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Search for efficient formulations for Hamiltonian simulation of non-Abelian lattice gauge theories

Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation, an area of research that is growing with advances in quantum-computing algorithms and hardware. It, therefore, remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories, considering the necessary truncation imposed on the Hilbert space of gauge bosons with any finite computing resources. This paper is a first step toward addressing this question in the case of non-Abelian LGTs, which further require the imposition of non-Abelian Gauss’s laws on the Hilbert space, introducing additional computational complexity. Focusing on the case of SU(2) LGT in 1+1 dimensions coupled to one flavor of fermionic matter, a number of different formulations of the original Kogut-Susskind framework are analyzed with regard to the dependence of the dimension of the physical Hilbert space on boundary conditions, system’s size, and the cutoff on the excitations of gauge bosons. The impact of such dependencies on the accuracy of the spectrum and dynamics obtained from a Hamiltonian computation is examined, and the (classical) computational-resource requirements given these considerations are studied. Besides the well-known angular-momentum formulation of the theory, the cases of purely fermionic and purely bosonic formulations (with open boundary conditions), and the Loop-String-Hadron formulation are analyzed, along with a brief discussion of a Quantum-Link-Model formulation of the same theory. Clear advantages are found in working with the Loop-String-Hadron framework which implements non-Abelian Gauss’s laws a priori using a complete set of gauge-invariant operators. Although small lattices are studied in the numerical analysis of this work, and only the simplest algorithms are considered, a range of conclusions will be applicable to larger systems and potentially to higher dimensions. Future studies will extend this investigation to the analysis of resource requirements for quantum simulations of non-Abelian LGT, with the goal of shedding light on the most efficient Hamiltonian formulation of gauge theories of relevance in nature

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improved information criteria for Bayesian model averaging in lattice field theory

Bayesian model averaging is a practical method for dealing with uncertainty due to model specification. Use of this technique requires the estimation of model probability weights. Here, we revisit the derivation of estimators for these model weights. Use of the Kullback-Leibler divergence as a starting point leads naturally to a number of alternative information criteria suitable for Bayesian model weight estimation. We explore three such criteria, known to the statistics literature before, in detail: a Bayesian analog of the Akaike information criterion which we call the BAIC, the Bayesian predictive information criterion, and the posterior predictive information criterion (PPIC). We compare the use of these information criteria in numerical analysis problems common in lattice field theory calculations. We find that the PPIC has the most appealing theoretical properties and can give the best performance in terms of model-averaging uncertainty, particularly in the presence of noisy data, while the BAIC is a simple and reliable alternative.

97 MATHEMATICS AND COMPUTING↗

Final burst of the moving mirror is unrelated to the partner mode of analog Hawking radiation

Flying mirrors with appropriate trajectories have been recognized as an analog system that mimics black hole Hawking evaporation and have been widely investigated. It has recently been suggested that the partner mode of the analog Hawking radiation emitted from a moving mirror would manifest itself through a final burst when the mirror executes a sudden stop. Here, in this study, we argue the opposite via the partner formula for the moving mirror model. By expanding the theoretical foundation of the partner formula and augmenting it with numerical analysis, we demonstrate that the supposed final burst is induced by a shock that requires the input of external energy, whereas the Hawking radiation partner mode, which is associated with the zero-point vacuum fluctuations, is not responsible for the burst.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Direct quarkonium production in DIS from a joint CGC and NRQCD framework

We compute the differential cross section for direct quarkonium production in high-energy electron-nucleus collisions at small 𝑥. Our computation is performed within the nonrelativistic QCD factorization formalism that separates the calculation into short distance coefficients and long distance matrix elements that depend on the color and spin of the state. We obtain the short distance coefficients of the production of the heavy quark pair within the framework of the color glass condensate effective field theory, which resums coherent multiple interactions of the heavy quark pair with the nucleus to all orders. Our results are expressed as the convolution of perturbatively calculable functions with multipoint lightlike Wilson line correlators. In the correlation limit, we establish the correspondence between our color glass condensate formulation with calculations employing the transverse momentum dependent (TMD) framework. We extend this correspondence by resumming kinematic power corrections within the improved TMD framework, which interpolates between the TMD formalism and 𝑘 ⊥ -factorization formalism. We present a detailed numerical analysis, focusing on 𝐽/𝜓 production in the kinematics accessible at the future Electron-Ion Collider, highlighting the importance of genuine higher-order saturation contributions when the electron collides with a large nucleus. Our results are also valid in the photoproduction limit where we expect the largest contribution from genuine higher-order saturation contributions which could be accessed in ultraperipheral collisions of relativistic heavy ions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Vacuum topology and the electroweak phase transition

We investigate if the topology of pure gauge fields in the electroweak vacuum can play a role in classical dynamics at the electroweak phase transition. Our numerical analysis shows that magnetic fields are produced if the initial vacuum has nontrivial Chern-Simons number, and the fields are helical if the Chern-Simons number changes during the phase transition.

79 ASTRONOMY AND ASTROPHYSICS↗

Local step-flow dynamics in thin film growth with desorption

Desorption of deposited species plays a role in determining the evolution of surface morphology during crystal growth when the desorption time constant is short compared with the time to diffuse to a defect site, step edge, or kink. However, experiments to directly test the predictions of these effects are lacking. Novel techniques such as in situ coherent x-ray scattering can provide significant new information. Herein we present x-ray photon correlation spectroscopy (XPCS) measurements during diindenoperylene (DIP) vapor deposition on thermally oxidized silicon surfaces. DIP forms a nearly complete two-dimensional first layer over the range of temperatures studied (40–120 ⁢°C), followed by mounded growth during subsequent deposition. Local step flow within mounds was observed, and we find that there was a terrace-length-dependent behavior of the step edge dynamics. This led to unstable growth with rapid roughening (β>0.5) and deviation from a symmetric error-function-like height profile. At high temperatures, the grooves between the mounds tend to close up leading to nearly flat polycrystalline films. In conclusion, numerical analysis based on a (1+1)-dimensional model suggests that terrace-length dependent desorption of deposited ad-molecules is an essential cause of the step dynamics, and it influences the morphology evolution.

36 MATERIALS SCIENCE↗

Floquet engineering of polaritonic amplification in dispersive photonic time crystals

In this study, we investigate the dynamics of dispersive photonic time crystals (PTCs) and their potential applications for controlling light-matter interaction. Using the Lorentz-Drude as dispersive material model, we analyze the effects of periodic modulation of dispersion parameters through both theoretical and numerical analysis, revealing the emergence of hybrid bandgaps from the interaction of polaritonic branches with distinctive characteristics. Our study demonstrates that dispersive PTCs offer novel excitation channels and amplification possibilities, that require lower modulation frequencies compared to nondispersive systems thus alleviating experimental challenges for the realization of PTCs in the optical regime. These findings pave the way for advancements in polaritonic lasing and resonant Raman scattering.

Classical optics↗

Robustness and Eventual Slow Decay of Bound States of Interacting Microwave Photons in the Google Quantum AI Experiment

Integrable models are characterized by the existence of stable excitations that can propagate indefinitely without decaying. This includes multimagnon bound states in the celebrated 𝑋⁢𝑋⁢𝑍 spin-chain model and its integrable Floquet counterpart. A recent Google Quantum AI experiment [A. Morvan et al., Nature 612, 240 (2022)] realizing the Floquet model has demonstrated the persistence of such collective excitations even when the integrability is broken: this observation is at odds with the expectation of ergodic dynamics in generic nonintegrable systems. Here, we study the spectrum of the model realized in the experiment using exact diagonalization and physical arguments. We find that isolated bands corresponding to the descendants of the exact bound states of the integrable model are clearly observable in the spectrum for a large range of system sizes. However, our numerical analysis of the localization properties of the eigenstates suggests that the bound states become unstable in the thermodynamic limit. A perturbative estimate of the decay rate agrees with the prediction of an eventual instability for large system sizes.

Exact diagonalization↗

Signs of nonmonotonic finite-volume corrections to 𝑔 𝐴

We study finite-volume (FV) corrections to determinations of 𝑔 𝐴 via lattice quantum chromodynamics (QCD) using analytic results and numerical analysis. We observe that 𝑆⁢𝑈⁡(2) heavy Baryon chiral perturbation theory does not provide an unambiguous prediction for the sign of the FV correction, which is not surprising when one also considers large-𝑁 𝑐 constraints on the axial couplings. We further show that nonmonotonic FV corrections are naturally allowed when one considers either including explicit Δ-resonance degrees of freedom or one works to higher orders in the chiral expansion. We investigate the potential impact of these FV corrections with a precision study of 𝑔 𝐴 using models of FV corrections that are monotonic and nonmonotonic. Using lattice QCD data that is approximately at the 1% level of precision, we do not see significant evidence of nonmonotonic corrections. Looking forward to the next phase of lattice QCD calculations, we estimate that calculations that are between the 0.1% and 1% level of precision may be sensitive to these FV artifacts. Finally, we present an update of the CalLat prediction of 𝑔 𝐴 in the isospin limit with subpercent precision, 𝑔$^{QCD}_{𝐴}$ = 1.2674⁢(96).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Precision study of the massive Schwinger model near quantum criticality

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different “criticality criteria,” observing perfect agreement among them Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

Critical phenomena↗

A GaN-Based Active Power Decoupling Approach for Enhancing the Efficiency and Reliability of Residential PV Microinverters

It is a common sense that, the reliability of a system is dictated by the life-time of its weakest component. In terms of a single-phase solar photovoltaic (PV) system, including PV panel and the microinverter, the reliability of the system is confined by the electrolytic dc-link capacitor at the input of its microinverter. To enhance the reliability of the system by providing the possibility of employing film capacitors, with higher life-time rather than their electrolytic counterparts, this paper presents a novel modeling, design, and control of a PV-side active power decoupling (APD) approach. Besides, GaN FETs are employed to achieve a superior efficiency and power density of the APD. The proposed methodology is verified through a thorough design, loss modeling, and numerical analysis.

14 SOLAR ENERGY↗

Bidding Curve Design for Hybrid Power Plants with Uncertain Solar Forecast

This paper presents a novel bidding curve design algorithm tailored for hybrid power plants (HPPs) to participate in the wholesale electricity market. Utilizing forecasts for photovoltaic (PV) generation and available battery power, our algorithm strategically computes the bidding curve to maximize HPP profit while adeptly managing the inherent uncertainty associated with PV power generation. In addition, the introduction of the penalty cost in HPP bidding curves provides the system operator a tool to effectively manage the system-level uncertainty that caused by HPPs. Numerical analysis through Monte Carlo simulations confirms that our bidding curve methodology outperforms the benchmark across various scenarios.

bidding curve↗

Optimal Coordination of Electric Vehicles for Grid Services using Deep Reinforcement Learning

Recent research has shown the effectiveness of reinforcement learning (RL) in coordinating electric vehicles (EVs) with vehicle-to-grid capabilities for grid services. However, many of these studies rely on lookup table and deep Q-network techniques, which can be impractical when dealing with continuous states and actions. In addition, existing RL designs inadequately account for battery aging effects, EV user satisfaction, uncertain departure and arrival time, and trip distance, which may compromise effective coordination. This paper aims to bridge these gaps by developing an innovative deep deterministic policy gradient-based RL framework for optimal coordination of EVs. Case studies were carried out using a test system with 100 EVs, and numerical analysis results showed that the proposed RL framework can effectively coordinate EVs to maximize economic benefits and user satisfaction while ensuring the expected battery lifespan.

Das, Avijit↗

Support Structure Design of the $\hbox{Nb}_{3}\hbox{Sn}$ Quadrupole for the High Luminosity LHC

New low-β quadrupole magnets are being developed within the scope of the High Luminosity LHC (HL-LHC) project in collaboration with the US LARP program. The aim of the HLLHC project is to study and implement machine upgrades necessary for increasing the luminosity of the LHC. The new quadrupoles, which are based on the Nb₃Sn superconducting technology, will be installed in the LHC Interaction Regions and will have to generate a gradient of 140 T/m in a coil aperture of 150 mm. In this paper, we describe the design of the short model magnet support structure and discuss results of the detailed 3D numerical analysis performed in preparation for the first short model test.

43 PARTICLE ACCELERATORS↗

Mechanical Design Studies of the MQXF Long Model Quadrupole for the HiLumi LHC

The Large Hadron Collider Luminosity upgrade (HiLumi) program requires new low-β triplet quadrupole magnets, called MQXF, in the Interaction Region (IR) to increase the LHC peak and integrated luminosity. The MQXF magnets, designed and fabricated in collaboration between CERN and the U.S. LARP, will all have the same cross section. The MQXF long model, referred as MQXFA, is a quadrupole using the Nb3Sn superconducting technology with 150 mm aperture and a 4.2 m magnetic length and is the first long prototype of the final MQXF design. The MQXFA magnet is based on the previous LARP HQ and MQXFS designs. In this paper we present the baseline design of the MQXFA structure with detailed 3D numerical analysis. A detailed tolerance analysis of the baseline case has been performed by using a 3D finite element model, which allows fast computation of structures modelled with actual tolerances. Tolerance sensitivity of each component is discussed to verify the actual tolerances to be achieved by vendors. In conclusion, tolerance stack-up analysis is presented in the end of this paper.

43 PARTICLE ACCELERATORS↗

Optimal Control of Biomass Feedstock Processing System Under Uncertainty in Biomass Quality

Planning of biorefinery operations is complicated by the stochastic nature of physical and chemical characteristics of biomass feedstock, such as, moisture level and carbohydrate content. Biomass characteristics affect the performance of the equipment which feed the reactor and the efficiency of the conversion process in a biorefinery. We propose a stochastic optimization model to identify a blend of feedstocks, inventory levels, and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor while meeting the requirements of the biochemical conversion process. We propose a sample average approximation (SAA) of the model, and develop an efficient algorithm to solve the SAA model. A feedstock preprocessing process consists of two-stage grinding and pelleting is used to develop a case study. Extensive numerical analysis are conducted which lead to a number of observations. Our main observation is that sequencing bales based on moisture level and carbohydrate content leads to robust solutions that improve processing time and processing rate of the reactor. We provide a number of managerial insights that facilitate the implementation of the model proposed. Note to Practitioners—This paper is motivated by the challenges faced in the bioenergy industry. The focus of this paper is on plants which use the biochemical conversion process to generate liquid fuels. It has been observed that variations in biomass characteristics, such as moisture content, cause variations in feeding of the system which lead to under-utilization of equipment. A requirement of biochemical conversion process is to maintain the carbohydrate content of biomass processed by the reactor, larger than a threshold. We propose a model that identifies the inventory levels and operating conditions of equipment to ensure a continuous flowing of biomass to the reactor. The goal is to improve equipment utilization while satisfying the requirements of the conversion process. The model is tested using real-life data. We found out that by sequencing bales based on moisture level and carbohydrate content, a plant can reduce variability in the system leading to improved system reliability, higher processing rates of the reactor, and higher throughput.

09 BIOMASS FUELS↗

Mild hybridisation of turboprop engine with high-power-density integrated electric drives

Here this paper shares with the aerospace community a case study of turboprop mild hybridisation using a recently developed integrated drive system in the University of Nottingham, UK, within the ACHIEVE project under EU H2020 CleanSky 2 program (project No. 737814). The developed drive system enables green taxiing of a turboprop aircraft while on the ground with its engine off, and as an electrical generator when the turboprop is in the air. The entire system is designed to be able to integrate within the power auxiliary gear box (PAGB) of a turboprop aircraft. Some of the key features of the developed system include a high-speed permanent magnet machine (up to 14,200rpm) with dual three-phase design, SiC-based high power density (11.8kW/L for the power converter, 35.3kW/L and 7.2kW/kg for the machine active parts), integrated cooling design for high-temperature operation (>130°C ambient temperature), fault tolerance consideration with dual channel operation capabilities and sensorless control for entire operational conditions. This paper is giving an overview of the design process of the electrical machine, power converters, and its cooling of the entire drive. Numerical analysis (FEM and CFD) and some experimental results are presented to demonstrate the effectiveness and the desired performance of the developed integrated drive system.

42 ENGINEERING↗

An agent based model for joint placement of PV panels and green roofs

Photovoltaic panels generate electricity directly from sunlight, making them a favored renewable technology. Green roofs are rooftops covered with vegetation, which provide a variety of benefits, namely, reducing stormwater runoff, improving air quality, and biodiversity. Green roofs are capable of improving the efficiency of Photovoltaic panels, as shown by the recent studies. Optimal placement of Photovoltaic panels and green roofs is a challenging problem due to the complications imposed by uncertainties associated with future climate conditions, specifically due to climate change. An agent based model to optimally place Photovoltaic panels and green roofs is developed in this study. We propose a tabu search metaheuristic algorithm to solve the developed model. Then, a real-world case for a mid-sized city in the U.S. is solved as a case study for the model. We further conduct numerical analysis and provide insights.

Li, Xueping↗