharide declined from 3.30 to 2.30. When the PAFC dosage increased, the concentration of Al3+ in EPS increased during the whole anaerobic-anoxic-aerobic cycle. The flocs of activated sludge became larger after PAFC addition, Zeta potential of the effluent dropped significantly from - 15.83 mV to -21.20 mV and sludge yield increased. Therefore, bio-flocculation of the activated sludge in the A2/O system improved when a proper amount of PAFC was added, subsequently improve the water quality of the effluent.

Performance of a subsurface-flow constructed wetland in southern China.

The operational performance of a full-scale subsurface-flow constructed wetland, which treated the mixed industrial and domestic wastewater with BOD5/COD mean ratio of 0.33 at Shatian, Shenzhen City was studied. The constructed wetland system consists of screens, sump, pumping station, and primary settling basin, facultative pond, first stage wetland and secondary stage wetland. The designed treatment capacity is 5000 m3/d, and the actual influent flow is in the range of < 2000 to > 10000 m3/d. Under normal operational conditions, the final effluent quality well met the National Integrated Wastewater Discharge Standard (GB 8978-1996), with the following parameters(mean values): COD 33.90 mg/L, BOD, 7.65 mg/L, TSS 7.92 mg/L, TN 9.11 mg/L and TP 0.56 mg/L. Seven species of plants were selected to grow in the wetland: Reed, Sweetcane flower Silvergrass, Great Bulrush, Powdery Thalia and Canna of three colours. The growing season is a whole year-round. The seasonal discrepancy could be observed and the plants growing in the wetland are vulnerable to lower temperature in winter. The recycling of the effluent in the first stage of the wetland system is an effective measure to improve the performance of the wetland system. The insufficient DO value in the wetland system not only had significant effect on pollutants removal in the wetland, but also was unfavourable to plant growth. The recycling of effluent to the inlet of wetland system and artificial pond to increase DO value of influent to the wetland is key to operate the subsurface constructed wetland steadily and effectively.

[Treatment performance of submerged membrane bioreactor treating brewery wastewater].

Under the condition of keeping the influent COD: TN: TP = 100:5:1, submerged MBR has an excellent treatment performance for COD and NH4+ -N, and the removals for COD and NH4+ -N are both beyond 90% under steady state, in addition, MBR has a strong adaptation ability for shock organics loading rate. When the organic loading rate was increased from 0.27g/(g x d) to 0.54g/(g x d) suddenly, there was no big fluctuation for COD in effluent. According to the results of GC/MS, the remaining organics in effluent was mainly alkyl hydrocarbon, and the membrane modules played a main role in stabling permeation quality. When the sludge in MBR was at the multiplication stage, the system has a removal of about 40% for TN because of biosynthesis and simultaneous nitrification and de-nitrification, in addition, a certain removal for TP was also observed. When the sludge was at the steady stage, the removal for TN decreased to about 30% due to simultaneous nitrification and de-nitrification, whereas, the removal efficiency for TP was very little, and sometimes even below zero.