Monte Carlo Simulations Research Articles

A new kernel two-parameter prediction under multicollinearity in partially linear mixed measurement error model

A Partially linear mixed effects model relating a response Y to predictors ( X , Z , T ) with the mean function X T β + Zb + g ( T ) is considered in this paper. When the parametric parts' variable X are measured with additive error and there is ill-conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper.

Pareto optimization of SPECT acquisition and reconstruction settings for 177Lu activity quantification

BackgroundThe aim was to investigate the noise and bias properties of quantitative 177Lu-SPECT with respect to the number of projection angles, and the number of subsets and iterations in the OS-EM reconstruction, for different total acquisition times.MethodsExperimental SPECT acquisition of six spheres in a NEMA body phantom filled with 177Lu was performed, using medium-energy collimators and 120 projections with 180 s per projection. Bootstrapping was applied to generate data sets representing acquisitions with 20 to 120 projections for 10 min, 20 min, and 40 min, with 32 noise realizations per setting. Monte Carlo simulations were performed of 177Lu-DOTA-TATE in an anthropomorphic computer phantom with three tumours (2.8 mL to 40.0 mL). Projections representing 24 h and 168 h post administration were simulated, each with 32 noise realizations. Images were reconstructed using OS-EM with compensation for attenuation, scatter, and distance-dependent resolution. The number of subsets and iterations were varied within a constrained range of the product number of iterations ×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} number of projections ≤2400\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\le 2400$$\\end{document}. Volumes-of-interest were defined following the physical size of the spheres and tumours, the mean activity-concentrations estimated, and the absolute mean relative error and coefficient of variation (CV) over noise realizations calculated. Pareto fronts were established by analysis of CV versus mean relative error.ResultsPoints at the Pareto fronts with low CV and high mean error resulted from using a low number of subsets, whilst points at the Pareto fronts associated with high CV but low mean error resulted from reconstructions with a high number of subsets. The number of projection angles had limited impact.ConclusionsFor accurate estimation of the 177Lu activity-concentration from SPECT images, the number of projection angles has limited importance, whilst the total acquisition time and the number of subsets and iterations are parameters of importance.

Yet another dose algorithm (YODA) for independent computations of dose and dose changes due to anatomical changes.

Objective:To assess the viability of a physics-based, deterministic and adjoint-capable algorithm for performing treatment planning system independent dose calculations and for computing dosimetric differences caused by anatomical changes.

Approach:A semi-numerical approach is employed to solve two partial differential equations for the proton phase-space density which determines the deposited dose. Lateral hetereogeneities are accounted for by an optimized (Gaussian) beam splitting scheme. Adjoint theory is applied to approximate the change in the deposited dose caused by a new underlying patient anatomy.

Main results:The quality of the dose engine was benchmarked through three-dimensional gamma index comparisons against Monte Carlo simulations done in TOPAS. The worst passing rate for the gamma index with (1 mm, 1 %, 10 % dose cut-off) criteria is 94.55 %. The effect of delivering treatment plans on repeat CTs was also tested. For a non-robustly optimized plan the adjoint component was accurate to 5.7 % while for a robustly optimized plan it was accurate to 4.8 %.

Significance:YODA is capable of accurate dose computations in both single and multi spot irradiations when compared to TOPAS. Moreover, it is able to compute dosimetric differences due to anatomical changes with small to moderate errors thereby facilitating its use for patient-specific quality assurance in online adaptive proton therapy.

Enabling analytical power calculations for multilevel models with autocorrelated errors through deriving and approximating the precision matrix.

To unravel how within-person psychological processes fluctuate in daily life, and how these processes differ between persons, intensive longitudinal (IL) designs in which participants are repeatedly measured, have become popular. Commonly used statistical models for those designs are multilevel models with autocorrelated errors. Substantive hypotheses of interest are then typically investigated via statistical hypotheses tests for model parameters of interest. An important question in the design of such IL studies concerns the determination of the number of participants and the number of measurements per person needed to achieve sufficient statistical power for those statistical tests. Recent advances in computational methods and software have enabled the computation of statistical power using Monte Carlo simulations. However, this approach is computationally intensive and therefore quite restrictive. To ease power computations, we derive simple-to-use analytical formulas for multilevel models with AR(1) within-person errors. Analytic expressions for a model family are obtained via asymptotic approximations of all sample statistics in the precision matrix of the fixed effects. To validate this analytical approach to power computation, we compare it to the simulation-based approach via a series of Monte Carlo simulations. We find comparable performances making the analytic approach a useful tool for researchers that can drastically save them time and resources.

Investigations on the beam quality correction factor for ionization chambers in high-energy brachytherapy dosimetry.

Objective:To enhance the investigations on MC calculated beam quality correction factors of thimble ionization chambers from high-energy brachytherapy sources and to develop reliable reference conditions in source and detector setups in water. 
Approach:The response of five different ionization chambers from PTW-Freiburg and Standard Imaging was investigated for irradiation by a high dose rate Ir-192 Flexisource in water. For a setup in a Beamscan water phantom, Monte Carlo simulations were performed to calculate correction factors for the chamber readings. After exact positioning of source and detector the absorbed dose rate at the TG-43 reference point at one centimeter nominal distance from the source was measured using these factors and compared to the specification of the calibration certificate. The Monte Carlo calculations were performed using the restricted cema formalism to gain further insight into the chamber response. Calculations were performed for the sensitive volume of the chambers, determined by the methods currently used in investigations of dosimetry in magnetic fields.
Main results:Measured dose rates and values from the calibration certificate agreed within the combined uncertainty (k=2) for all chambers except for one case in which the full air cavity was simulated. The chambers showed a distinct directional dependence. With the restricted cema formalism calculations it was possible to examine volume averaging and energy dependence of the perturbation factors contributing to the beam quality correction factor also differential in energy.
Significance:This work determined beam quality correction factors to measure the absorbed dose rate from a brachytherapy source in terms of absorbed dose to water for a variety of ionization chambers. For the accurate dosimetry of brachytherapy sources with ionization chambers it is advisable to use correction factors based on the sensitive volume of the chambers and to take account for the directional dependence of chamber response.

Stochastic eigenvalue computation for cantilever beam dynamics using eigenvector-based polynomial chaos expansion.

Abstract This paper presents a innovative technique for ascertaining the eigenfrequencies of beams characterized
by a random elastic modulus. Our method leverages Polynomial Chaos Expansion (PCE), uniquely
focusing on the expansion of eigen vectors rather than the conventional approach of expanding both
eigenvalues and eigenvectors. An exceptional aspect of our proposed methodology lies in its seam-
less integration with the widely-utilized MATLAB ’eig’ tool, offering a more accessible and efficient
solution.
To validate the accuracy of our proposed method, we performed comparisons against Monte Carlo
simulations, showcasing excellent agreement with both benchmarks. Notably, the mean of our method
demonstrates consistent alignment with Monte Carlo simulations, further affirming its precision. We
further investigated the computational cost of our method and contrasted it with Monte Carlo simu-
lations, demonstrating its efficiency and computational advantages.
Keywords: Eigen frequencies, Monte Carlo, Polynomial Chaos, Stochastic FEM, Vibration,

Experimental and Theoretical Investigation of the Inhibitor Efficiency of Eucalyptus globulus Leaf Essential Oil (EuEO) on Mild Steel Corrosion in a Molar Hydrochloric Acid Medium

As a corrosion inhibitor for mild steel in a molar hydrochloric acid medium, we investigated the potential of Eucalyptus globulus essential oil (EuEO). Through electrochemical impedance spectroscopy (EIS), potentiodynamic polarization curves, and theoretical methods, including DFT/B3LYP 6-31G (d, p) and Monte Carlo simulations, the interactions between the EuEO components and the steel surface were analyzed. D-Allose, Betulinaldehyde, and Uvaol were identified as the major active compounds in the GC-MS analysis. The experimental results showed that EuEO reached an inhibitory efficiency as high as 97% at a 1 g/L concentration. The findings suggest that EuEO operates as a mixed-type inhibitor, reducing both cathodic and anodic reactions, as well as building up a protective coating on the steel surface. Simulations also confirmed that EuEO molecules function as electron donors and acceptors, enhancing corrosion resistance.

PET digitization chain for Monte Carlo simulation in GATE.

We introduce a versatile methodology for the accurate modelling of PET imaging systems via Monte Carlo simulations, using the Geant4 application for tomographic emission (GATE) platform. Accurate Monte Carlo modelling involves the incorporation of a complete analytical signal processing chain, called the digitizer in GATE, to emulate the different count rates encountered in actual PET systems.

Approach: The proposed approach consists of two steps: 1) modelling the digitizer to replicate the detection chain of real systems, covering all available parameters, whether publicly accessible or supplied by manufacturers; 2) estimating the remaining parameters, i.e. background noise level, detection efficiency, and pile-up, using optimisation techniques based on experimental single and prompt event rates. We show that this two-step optimisation reproduces the other experimental count rates (true, scatter, and random), without the need for additional adjustments. This method has been applied and validated with experimental data derived from the NEMA count losses test for three state-of-the-art SiPM-based TOF-PET systems: Philips Vereos, Siemens Biograph Vision 600 and GE Discovery MI 4-ring.

Main results: The results show good agreement between experiments and simulations for the three PET systems, with absolute relative discrepancies below 3~\%, 6~\%, 6~\%, 7~\% and 12~\% for prompt, random, true, scatter and noise equivalent count rates, respectively, within the 0-10~kBq.mL$^{-1}$ activity concentration range typically observed in whole-body \isotope[18]{F} scans.

Significance: Overall, the proposed digitizer optimisation method was shown to be effective in reproducing count rates and NECR for three of the latest generation SiPM-based TOF-PET imaging systems. The proposed methodology could be applied to other PET scanners.

Model for bubble nucleation efficiency of low-energy nuclear recoils in bubble chambers for dark matter detection

Bubble chambers are promising technologies for detecting low-energy nuclear recoils from the elastic scattering of dark matter particle candidates. Bubble nucleation occurs when the energy deposition exceeds a specific threshold defined traditionally by the “heat-spike” Seitz threshold. In this paper, we report on a physical model that can account for observed discrepancies between the current Seitz model and the measured nucleation efficiency of low-energy nuclear recoils, which is necessary for interpreting dark matter signals. In our work, we combine molecular dynamics and Monte Carlo simulations together with the Lindhard model to predict bubble nucleation efficiency and energy thresholds for C3F8, CF3I, and xenon with enhanced accuracy over the Seitz model when compared to existing experimental data. We use our model to determine the effect on cross-section limits for spin-dependent and spin-independent interactions and compare it to the current PICO dark matter experiment. Our technique can also be applied to estimate the efficiency of future target fluids where no experimental data are available. As an example, we predict the nucleation efficiency, the energy threshold, and the cross-section limits in the spin-independent channel for the Scintillating Bubble Chamber experiment filled with superheated liquid argon. Published by the American Physical Society 2024

THz generation by AlGaAs/GaAs heterostructured p-i-n diode

The generation of terahertz radiation by heterostructure p-i-n AlxGa1−xAs/GaAs diodes excited by femtosecond optical pulses was studied experimentally and using the Monte Carlo method. It is shown that when the reverse bias varies, the terahertz generation mechanism changes. With a positive bias on the p-i-n diode, the THz generation mechanism is due to the reflection of the photoexcited electrons from the interface. With a large internal electric field, THz generation in the p-i-n diode occurs due to the acceleration of electrons at the ballistic stage of their movement in the electric field to velocities significantly exceeding the steady state velocity (“velocity overshoot”). The subsequent sharp decrease in velocity of electrons is associated with their inter-valley transitions from the Γ-valley to the L-valley of the conduction band. At electric fields less than 22 kV/cm, the effect of electric field screening by photoexcited carriers has a significant impact on the formation of photocurrent and, accordingly, on the THz generation mechanism. As the reverse bias decreases, this effect leads to a shift in the maximum of the THz pulse toward shorter times and it begins to dominate at electric fields less than 10 kV/cm.

Optimum management of microgrid generation containing distributed generation sources and energy storage devices by considering uncertainties

In recent years, the financial and energy crises have made the economical and safe operation of distribution microgrids one of the main challenges for operators. In this regard, the optimal distribution of the microgrid, considering the favorable indicators of Generation and consumption, significantly improves the quality of the development and economic operation of electricity grids. On the other hand, distribution microgrids have many problems and complications due to the presence of DG sources and the uncertainties caused by them in Generation and consumption, such as the inability to solve optimal load distribution using common and common calculation methods. Therefore, grid technical indicators such as voltage deviation and losses in solving load distribution add to the complexity of related issues. To solve the challenges raised in the distribution microgrid, this paper proposes an optimal load distribution model that models the uncertainties in the distribution microgrids using the Monte Carlo method. Using meta-heuristic algorithms, the optimal Generation function by modeling grid security constraints such as voltage deviation, losses, and a load limit of the system should be in economic operation mode, and then the power distribution equations should be solved. The battery can supply 1 kW of active power to the system at a cost of 1 unit/kW during the high cost period if it absorbs 1 kW of active power at a cost of 0.92 units/kW during the low cost period. Additionally, the active and reactive power losses have been decreased to 0.3kW and 0.2kW, respectively, by utilizing the suggested methodology. The simulation results show that the proposed method performs satisfactorily and that the modeling is simulated in MATLAB software.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Retrieval and analysis of the composition of an aerosol mixture through Mie–Raman–fluorescence lidar observations

Abstract. In the atmosphere, aerosols can originate from numerous sources, leading to the mixing of different particle types. This paper introduces an approach to the partitioning of aerosol mixtures in terms of backscattering coefficients. The method utilizes data collected from the Mie–Raman–fluorescence lidar, with the primary input information being the aerosol backscattering coefficient (β), particle depolarization ratio (δ), and fluorescence capacity (GF). The fluorescence capacity is defined as the ratio of the fluorescence backscattering coefficient to the particle backscattering coefficient at the laser wavelength. By solving a system of equations that model these three properties (β, δ and GF), it is possible to characterize a three-component aerosol mixture. Specifically, the paper assesses the contributions of smoke, urban, and dust aerosols to the overall backscattering coefficient at 532 nm. It is important to note that aerosol properties (δ and GF) may exhibit variations even within a specified aerosol type. To estimate the associated uncertainty, we employ the Monte Carlo technique, which assumes that GF and δ are random values uniformly distributed within predefined intervals. In each Monte Carlo run, a solution is obtained. Rather than relying on a singular solution, an average is computed across the whole set of solutions, and their dispersion serves as a metric for method uncertainty. This methodology was tested using observations conducted at the ATOLL (ATmospheric Observation at liLLe) observatory, Laboratoire d'Optique Atmosphérique, University of Lille, France.

Path Tracking Controller Design of Automated Parking Systems via NMPC with an Instructible Solution

Parking difficulties have become a social issue that people have to solve. Automated parking system is practicable for quick par operations without a driver which can also greatly reduces the probability of parking accidents. The paper proposes a Lyapunov-based nonlinear model predictive controller embedding an instructable solution which is generated by the modified rear-wheel feedback method (RF-LNMPC) in order to improve the overall path tracking accuracy in parking conditions. Firstly, A discrete-time RF-LNMPC considering the position and attitude of the parking vehicle is proposed to increase the success rate of automated parking effectively. Secondly, the RF-LNMPC problem with a multi-objective cost function is solved by the Interior-Point Optimization, of which the iterative initial values are described as the instructable solutions calculated by combining modified rear-wheel feedback to improve the performance of local optimal solution. Thirdly, the details on the computation of the terminal constraint and terminal cost for the linear time-varying case is presented. The closed-loop stability is verified via Lyapunov techniques by considering the terminal constraint and terminal cost theoretically. Finally, the proposed RF-LNMPC is implemented on a self-driving Lincoln MKZ platform and the experiment results have shown improved performance in parallel and vertical parking conditions. The Monte Carlo analysis also demonstrates good stability and repeatability of the proposed method which can be applied in practical use in the near future.

Uncertain vibration response of vehicles passing through barricades based on approximate models

In vibration analysis, a vehicle system encounters dimensionality issues due to its high-dimensional uncertain parameters. An approximate model offers a viable solution for analyzing such uncertain responses. This study introduces an efficient approximate model, called PCE-HDMR, which is founded on the Legendre Polynomial Chaos Expansion (PCE) and High-Dimensional Model Representation (HDMR). Specifically, the Legendre PCE in interval space is employed to delineate the lower and upper bounds of uncertain responses. At the same time, the HDMR is harnessed to develop a high-dimensional uncertainty model that approximates the dynamic response. To demonstrate the application of PCE-HDMR, a model for a vehicle with interval parameters was constructed using a 9-DOF dynamics model for testing. In this framework, all stiffness and damping parameters are treated as interval uncertainty parameters. The numerical results validate the effectiveness of the proposed method for high-dimensional uncertain parameters, demonstrating that PCE-HDMR outperforms Monte Carlo simulation (MCS) in terms of efficiency. This study advances an effective interval uncertainty analysis approach for assessing vehicle performance, particularly when dealing with high-dimensional interval uncertainty parameters. The proposed method serves as a viable alternative for interval analysis and subsequent optimization design for complex vehicle systems characterized by high-dimensional uncertain parameters.

A New Latin Hypercube Sampling with Maximum Diversity Factor for Reliability-Based Design Optimization of HLM

This research paper presents a new Latin hypercube sampling method, aimed at enhancing its performance in quantifying uncertainty and reducing computation time. The new Latin hypercube sampling (LHS) method serves as a tool in reliability-based design optimization (RBDO). The quantification technique is termed LHSMDF (LHS with maximum diversity factor). The quantification techniques, such as Latin hypercube sampling (LHS), optimum Latin hypercube sampling (OLHS), and Latin hypercube sampling with maximum diversity factor (LHSMDF), are tested against mechanical components, including a circular shaft housing, a connecting rod, and a cantilever beam, to evaluate its comparative performance. Subsequently, the new method is employed as the basis of RBDO in the synthesis of a six-bar high-lift mechanism (HLM) example to enhance the reliability of the resulting mechanism compared to Monte Carlo simulation (MCS). The design problem of this mechanism is classified as a motion generation problem, incorporating angle and position of the flap as an objective function. The six-bar linkage is first adapted to be a high-lift mechanism (HLM), which is a symmetrical device of the aircraft. Furthermore, a deterministic design, without consideration of uncertainty, may lead to unacceptable performance during the manufacturing step due to link length tolerances. The techniques are combined with an efficient metaheuristic known as teaching–learning-based optimization with a diversity archive (ATLBO-DA) to identify a reliable HLM. Performance testing of the new LHSMDF reveals that it outperforms the original LHS and OLHS. The HLM problem test results demonstrate that achieving optimum HLM with high reliability necessitates precision without sacrificing accuracy in the manufacturing process. Moreover, it is suggested that the six-bar HLM could emerge as a viable option for developing a new high-lift device in aircraft mechanisms for the future.

SECRET: Statistical Emulation for Computational Reverse Engineering and Translation with applications in healthcare

There have been impressive advances in the physical and mathematical modelling of complex physiological systems in the last few decades, with the potential to revolutionise personalised healthcare with patient-specific evidence-based diagnosis, risk assessment and treatment decision support using digital twins. However, practical progress and genuine clinical impact hinge on successful model calibration, parameter estimation and uncertainty quantification, which calls for novel innovative adaptions and methodological extensions of contemporary state-of-the-art inference techniques from Statistics and Machine Learning. In the present study, we focus on two computational fluid-dynamics (CFD) models of the blood systemic and pulmonary circulation. We discuss state-of-the-art emulation techniques based on deep learning and Gaussian processes, which are coupled with established inference techniques based on greedy optimisation, simulated annealing, Markov Chain Monte Carlo, History Matching and rejection sampling for computationally fast inference of unknown parameters of the CFD models from blood flow and pressure data. The inference task was set as a competitive challenge which the participants had to conduct within a limited time frame representative of clinical requirements. The performance of the methods was assessed independently and objectively by the challenge organisers, based on a ground truth that was unknown to the method developers. Our results indicate that for the systemic challenge, in which an idealised case of noise-free data was considered, the relative deviation from the ground-truth in parameter space ranges from 10−5% (highest-performing method) to 3% (lowest-performing method). For the pulmonary challenge, for which noisy data was generated, the performance ranges from 0.9% to 7% deviation for the parameter posterior mean, and from 35% to 570% deviation for the parameter posterior variance.

A Markov‐switching spatio‐temporal ARCH model

Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by sudden shocks that may lead to an overestimation of persistence, causing an upward bias in the estimates. Different regime‐switching models that have abrupt regime‐switching governed by a Markov chain were developed to model volatility in financial time series data. Volatility modelling was also extended to spatially interconnected time series, resulting in spatial variants of ARCH models. This inspired us to propose a Markov switching framework of the spatio‐temporal log‐ARCH model. In this article, we discuss the Markov‐switching extension of the model, the estimation procedure and the smooth inferences of the regimes. The Monte Carlo simulation studies show that the maximum likelihood estimation method for our proposed model has good finite sample properties. The proposed model was applied to 28 stock indices' data that were presumably affected by the 2015–2016 Chinese stock market crash. The results showed that our model is a better fit compared to that of the one‐regime counterpart. Furthermore, the smoothed inference of the data indicated the approximate periods where structural breaks occurred. This model can capture structural breaks that simultaneously occur in nearby locations.

Investigating polyurethane foam loaded with high-z nanoparticles for gamma radiation shielding compared to Monte Carlo simulations

Since the beginning of research into radiation and protection against it, the importance of searching for proper materials against radiation hazards has been recognized. Gamma radiation protection materials usually deal with heavy elements with high prices, which are hard to maintain. Polyurethane-based (PU) materials are popular in sound and thermal insulation due to, their low-weight properties and, most importantly, fast and convenient construction ingredients. PU foams (PUF) can be used as radiation shield and noise and heat resistance due to their approachability, light-weight, high resistance, and comfortable construction. This study involved simulation and an experiment to construct and investigate the properties of Polyurethane material doped with lead oxide as a gamma shield. The shield was considered in several weight fractions of lead, yielding several samples. The MCNPX 2.6 Monte Carlo code has been utilized for simulation procedure, and 137Cs was employed as the gamma source in both simulation and experiment. The results offer a promising response against the gamma radiation and are suitable for attenuating gamma rays.

Exact evaluation of large-charge correlation functions in nonrelativistic conformal field theory

The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in nonrelativistic conformal field theory is obtained. This field is used to compute Schrödinger-invariant n-point correlation functions of large-charge operators via a direct evaluation of the path integral. Conformal dimensions are found to agree with calculations based on the state-operator correspondence. The master field solution exhibits an emergent harmonic trap whose frequency is a function of the Euclidean time. The large-charge effective action with operator insertions describes a droplet of superfluid matter whose spatial size scales with the time separation of sources. The solution is used to compute Schrödinger symmetry breaking corrections in the large-charge effective field theory (EFT) due to a finite scattering length in the fundamental theory of fermions near unitarity. The scaling of these effects in the large-charge power counting scheme is established, and the size of the effects is quantified using input from quantum Monte Carlo simulations of the near-unitary gas, as well as from the large-N expansion at large charge. Published by the American Physical Society 2024