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At least 37 records · Page 2

Simulations of the churning mode: Toroidally symmetric plasma convection and turbulence around the X-points in a snowflake divertor

Using a reduced MHD model, extended to include field-aligned thermal conduction, we present numerical simulations of the churning mode (CM): a toroidally symmetric, non-linear plasma vortex in the vicinity of the null points in a snowflake (SF) divertor [D. D. Ryutov et al., Phys. Scr. 89, 088002 (2014)]. Simulations are carried out across a range of inter-null separations, d xx ⁠, and inter-null orientations, θ⁠, primarily in conditions relevant to the MAST-U tokamak. We find that, when d xx is small, the CM induces additional transport across the X-points when β pm ≳8%, where β pm is the ratio of the plasma pressure in the null region to poloidal magnetic pressure at the midplane. This transport also increases approximately linearly as d xx is reduced. A diffusive model of this transport is shown to predict the total transport across the null points, where diffusion coefficients of up to ∼ 10 2 m 2 s −1 centered on a small region around the X-points are used. However, the CM also results in significant changes to the flux surfaces in the null region, which is not captured by this diffusive model. The changes in magnetic geometry mean the fractional exhaust power delivered to each divertor leg is highly sensitive to β pm ⁠, d xx ⁠, and θ⁠. For small values of θ⁠, the CM can induce a change in topology, redirecting exhaust power from a secondary divertor leg on the high field side to one on the low field side. Similar behavior is found in the fraction of exhaust power going to the inner and outer divertor. Such changes in the flux surfaces may not be captured by Grad–Shafranov solvers and so may be a source of error in the magnetic reconstruction of SF experiments. We consistently find that the fractional exhaust power going to a secondary divertor leg on the high field side is small, consistent with SF experiments.

Computer simulation

Autler-Townes spectroscopy of a Rydberg ladder

Ladder-type two-photon excitation of an atom from a ground state $|g\rangle$, to an intermediate excited state $|e\rangle$, and finally, to a Rydberg state $|r\rangle$ has a variety of uses from quantum information to sensing. A common scheme for detecting this transition optically is through electromagnetically induced transparency (EIT). However, in inverted wavelength schemes, where the ground-to-excited transition wavelength is shorter than the excited-to-Rydberg transition wavelength, the strength of the EIT feature on the lower-leg beam is strongly reduced in a Doppler-broadened medium. Here, in this study, we report on an alternative two-photon spectroscopic feature, which we term the two-photon Autler-Townes resonance, observed on the upper-leg beam. Compared to the EIT signal, this feature's superior signal-to-noise ratio allows one to resolve Rydberg resonances with principal quantum number as high as n=80. We also show that such a feature can be utilized to generate an error signal for stabilizing the frequency of the upper-leg beam.

Xiang, Tai [University of California, Berkeley, CA

Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. Published by the American Physical Society 2024

Physics

Heterogeneous Integration Technologies for High-temperature, High-density, Low-profile Power Modules of Wide Bandgap Devices in Electric Drive Applications (Final Technical Report)

The goal of this project is to develop packaging technologies for making high-temperature, high-density, and low-profile wide-bandgap (WBG) power electronics modules for electric drives. These modules are aimed at enabling the DOE’s University Consortium to reach its 2025 inverter targets of ≥ 100 kW/L and ≤ 2.7 $/kW. The specific objectives are to: design and fabricate SiC half-bridge power modules with double-sided cooling and parasitic inductances < 5 nH, heat flux density > 400 W/cm 2 , and working junction temperature of 200 o C; design, fabricate, and deliver a gate driver with double-sided cooled modules for the construction of a 100 kW/L inverter at Oak Ridge National Lab; and design and prototype intelligent gate drivers with integrated current sensor and a low-profile DC-DC power supply with air-core transformer for testing power modules at 200 o C junction temperature. We followed an iterative technical approach of design, simulation, fabrication, and testing of various versions of modules, current sensors, and power supply. The state-of-the-art silicon carbide devices rated at 1.2 kV and 149 A were packaged by sintered-silver bonding on an aluminum nitride direct-bond-copper substrate for high thermal conductivity, high working temperature, and high joint reliability. Porous silver posts were used to interconnect the device’s source pads to the other direct-bond-copper substrate for low mechanical stresses, ease of manufacturing, and double-sided cooling. A current sensor based on package parasitic inductance was developed to measure switching current. A dynamic feedback scheme was developed to compensate the effect of parasitic resistance and temperature variation. A constant-current class-E dc-dc converter with air-core transformer was developed. Air-core transformer was used due to the unavailability of magnetic core at high temperatures. Gate driver and power supply were integrated with the double-side cooled, high temperature SiC power modules for testing the modules at 200 o C junction temperature. Double-pulse and continuous testing of the integrated technologies validated the design and fabrication of the three component technologies. Throughout the project, we overcame the challenge for design verification caused by low prototyping yield, which then helped train the graduate students, the future workforce, to learn the engineering know-how for low-cost manufacturing of reliable products. Below is a summary of the major accomplishments of this project: development of a prototyping process for fabricating double-side cooled (1200 V, 149 A) SiC phase-leg modules capable of working to 200 o C Tj; simulation and experimental verification of the improvement of thermo-mechanical reliability of the double-side cooled SiC phase-leg module by using rigid encapsulant; design and experimental validation of a current sensor based on package parasitic inductance and a compensation solution for eliminating the effect of parasitic resistance; design and experimental validation of a low-profile power supply with six-output air-core transformer for gate driver; functional demonstration of a SiC phase-leg module integrated with its gate driver, current sensor, and an air-core power supply at 200 o C Tj in a double-pulse switching test setup and Buck converter continuous test setup; successful completion of six PhD and two MS students who are or will work at Apple Inc., Tesla Inc., Wolfspeed Inc., Microchip Inc., Monolithic Power Systems Inc., and LG Magna Inc.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI

An innovative SR-WEC for a market-disruptive LCOE

The objective of DE-EE0008630: An innovative SR-WEC for a market-disruptive LCOE was to develop and test a scaled prototype of the Surface-Riding Wave Energy Converter that can result in a market-disruptive Levelized Cost of Energy by a combination of an extended operating window, substantially lowered cost and amplified average power output by simple optimum control. Initially conceptualized as a floating linear electrical generator (LEG), the SR-WEC evolved into an intermediate-scale version where multiple LEGs were mounted on a floating cylindrical body, driven by the need to enhance scalability and improve power performance.

16 TIDAL AND WAVE POWER

An International Round-Robin Study on Thermoelectric Module Testing and Development of Standard Power Generation Modules

An international round-robin study on thermoelectric power generation modules was conducted with nine participating laboratories. Two types of commercially available bismuth telluride modules, 30 mm × 30 mm and 40 mm × 40 mm, were used. A test protocol was followed with five temperature set points from 50°C to 150°C. Graphite sheets were used as thermal interface materials with test pressure at 100 psi (0.69 MPa). The results showed large lab-to-lab variations and the key source of uncertainty for module efficiency was identified as the heat flux measurement. In the meantime, significant uncertainty was also found in maximum electrical power (P max ) measurements. As a result of the round-robin, a “standard module” with 4 × 4 legs on a 20 mm × 20 mm platform was suggested. A skutterudite module and a half-Heusler module were produced with identical geometry and 4 mm × 4 mm × 8 mm legs. All transport properties to calculate the figure-of-merit, zT, were measured from ambient temperature to 500°C. Module performance was measured by two laboratories. Two finite-element-analysis (FEA)-based models were developed independently to simulate and predict the module performance. In conclusion, the standard modules eliminated significant test uncertainties and are aimed at assisting device design and achieving more accurate performance predictions.

Round-robin

CFD modeling of natural circulation in LiCl-KCl molten salt closed loop

Characterizing flow within a molten salt closed-loop system is crucial for assessing system requirements, evaluating performance, and identifying potential flaws. Direct flow measurement using instrumentation is challenging due to extreme environmental conditions and the limitations associated with measuring molten salt flow under natural convection. Here, this study aims to provide comprehensive insights into the thermal-hydraulic behavior of a closed loop, with a particular focus on temperature distribution and velocity prediction. The Computational Fluid Dynamics (CFD) model demonstrated the capability to effectively simulate and predict both temperature distributions and flow velocities within the molten salt loop. The CFD model's predictive capability was validated by its ability to replicate temperature measurements under varying boundary conditions. The analysis revealed that the CFD model tends to underpredict temperatures in the cold leg and overpredict them in the hot leg, highlighting the need for continuous model refinement and acknowledging the limitations of using a steady-state approach. Furthermore, the potential of using external temperature measurements to estimate internal molten salt temperatures and predict flow velocity was explored, revealing that this approach could introduce up to a 5.5% error in flow velocity calculations. Line probes mapping temperature distributions across the tube's cross-section and molten salt provided valuable insights into temperature gradients, emphasizing the need for a thermal conductivity equation for molten salt with lower uncertainty to achieve more accurate temperature predictions of the system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS

2D analysis of tokamak divertor-plasma detachment-bifurcation with operational parameters and geometries

UEDGE simulations with density scans for various input power, transport coefficients and outer poloidal leg length are performed to study the conditions for the existence of a bifurcation-like drop of T e at the outer strike point, commonly referred to as a detachment cliff, when transitioning to a detached plasma from an attached plasma in the outer divertor as the upstream density increases (McLean et al., 2015). The simulation results show that a detachment cliff tends to occur with a higher power input regardless of diffusivities and leg length. Further analysis of change of plasma profiles at a cliff indicate that, in addition to the sharp reduction of the E x B drift fluxes in the outer divertor studied in Jaervinen et al., (2018), the substantial change of the Mach number in the outer divertor and the decrease of the outer mid-plane T e due to the radiation front moving across the separatrix into the confinement region above the X-point consistently occur for all UEDGE density scans that have a detachment cliff. UEDGE time-dependent simulation of the evolution of a detachment cliff shows that the rapid increase of radiation above the X-point occurs in a time scale of ~0.3–0.5, which could possibly be the trigger for the formation of a detachment cliff, quicker than the Mach number change in a time scale of ~1 ms and the drop of T e in a time scale of ~2–3 ms in the outer divertor.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Power and particle exhaust for the ARC fusion power plant

To successfully show that fusion is an attractive energy source, the ARCTM fusion power plant will need to operate with a robust, integrated power and particle exhaust solution. To maximise ARC’s fusion power output while avoiding excessive erosion of the plasma-facing components, we will need to radiatively dissipate most of the power crossing the last-closed flux surface, injecting radiating impurities such as argon or neon to access divertor detachment. Divertor detachment will need to be integrated with a high-performance core plasma, and with efficient impurity pumping to prevent the accumulation of helium ash in the core. To access and control detachment in high-performance plasmas, we have designed ARC with up–down-symmetric divertors, with secondary X-points in long, tightly baffled outer legs. Using a core-edge modelling workflow, we predict that with this divertor design, ARC will access detachment with modest argon seeding in the divertor (c Ar,div ∼0.9%), which should have minimal impact on the core ( Z eff,core <0.5) for reasonable argon enrichment (c Ar,div /c Ar,core =6). Due to the high predicted divertor neutral pressure (p div ∼20 Pa), we predict that ARC will sufficiently pump helium to limit ash accumulation in the core (c He,core <2%) for a helium enrichment of c He,div /c He,core =0.4. ARC’s divertor design is expected to increase the stability of a detachment front in the outer divertor leg, helping to prevent divertor reattachment during smaller heat-flux transients such as scrape-off-layer filaments associated with the quasi-continuous exhaust regime. However, this buffering will not be sufficient to prevent divertor reattachment during large type-I edge-localised modes (ELMs), and as such these will need to be avoided on ARC. Experiments on SPARC will be used to select an integrated scenario which avoids or mitigates type-I-ELMs while maintaining access to detachment, good core fusion performance and sufficient impurity exhaust. SPARC experiments will also be used to finalise ARC’s divertor design, by studying the impact of magnetic and first-wall geometry on detachment stability, impurity enrichment and neutral baffling under conditions similar to those expected for ARC. In conclusion, our analysis finds that ARC will have a viable power and particle exhaust solution which is compatible with high-power operations, and this solution will be validated in experiments on SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Divertor shaping with neutral baffling as a solution to the tokamak power exhaust challenge

Exhausting power from the hot fusion core to the plasma-facing components is one fusion energy’s biggest challenges. The MAST Upgrade tokamak uniquely integrates strong containment of neutrals within the exhaust area (divertor) with extreme divertor shaping capability. By systematically altering the divertor shape, this study shows the strongest evidence to date to our knowledge that long-legged divertors with a high magnetic field gradient (total flux expansion) deliver key power exhaust benefits without adversely impacting the hot fusion core. These benefits are already achieved with relatively modest geometry adjustments that are more feasible to integrate in reactor designs. Benefits include reduced target heat loads and improved access to, and stability of, a neutral gas buffer that ‘shields’ the target and enhances power exhaust (detachment). Analysis and model comparisons shows these benefits are obtained by combining multiple shaping aspects: long-legged divertors have expanded plasma-neutral interaction volume that drive reductions in particle and power loads, while total flux expansion enhances detachment access and stability. Containing the neutrals in the exhaust area with physical structures further augments these shaping benefits. These results demonstrate strategic variation in the divertor geometry and magnetic topology is a potential solution to one of fusion’s power exhaust challenge.

magnetically confined plasmas

Power handling in a highly-radiative negative triangularity pilot plant

Abstract This work explores detailed power handling solutions for a class of high-field, highly-radiative negative triangularity (NT) reactors based around the MANTA concept (Rutherford et al 2024 Plasma Phys. Control. Fusion ). The divertor design is kept as simple as possible, opting for a standard divertor with standard leg length. FreeGS is used to create an equilibrium for the boundary region, prioritizing a short outer leg length of only ∼50 cm (∼40% of the minor radius). The UEDGE code package is used for the boundary plasma solution to track plasma temperatures and fluxes to the divertor targets. It is found that for P SOL = 25 MW and n sep = 0.96 × 10 20 m −3 , conditions consistent with initial core transport modeling, little additional power mitigation is necessary. For a fixed impurity fraction of just 0.13% Ne in the plasma, the peak heat flux density at the more heavily loaded outer targets falls to 7.8 MW m −2 , while the electron temperature T e remains just under 5 eV. Scans around the parameter space reveal that even at densities lower than in the primary operating scenario, P SOL can be increased up to 50 MW, so long as a slightly higher fraction of extrinsic radiator is used. With less than 1% neon (Ne) impurity content, the divertor still experiences less than 10 MW m −2 at the outer target. Design of the plasma-facing components includes a close-fitting vacuum vessel with a tungsten inner surface as well as FLiBe-carrying cooling channels fashioned into the VV wall directly behind the divertor targets. For the seeded heat flux profile, Ansys Fluent heat transfer simulations estimate that the outer target temperature remains at just below 1550 ∘ C. Initial scoping of advanced divertor designs shows that for an X-divertor, detachment of the outer target becomes much simpler, and plasma fluxes to the targets drop considerably with only 0.01% Ne content.

Miller, M. A. (ORCID:0000000265406533)

First simultaneous observation of co- and counter-current fast-ion losses in the ASDEX Upgrade tokamak

In ITER and future fusion power plants, the source of the fusion born alpha particles is almost isotropic in pitch angle, thus having co- and counter-current populations. For trapped ions, the co-current side of the orbit corresponds to its outer leg, while the counter-current side corresponds to the inner leg. Understanding the mechanisms responsible for the fast-ion losses (FILs) is critical for future magnetically confined fusion power plants. To further study the interplay of fast ions with plasma instabilities, a double pinhole collimator has been developed for a Fast-Ion Loss Detector (FILD) in the ASDEX Upgrade tokamak (AUG). This new FILD opens the operational window to simultaneous measurements of the co- and counter-current ion velocity-space. In this paper, the first results for the AUG double collimator FILD detector are shown. The commissioning of this new probe is carried out in H-mode plasmas with an on-axis magnetic field $B_0 = -2.5$ T, and a plasma current $I_{\textrm{p}} = 0.7$ MA. Simultaneous co- and counter-current FILs have been measured. Both have shown a similar dependence on Ion Cyclotron Resonance Heating (ICRH) power, where the main difference is the intensity of the losses, with the co-losses being an order of magnitude larger. Toroidal Alfvén eigenmode-coherent ICRH-only losses have been identified for the co-current ions. Additionally, the presence of Edge Localized Modes during the discharge were shown to increment Neutral Beam Injection prompt losses, while partially mitigating ICRH-driven losses on both co- and counter- sides of the velocity-space. Finally, a very trapped and high gyroradius losses, with an unclear origin, have been measured in the co- and counter-current velocity-space. The computed ion trajectories show that these ions remain permanently near the vessel wall, suggesting that they are accelerated within the scrape-off layer.

ELM

Solar Heat for Industrial Processes: Integration with Chemical Reactors

The integration of solar thermal systems with chemical reactors has been proposed as part of a larger effort to develop and deploy solar heat for industrial processes (SHIP) technologies. A strong motivation for SHIP processes and technologies is the potential for high thermal efficiency coupled with low-cost thermal energy storage (TES) which can enable commercial deployment of such systems. While there are different ways to categorize SHIP technologies, one important such distinction is between directly irradiated systems and indirect off-sun process driven by a SHIP system. While directly irradiated systems can provide high thermal efficiencies and high fluxes, they usually require complex engineering solutions due to the need for redesigning the established processes and unit operations. In most cases, it is also more challenging to couple such a process to a TES system, losing some of the benefits of SHIP. On the other hand, using a SHIP system to drive an industrial process off-sun can allow better integration with existing process chains, easier TES capabilities, and potential for more applications fitting a specific SHIP technology. However, the integration of SHIP systems with the industrial processes is not fully explored in detail, especially in the case of high-temperature processes such as reforming, cracking, cement manufacturing, and iron/steelmaking. Many of these systems require heating fluxes of >50 kW/m^2, supplied via combustion of hydrocarbons in a fire box and benefitting from radiative heat transfer between the flue gases and the reaction zones. As such, using SHIP systems for such processes is more complex than providing the same thermal input in the form of a heat transfer medium (HTM) entering the reactor, kiln, or furnace. Moreover, in case convective heat transfer using SHIP is envisioned, for example using supercritical CO2 as the HTM from a particle receiver, the thermal integration might be more challenging than initially envisioned: lower heat transfer coefficients and limited approach temperature might require large flow rates, causing a mismatch between the process thermal requirements and the thermal capacity of the SHIP system. In addition, even if the heat exchange between SHIP and reactor is effective, there is still a cold leg HTM at the reaction temperature or slightly below it. Chemical plants usually include a set of heat exchangers, heat recovery steam generators, and even power generation units - in a tightly integrated design - to recover the flue gases which are eventually vented. With SHIP systems mostly operating on a closed HTM loop, bottoming the cold leg is crucial. In this talk, we will present different modeling results for a variety of syngas production reactions, using catalytic and chemical looping processes, and discuss some of the challenges and design considerations for off-sun chemical reactors using SHIP systems.

14 SOLAR ENERGY

Initial Engineering Framework for Species Tracking in MSRs Involving Fuel Salt and Structures

This report implements a high-fidelity multiphysics modeling framework using the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program tools to track leaching and plating of materials between the fuel salt and structures in Molten Salt Reactors (MSRs). Specifically, this framework is demonstrated in modeling various processes within MSRs including hot and cold leg corrosion, redox potential driven corrosion, colloid precipitation and deposition, and noble metal plating and decay heat modeling. The model integrates neutronics, thermal-hydraulics, depletion, and thermochemistry to simulate the evolving chemical behavior of the fuel salt in interactions with structural materials. Initial findings suggest that hot-cold leg corrosion in MSR systems may become significant if the redox potential of the fuel salt is not sufficiently controlled. Additionally, the impact of noble metal decay heat deposition in large power reactors is explored. The resulting engineering framework for species tracking will be applied in the future toward specific validation work with ongoing experimental efforts focusing on both chloride and fluoride salt loop experiments with in-situ corrosion and redox control instrumentation.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Exact Fock-State Preparation with $n^{1/4}$ Circuit Depth

Efficient, deterministic, and high-fidelity preparation of large Fock states is essential for scaling bosonic quantum technologies and exploring quantum phenomena at large excitation energies. We introduce a deterministic one-parameter (D1p) protocol that maps Fock-state preparation in an infinite-dimensional Hilbert space onto two-dimensional amplitude amplification. Starting from a coherent state with $|α|\simeq\sqrt{n}$, the initial target-state population scales as $n^{-1/2}$, yielding an iteration count and circuit depth of $\mathcal{O}(n^{1/4})$. Phase matching guarantees unit fidelity in the ideal model; remarkably, preparing $|{10^6}\rangle$ requires only 39 iterations. The protocol uses only displacements and number-selective phase operations, requires no numerical optimization, and further extends to state transfer, general superpositions, finite-dimensional systems, and multipartite entangled states. In the large-amplitude regime, its multi-target form prepares $L$-legged cat states with an iteration count determined only by $L$; cats with up to ten legs require only two iterations, independent of the coherent-state amplitude. This framework provides a broadly applicable route to highly excited bosonic states on platforms supporting these elementary controls.

Roy, Tanay [Fermilab] (ORCID:000000019442862X)

Ink Casting and 3D‐Extrusion Printing of Yb 14 MnSb 11 for High‐Temperature Thermoelectric Material

Abstract Complex shapes are created from Yb 14 MnSb 11 , a high‐temperature thermoelectric Zintl phase, via a two‐step process: i) layer‐by‐layer 3D‐extrusion of ink containing partially‐reacted powders which are ball‐milled from a blend of Yb, MnSb, and Sb powders; ii) heat treatment to synthesize the ternary compound Yb 14 MnSb 11 and densify the extruded powders. A high phase purity for Yb 14 MnSb 11 (83–94%) is achieved in both cast and 3D‐extruded ink specimens via a solid‐state reaction between Yb, MnSb, and Yb 4 Sb 3 during reactive sintering. Pressure‐free sintering at temperatures of 1200–1400 °C densifies the powders to 82% relative density but can also induce the decomposition of the Yb 14 MnSb 11 phase due to Yb sublimation. A process window with optimized sintering temperature and time is identified, achieving both low porosity and high phase purity and reaching a maximum zT = 0.61 at 1000 °C, about half of the maximum zT value for bulk Yb 14 MnSb 11 made via conventional processes (pressure sintering of precursor powders). The present approach – direct ink writing of ball‐milled powders, combined with reactive sintering – is a scalable and affordable method to fabricate thermoelectric legs with intricate 3D shapes, for enhanced performances in high‐temperature thermoelectric applications.

Chen, Ming [Department of Materials Science &amp,

Hollow-grams: generalized entanglement wedges from the gravitational path integral

Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the “hollowed” RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the Rényi entropy Sn depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the n → 1 limit.

2D Gravity

Analytic amplitudes for a pair of Higgs bosons in association with three partons

The pair production of Higgs bosons at the LHC can give information about the triple Higgs boson coupling. We perform an analytic one-loop calculation of the amplitudes for a pair of Higgs bosons in association with three partons, retaining the exact dependence on the quark mass circulating in the loop. These amplitudes constitute the real radiation corrections in the calculation of Higgs boson pair production at next-to-leading order in the strong coupling. The results of an analytic generalised-unitarity computation are simplified via analytic reconstruction in spinor variables. Compact ansätze for kinematic pole residues are iteratively fitted via p-adic evaluations near said poles and subtracted until no pole remains. A new ansatz construction is introduced to minimally parametrise coefficients of amplitudes with multiple massive external legs. The simplified expressions are faster to evaluate than automatic codes and can lead to more stable results near singular regions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS