Background Field Research Articles

Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition

We formulate a model for quantum gravity based on the local Lorentz symmetry and general-coordinate invariance. A key idea is the irreversible vierbein postulate that a tree-level action for the model at a certain energy scale does not contain an inverse vierbein. Under this postulate, only the spinor becomes a dynamical field, and no gravitational background field is introduced in the tree-level action. In this paper, after explaining the transformation rules of the local Lorentz and general-coordinate transformations in detail, a tree-level action is defined. We show that fermionic fluctuations can induce a nonvanishing gravitational background field. Published by the American Physical Society 2024

Stability of the de-Sitter universe: one-loop nonlocal f (R) gravity

With the method of the background field expansion, we investigate the one-loop quantization of the Euclidean nonlocal f (R) model in the de-Sitter universe. We obtain the ghost-free condition (GFC) based on the transformation from the Jordan frame to the Einstein frame and the classical stability condition (CSC) satisfied \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${f}_{RR}^{\\left(0\\right)}-{\\phi }_{0}{F}_{RR}^{\\left(0\\right)}<0$$\\end{document}. We present the on-shell and off-shell one-loop effective action and quantum stability condition (QSC) by utilizing the generalized zeta-function. We find that under the fulfillment of GFC, CSC and QSC are inconsistent.

Impacts of Fengyun-4A and Ground-Based Observation Data Assimilation on the Forecast of Kaifeng’s Heavy Rainfall (2022) and Mechanism Analysis of the Event

The advancement of Numerical Weather Prediction (NWP) is pivotal for enhancing high-impact weather forecasting and warning systems. However, due to the high spatial and temporal inhomogeneity, the moisture field is difficult to describe by initial conditions in NWP models, which is the essential thermodynamic variable in the simulation of various physical processes. Data Assimilation techniques are central to addressing these challenges, integrating observational data with background fields to refine initial conditions and improve forecasting accuracy. This study evaluates the effectiveness of integrating observations from the Fengyun-4A (FY-4A) Advanced Geosynchronous Radiation Imager (AGRI) and ground-based microwave radiometer (MWR) in forecasts and mechanism analysis of a heavy rainfall event in the Kaifeng region of central China. Our findings reveal that jointly assimilating AGRI radiance and MWR data significantly enhances the model’s humidity profile accuracy across all atmospheric layers, resulting in improved heavy rainfall predictions. Analysis of the moisture sources indicates that the storm’s water vapor predominantly originates from westward air movement ahead of a high-altitude trough, with sustained channeling towards the rainfall zone, ensuring a continuous supply of moisture. The storm’s development is further facilitated by a series of atmospheric processes, including the interplay of high and low-level vorticity and divergence, vertical updrafts, the formation of a low-level jet, and the generation of unstable atmospheric energy. Additionally, this study examines the influence of Tai-hang Mountain’s terrain on precipitation patterns in the Kaifeng area. Our experiments, comparing a control setup (CTL) with varied terrain heights, demonstrate that reducing terrain height by 50–60% significantly decreases precipitation coverage and intensity. In contrast, increasing terrain height enhances precipitation, although this effect plateaus when the elevation increase exceeds 100%, closely mirroring the precipitation changes observed with a 75% terrain height increment.

Electron Imaging of Nanoscale Charge Distributions Induced by Femtosecond Light Pulses.

Surface charging is ubiquitously observable during in situ transmission electron microscopy of nonconducting specimens as a result of electron beam/sample interactions or optical stimuli and often limits the achievable image stability and spatial or spectral resolution. Here, we report on the electron-optical imaging of surface charging on a nanostructured surface following femtosecond multiphoton photoemission. By quantitatively extracting the light-induced electrostatic potential and studying the charging dynamics on relevant time scales, we gain insights into the details of the multiphoton photoemission process in the presence of an electrostatic background field. We study the interaction of the charge distribution with the high-energy electron beam and secondary electrons and propose a simple model to describe the interplay of electron- and light-induced processes. In addition, we demonstrate how to mitigate sample charging by simultaneously optically illuminating the sample.

Double space T dualization and coordinate dependent RR field

In this article, we examine T dualization in the double space formalism of type II superstring theory in pure spinor formulation. All background fields are constant except the Ramond-Ramond field, which depends infinitesimally on bosonic coordinates xμ. In double space, T dual transformations are represented as permutations of the starting xμ and dual coordinates yμ. Combining these two sets of coordinates into the double coordinate ZM=(xμ,yμ), while demanding that the T dual double coordinate has the same T dual transformation law as the initial ones, we obtain how background fields transform under T duality. Comparing these results with ones obtained using the Buscher T dualization procedure, we conclude that these two approaches are equivalent for the considered choice of the background fields. Published by the American Physical Society 2024

Controllable nonautonomous localized waves and dynamics for a quasi-1D Gross-Pitaevskii equation in Bose-Einstein condensations with attractive interaction.

This paper investigates dynamical behaviors and controllability of some nonautonomous localized waves based on the Gross-Pitaevskii equation with attractive interatomic interactions. Our approach is a relation constructed between the Gross-Pitaevskii equation and the standard nonlinear Schrödinger equation through a new self-similarity transformation which is to convert the exact solutions of the latter to the former's. Subsequently, one can obtain the nonautonomous breather solutions and higher-order rogue wave solutions of the Gross-Pitaevskii equation. It has been shown that the nonautonomous localized waves can be controlled by the parameters within the self-similarity transformation, rather than relying solely on the nonlinear intensity, spectral parameters, and external potential. The control mechanism can induce an unusual number of loosely bound higher-order rogue waves. The asymptotic analysis of unusual loosely bound rogue waves shows that their essence is energy transfer among rogue waves. Numerical simulations test the dynamical stability of obtained localized wave solutions, which indicate that modifying the parameters in the self-similarity transformation can improve the stability of unstable localized waves and prolong their lifespan. We numerically confirm that the rogue wave controlled by the self-similarity transformation can be reproduced from a chaotic initial background field, hence anticipating the feasibility of its experimental observation, and propose an experimental method for observing these phenomena in Bose-Einstein condensates. The method presented in this paper can help to induce and observe new stable localized waves in some physical systems.

The different dynamic influences of Typhoon Kalmaegi on two pre-existing anticyclonic ocean eddies

Abstract. Using multi-source observational data and GLORYS12V1 reanalysis data, we conduct a comparative analysis of different responses of two warm eddies, AE1 and AE2 in the northern South China Sea, to Typhoon Kalmaegi during September 2014. The findings of our research are as follows: (1) for horizontal distribution, the area and the sea surface temperature (SST) of AE1 and AE2 decrease by about 31 % (36 %) and 0.4 °C (0.6 °C). The amplitude, Rossby number (Ro = relative vorticity / Coriolis parameter) and eddy kinetic energy (EKE) of AE1 increase by 1.3 cm (5.7 %), 1.4×10-2 (20.6 %) and 107.2 cm2 s−2 (49.2 %) after the typhoon, respectively, while AE2 weakens and the amplitude, Rossby number and EKE decrease by 3.1 cm (14.6 %), 1.6×10-2 (26.2 %) and 38.5 cm2 s−2 (20.2 %), respectively. (2) In the vertical direction, AE1 demonstrates enhanced convergence, leading to an increase in temperature and a decrease in salinity above 150 m. The response below the mixed-layer depth (MLD) is particularly prominent (1.3 °C). In contrast, AE2 experiences cooling and a decrease in salinity above the MLD. Below the MLD, it exhibits a subsurface temperature drop and salinity increase due to the upwelling of cold water induced by the suction effect of the typhoon. (3) The disparity in the responses of the two warm eddies can be attributed to their different positions relative to Typhoon Kalmaegi. Under the influence of negative wind stress curl outside the maximum wind radius (Rmax) of the typhoon, triggering negative Ekman pumping velocity (EPV) and quasi-geostrophic adjustment of the eddy, the warm eddy AE1, with its center to the left of the typhoon's path, further enhances the converging sinking of the upper warm water, resulting in its intensification. On the other hand, the warm eddy AE2, situated closer to the center of the typhoon, weakens due to the cold suction caused by the strong positive wind stress curl within the typhoon's Rmax. The same polarity eddies may have different response to typhoons. The distance between eddies and typhoons, eddy intensity, and the background field need to be considered.

Development and preliminary validation of a land surface image assimilation system based on the Common Land Model

Abstract. Data assimilation is an essential approach to improve the predictions of land surface models. Due to the characteristics of single-column models, assimilation of land surface information has mostly focused on improving the assimilation of single-point variables. However, land surface variables affect short-term climate more through large-scale anomalous forcing, so it is indispensable to pay attention to the accuracy of the anomalous spatial structure of land surface variables. In this study, a land surface image assimilation system capable of optimizing the spatial structure of the background field is constructed by introducing the curvelet analysis method and taking the similarity of image structure as a weak constraint. The fifth-generation ECMWF Reanalysis – Land (ERA5-Land) soil moisture reanalysis data are used as ideal observation for the preliminary effectiveness validation of the image assimilation system. The results show that the new image assimilation system is able to absorb the spatial-structure information of the observed data well and has a remarkable ability to adjust the spatial structure of soil moisture in the land model. The spatial correlation coefficient between the model surface soil moisture and observation increased from 0.39 to about 0.67 after assimilation. By assimilating the surface soil moisture data and combining these with the model physical processes, the image assimilation system can also gradually improve the spatial structure of soil moisture content at a depth of 7–28 cm, with the spatial correlation coefficient between the model soil moisture and observation increased from 0.35 to about 0.57. The forecast results show that the positive assimilation effect could be maintained for more than 30 d. The results of this study adequately demonstrate the application potential of image assimilation system in short-term climate prediction.

Measuring Human Auditory Evoked Fields with a Flexible Multi-Channel OPM-Based MEG System.

Magnetoencephalography (MEG) is a non-invasive imaging technique for directly measuring the external magnetic field generated from synchronously activated pyramidal neurons in the brain. The optically pumped magnetometer (OPM) is known for its less expensive, non-cryogenic, movable and user-friendly custom-design provides the potential for a change in functional neuroimaging based on MEG. An array of OPMs covering the opposite sides of a subject's head is placed inside a magnetically shielded room (MSR) and responses evoked from the auditory cortices are measured. High signal-to-noise ratio auditory evoked response fields (AEFs) were detected by a wearable OPM-MEG system in a MSR, for which a flexible helmet was specially designed to minimize the sensor-to-head distance, along with a set of bi-planar coils developed for background field and gradient nulling. Neuronal current sources activated in AEF experiments were localized and the auditory cortices showed the highest activities. Performance of the hybrid optically pumped magnetometer-magnetoencephalography/electroencephalography (OPM-MEG/EEG) system was also assessed. The multi-channel OPM-MEG system performs well in a custom built MSR equipped with bi-planar coils and detects human AEFs with a flexible helmet. Moreover, the similarities and differences of auditory evoked potentials (AEPs) and AEFs are discussed, while the operation of OPM-MEG sensors in conjunction with EEG electrodes provides an encouraging combination for the exploration of hybrid OPM-MEG/EEG systems.

Assessment of Self-Medication Practices among Undergraduate Students Before and During COVID-19

Objective: To assess self-medication knowledge, prevalence, reasons, and conditions among undergraduate medical students. Material and Methods: A survey was conducted among 329 undergraduate healthcare students in tertiary care hospitals &amp; IOD using a self-administered questionnaire. Descriptive statistics were used to summarize the data, and categorical variables were analyzed with Chi-square and logistic regression tests at a significance level of p &lt; 0.05. Results: Self-medication was prevalent among 202 (61.4%) participants: 54 (26.7%) before COVID-19, 16 (7.9%) during COVID-19, and 132 (65.3%) both periods. Knowledge levels varied: 179 (54.4%) with poor knowledge, 150 (45.6%) with good knowledge regarding self-medication. Painkillers 176 (87.1%) were commonly self-administered class of drug, with fever 166 (82.6%) being the most treated condition. Individuals often used their own prior prescriptions 125 (62.5%) as a source of information for self-medication. The predominant reason for self-medication was fear of contact with the infected person during the pandemic, along with fear of quarantine or isolation. Conclusion: In conclusion, this study reveals concerning self-medication practices among undergraduate healthcare students, particularly with painkillers for common ailments. Field of study, academic year, and personal background influenced self-medication tendencies, while highlighting knowledge gaps. The COVID- 19 pandemic exacerbated these behaviours, necessitating immediate attention. Healthcare education must adapt to equip future professionals with decision-making skills amid rising self-medication practices.

Far-Field Super-Resolution Optical Microscopy for Nanostructures in a Reflective Substrate

The resolution of an optical microscope is determined by the overall point spread function of the system. When examining structures significantly smaller than the wavelength of light, the contribution of the background or surrounding environment can profoundly affect the point spread function. This research delves into the impact of reflective planar substrate structures on the system’s resolution. We establish a comprehensive forward imaging model for a reflection-type confocal laser scanning optical microscope, incorporating vector field manipulation to image densely packed nanoparticle clusters. Both theoretical and experimental findings indicate that the substrate causes an interference effect between the background field and the scattered field from the nanoparticles, markedly enhancing the overall spatial resolution. The integration of vector field manipulation with an interferometric scattering approach results in superior spatial resolution for imaging isolated particles and densely distributed nanoscale particle clusters even with deep subwavelength gaps as small as 20 nm between them. However, the method still struggles to resolve nanoparticles positioned directly next to each other without any gap, necessitating further work to enhance the resolving ability. This may involve techniques like deconvolution or machine learning-based post-processing methods.

Conceptual design study of a large bore superconducting test facility magnet, SUCCEX

A 16 Tesla, large bore superconducting magnet for testing the superconducting Cable-in-Conduit Conductor (CICC) is being designed in parallel with the design of the steady state Korea fusion demonstration reactor (K-DEMO) magnet system. The test facility magnet, named SUperConducting Conductor Experiment (SUCCEX), was designed in 2014 and some design modifications of the magnet have been conducted since 2020. The peak magnetic field of the K-DEMO toroidal field coil is about 16 T, and thus the required background field of the conductor test magnet is expected to be over 15 T in a large bore of 600 mm diameter. The background field will be in addition to the K-DEMO conductor sample's self-field. To reach the target magnetic field, high current density Nb3Sn strands (Jc > 1100 A/mm2 at 4.2 K, 16 T) were employed in the design of the high field CICC. The modified SUCCEX magnet consists of concentric solenoids, with a high field inner coil (IC) and low field outer coil (OC). They are connected in series with each other, and the operating current is about 24 kA. In this study, the overall design concept is presented in relation to the results of electro-magnetic, structural analyses.

Multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate in a cavity

Ramsey interferometry as one of the most important high-precision measurement methods has prospects for inferring various properties of ultracold atoms and molecules. We investigate the multi-pulse Ramsey interferometry of a double-well Bose–Einstein condensate (BEC) in an optical cavity. Compared with the standard two-pulse Ramsey scheme, our multi-pulse Ramsey proposal greatly relaxes the requirements for both intensity and width of the pulses, allowing the interferometry to be achieved using weak and narrow pulses. When the pumping pulses characterizing the coupling between the cavity field and the atomic BEC are applied to the zero background field, we demonstrate the atomic Ramsey fringes in the time domain for different pulse numbers and different pulse widths. We find that although the multi-pulse Ramsey fringes are no longer sensitive to cavity-pump detuning, they can still record the information of the interaction between coherent atoms. We obtain the fundamental frequency of the multi-pulse Ramsey fringes analytically and find that it is proportional to the number of pulses. Particularly, it is shown that the minimum of the fundamental frequency is exactly the critical point of the phase transition of the system. For a nonzero background field, the results indicate that a nondestructive observation of atomic Ramsey fringes by cavity transmission spectroscopy is feasible. Our findings provide insights for improving the accuracy of Ramsey interferometry and for using interferometry to observe phase transitions.

Linear instability of hairy black holes in Horndeski theory* *Supported in part by the National Key Research and Development Program of China (2020YFC2201503), the National Natural Science Foundation of China (12205254, 12275238, 11675143), the Natural Science Foundation of Zhejiang Province, China (LR21A050001, LY20A050002), the Fundamental Research Funds for the Provincial Universities of Zhejiang Province, China (RF-A2019015), and the Science Foundation

Horndeski theory constitutes the most general model of scalar-tensor theories. It has attracted much attention in recent years in relation with black holes, celestial dynamics, stability analysis, etc. It is important to note that, for certain subclasses of Horndeski models, one can obtain analytic solutions for the background fields. This facilitates the investigation of the corresponding stability problems in detail. In particular, we aim to determine the constraints to the model or theory under which the stability conditions can be satisfied. In this study, we focused on a subclass of Horndeski theory and a set of analytic background solutions. In addition, the odd-parity gravitational perturbation and 2nd-order Lagrangian were investigated. Through careful analysis, the instability was identified within the neighborhood of the event horizon. This allows exclusion of a specific geometry for the model. Such an instability is implanted in the structure of the corresponding Lagrangian and is not erased by simply adding numerical constraints on the coupling parameters. As a starting point of our research, the current study provides insights for further exploration of the Horndeski theory.

DeepFLAIR: A neural network approach to mitigate signal and contrast loss in temporal lobes at 7 Tesla FLAIR images

Background and purposeHigher magnetic field strength introduces stronger magnetic field inhomogeneities in the brain, especially within temporal lobes, leading to image artifacts. Particularly, T2-weighted fluid-attenuated inversion recovery (FLAIR) images can be affected by these artifacts. Here, we aimed to improve the FLAIR image quality in temporal lobe regions through image processing of multiple contrast images via machine learning using a neural network. MethodsThirteen drug-resistant MR-negative epilepsy patients (age 29.2 ± 9.4y, 5 females) were scanned on a 7 T MRI scanner. Magnetization-prepared (MP2RAGE) and saturation-prepared with 2 rapid gradient echoes, multi-echo gradient echo with four echo times, and the FLAIR sequence were acquired. A voxel-wise neural network was trained on extratemporal-lobe voxels from the acquired structural scans to generate a new FLAIR-like image (i.e., deepFLAIR) with reduced temporal lobe inhomogeneities. The deepFLAIR was evaluated in temporal lobes through signal-to-noise (SNR), contrast-to-noise (CNR) ratio, the sharpness of the gray-white matter boundary and joint-histogram analysis. Saliency mapping demonstrated the importance of each input image per voxel. ResultsSNR and CNR in both gray and white matter were significantly increased (p < 0.05) in the deepFLAIR's temporal ROIs, compared to the FLAIR. The gray-white matter boundary sharpness was either preserved or improved in 10/13 right-sided temporal regions and was found significantly increased in the ROIs. Multiple image contrasts were influential for the deepFLAIR reconstruction with the MP2RAGE second inversion image being the most important. ConclusionsThe deepFLAIR network showed promise to restore the FLAIR signal and reduce contrast attenuation in temporal lobe areas. This may yield a valuable tool, especially when artifact-free FLAIR images are not available.

Hadronic Light-by-Light Corrections to the Muon Anomalous Magnetic Moment

We review the hadronic light-by-light (HLbL) contribution to the muon anomalous magnetic moment. Upcoming measurements will reduce the experimental uncertainty of this observable by a factor of four; therefore, the theoretical precision must improve accordingly to fully harness such an experimental breakthrough. With regards to the HLbL contribution, this implies a study of the high-energy intermediate states that are neglected in dispersive estimates. We focus on the maximally symmetric high-energy regime and in-quark loop approximation of perturbation theory, following the method of the OPE with background fields proposed by Bijnens et al. in 2019 and 2020. We confirm their results regarding the contributions to the muon g−2. For this, we use an alternative computational method based on a reduction in the full quark loop amplitude, instead of projecting on a supposedly complete system of tensor structures motivated by first principles. Concerning scalar coefficients, mass corrections have been obtained by hypergeometric representations of Mellin–Barnes integrals. By our technique, the completeness of such kinematic singularity/zero-free tensor decomposition of the HLbL amplitude is explicitly checked.

Evolutionary Games‐Assisted Synchronization Metasurface for Simultaneous Multisource Invisibility Cloaking

AbstractThe realization of a metasurface cloak for the simultaneous invisibility of multiple sources presents a long‐standing scientific challenge. Ideally, for the establishment of a simultaneous multisource invisibility cloak, the metasurface must provide a wide phase coverage and angular stability in a single architecture, especially for broadband, wide‐angle, and even omnidirectional scenarios. However, achieving this goal has proven to be elusive thus far. Current approaches for implementing metasurface‐based invisibility cloak involve both active and passive metasurface. These approaches often rely on phase‐compensation mechanisms, which inevitably encounter issues related to limited incidence angles or narrow working bands. Here, a novel paradigm of synchronization metasurface optimized through an evolution‐optimization strategy, enabling the realization of simultaneous multisource invisibility cloaking, is proposed. The underlying physics of the synchronization metasurface relies on an evolution‐optimization strategy (an evolutionary game algorithm), which is used to get rid of the entanglement between incident directions, frequencies, and metasurface phase gradients. Consequently, the synchronization metasurface is capable of manipulating simultaneous incoming waves at any angle over a wide range (cloak). In experimental validation, the synchronization metasurface demonstrates an impressive capability to cloak both single and simultaneous double sources in any direction, highly resembling background fields.

Robust multiple focusing through scattering media via feedback wavefront shaping

The control of multiply-scattered light has greatly boosted the understanding of optics in complex photonic systems, leading to many applications including imaging, information processing, random lasing, to name just a few. Here, we demonstrate a real-time feedback approach to realize multiple focusing of multiply-scattered light, which is more robust to the inherent background field compared to the time reversal approach. Our method retrieves the optimized wavefront by aligning the high-dimensional vector of the measured pattern with that of the target pattern. Our theoretical simulations and experimental results show that the feedback approach is capable of constructing homogeneous diffraction-limited spots at predefined positions. Moreover, the peak-to-background ratio exhibits a sub-1/m decay with m being the number of focuses, indicating the excellent capability of the proposed approach to focus scattered light at multiple positions. This efficient approach provides a promising avenue toward complex control on scattered light in complex photonic media, and therefore would be useful in relevant applications such as optical imaging and optical manipulation.

The impact of interactions between various systems caused by three consecutive years of La Nina events on the abnormal summer high temperatures in China in 2022

In the summer of 2022, like in many other regions of the world, an unprecedented period of continuous high-temperature weather occurred in eastern China. The degree and duration of this event far exceeded normal standards. Between 2020 and 2022, the tropical Pacific experienced the most significant three-year consecutive La Nina event recorded in recent decades. We investigate linkages between these events: the high-temperature response in eastern China and Asia under the background of such La Nina events. Development of summer La Nina events contributed to a high-temperature heat wave during the summer of 2022. Rapid development of these events in the third year exacerbated negative Indian Ocean Dipole phases because of energy accumulation from abnormal easterly winds. The combined effects of the negative Indian Ocean Dipole phase and La Nina provided background field support that strengthened the West Pacific Subtropical High (WPSH) and the Iranian High, leading to high terrestrial temperature anomalies. An empirical orthogonal function (EOF) analysis of the vertical velocity in the middle and low latitudes of the tropical Indian Ocean and the Asian continent reveals the first two empirical orthogonal function modes to be conducive to the strengthening of Walker circulation in 2022. These two main modes jointly reflect the rising movement of the equatorial East Indian Ocean and South China Sea in 2022, and the sinking movement to the west of the Tibet Plateau and eastern China, which was conducive to generating high temperatures in eastern China. Finally, the South Asian High was affected by the La Nina event that lasted for three years, showing a strong trend towards the north, thus making an important contribution to this high temperature.

Local momentum balance in electromagnetic gyrokinetic systems

The Eulerian variational formulation is presented to obtain governing equations of the electromagnetic turbulent gyrokinetic system. A local momentum balance in the system is derived from the invariance of the Lagrangian of the system under an arbitrary spatial coordinate transformation by extending the previous work [H. Sugama et al., Phys. Plasmas 28, 022312 (2021)]. Polarization and magnetization due to finite gyroradii and electromagnetic microturbulence are correctly described by the gyrokinetic Poisson equation and Ampère's law which are derived from the variational principle. Also shown is how the momentum balance is influenced by including collisions and external sources. Momentum transport due to collisions and turbulence is represented by a symmetric pressure tensor, which originates in a variational derivative of the Lagrangian with respect to the metric tensor. The relations of the axisymmetry and quasi-axisymmetry of the toroidal background magnetic field to a conservation form of the local momentum balance equation are clarified. In addition, an ensemble-averaged total momentum balance equation is shown to take the conservation form even in the background field with no symmetry when a constraint condition representing the macroscopic Ampère's law is imposed on the background field. Using the WKB representation, the ensemble-averaged pressure tensor due to the microturbulence is expressed in detail and it is verified to reproduce the toroidal momentum transport derived in previous works for axisymmetric systems. The local momentum balance equation and the pressure tensor obtained in this work present a useful reference for elaborate gyrokinetic simulation studies of momentum transport processes.