Expected Value Research Articles

BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data

We compute the expectation values of BPS Wilson loops in the mass-deformed ABJM theory using the Fermi gas technique. We obtain explicit results in terms of Airy functions, effectively resumming the full 1/N expansion up to exponentially small terms. These expressions enable us to derive multi-point correlation functions for topological operators belonging to the stress tensor multiplet, in the presence of a 1/2-BPS Wilson line. From the one-point correlator, we recover the ABJM Bremsstrahlung function, confirming nicely previous results obtained through latitude Wilson loops. Likewise, higher point correlators can be used to extract iteratively new defect CFT data for higher dimensional topological operators. We present a detailed example of the dimension-two operator appearing in the OPE of two stress tensor multiplets.

Conformal anomalies and renormalized stress tensor correlators for nonconformal theories

We analyze the proposal of defining the Weyl anomaly for classically nonconformal theories as gmn⟨Tmn⟩−⟨gmnTmn⟩, originally put forward by Duff, in the case of a scalar field with quartic self-interaction in 4d. We work in the context of dimensional regularization in curved background to two loops (first order in the coupling). We review the original regularized but not renormalized prescription and its ambiguities; we argue that it cannot be extended to the interacting theory as it fails to provide a finite result. We then propose an alternative prescription via renormalized expectation values. At one loop, our candidate reproduces the local heat kernel result, while its extension to interacting theories contains nonlocal contributions. Published by the American Physical Society 2024

Measuring the Loschmidt Amplitude for Finite-Energy Properties of the Fermi-Hubbard Model on an Ion-Trap Quantum Computer

Calculating the equilibrium properties of condensed-matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude ⟨ψ|e−iH^t|ψ⟩ from initial states |ψ⟩ and a time evolution under the Hamiltonian H^ up to short times t. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a 16-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error-mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm. Published by the American Physical Society 2024

Local Readout and Control of Current and Kinetic Energy Operators in Optical Lattices

Quantum gas microscopes have revolutionized quantum simulations with ultracold atoms, allowing one to measure local observables and snapshots of quantum states. However, measurements so far were mostly carried out in the occupation basis. Here, we demonstrate how all kinetic operators, such as kinetic energy or current operators, can be measured and manipulated with single-bond resolution. Beyond simple expectation values of these observables, the single-shot measurements allow one to access full counting statistics and complex correlation functions. Our work paves the way for the implementation of efficient quantum state tomography and hybrid quantum computing protocols for itinerant particles on a lattice. In addition, we demonstrate how site-resolved programmable potentials enable a spatially selective, parallel readout in different bases as well as the engineering of arbitrary initial states. Published by the American Physical Society 2024

Scared, Bored or Happy? Latent Profile Analyses of Primary School Students’ Academic Emotions about Math

Emotions and motivation are central to learning. Control–value theory (CVT) and expectancy–value theory (EVT) explain how emotions and expectations of success affect students’ task engagement. Supported by these two frameworks, this study investigates the emotion profiles for maths among fourth- and fifth-grade students (N = 6778) from three European countries and their links to motivation and achievement. Methods: Using latent profile analysis (LPA), we analysed the emotional profiles in students, as well as their associations with gender, country, grade, motivation and maths achievement. Results: Five profiles emerged in the grade 4 data (Bored, Bored and Anxious, Moderate, Happy and Anxious). All five profiles were visible in the grade 5 data, coupled with an additional sixth profile, which appeared only in grade 5 (i.e., Apprehensive–Happy). Girls were found more commonly in the Anxious profile and were less likely to appear in the Happy profile. Norwegian students were more prominent in the Bored and Moderate profiles. Conversely, Portuguese students stood out more in the Anxious profile and were less present in the Bored and Moderate profiles. The Serbian dataset did not stand out, with a particular pattern observed in grade 4. Nevertheless, Serbian fifth graders were overly visible in the Bored and Anxious profile and less present in the Happy and Apprehensive–Happy groups. The Happy profile had higher scores for all task values except for cost and was, along with the Moderate profile, associated with higher achievement; the Bored and Anxious profile was associated with higher scores of cost value and lower achievement. Conclusions: A person-centred approach allowed for a more diverse view of how students experience emotions. These findings highlight the complex interplay between emotions, motivation and achievement, which is affected by cultural and educational contexts.

Light-ray sum rules and the c-anomaly

In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly ∆a has been related to the average null energy. We extend this result to derive a sum rule for the other anomaly coefficient, ∆c, in terms of the stress tensor three-point function. While the sum rule for ∆a is an expectation value of the averaged null energy operator, and therefore positive, the result for ∆c involves the off-diagonal matrix elements, so it does not have a fixed sign.

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation

Quantum Volume is a full-stack benchmark for near-term quantum computers. It quantifies the largest size of a square circuit which can be executed on the target device with reasonable fidelity. Error mitigation is a set of techniques intended to remove the effects of noise present in the computation of noisy quantum computers when computing an expectation value of interest. Effective quantum volume is a proposed metric that applies error mitigation to the quantum volume protocol in order to evaluate the effectiveness not only of the target device but also of the error mitigation algorithm. Digital Zero-Noise Extrapolation (ZNE) is an error mitigation technique that estimates the noiseless expectation value using circuit folding to amplify errors by known scale factors and then extrapolating computed expectation values to the zero-noise limit. Here we demonstrate that ZNE, with global and local unitary folding with fractional scale factors, in conjunction with dynamical decoupling, can increase the effective quantum volume over the vendor-measured quantum volume. Specifically, we measure the effective quantum volume of four IBM Quantum superconducting processor units, obtaining values that are larger than the vendor-measured quantum volume on each device. This is the first such increase reported.

Transport of orbital currents in systems with strong intervalley coupling: The case of Kekulé distorted graphene

We show that orbital currents can describe the transport of orbital magnetic moments of Bloch states in models where the formalism based on valley current is not applicable. As a case study, we consider Kekulé-OO distorted graphene. We begin by analyzing the band structure in detail and obtain the intrinsic orbital magnetic moment operator of Bloch states for this model. Despite the simultaneous presence of time-reversal and spatial-inversion symmetries, such operator may be defined, although its expectation value at a given energy is zero. Nevertheless, its presence can be exposed by the application of an external magnetic field. We then proceed to study the transport of these quantities. In the Kekulé-OO distorted graphene model, the strong coupling between different valleys prevents the definition of a bulk valley current. However, the formalism of the orbital Hall effect together with the non-Abelian description of the magnetic moment operator can be directly applied to describe its transport in these types of models. We show that the Kekulé-OO distorted graphene model exhibits an orbital Hall insulating plateau whose height is inversely proportional to the energy band gap produced by intervalley coupling. Our results strengthen the perspective of using the orbital Hall effect formalism as a preferable alternative to the valley Hall effect approach.

Effective potential in finite formulation of QFT

In recent works [1,2], we have shown how n-point correlation functions in perturbative QFT can be computed without running into intermediate divergences. Here we want to illustrate explicitly that one can calculate the quantum effective potential by the same method. As a main example, we consider a theory with two fields having large and small vacuum expectation values (vev). We show that no fine-tuning between the physical quantities is needed to keep the hierarchy between the vevs of different fields.

Imprints of the operator ordering ambiguity on the dynamics of perfect fluid dominated quantum Universe

Abstract Sharply peaked quantum states are conjectured to be conducive to the notion of a quantum-corrected spacetime. We investigate this conjecture for a flat-FLRW model with perfect fluid, where a generalized ordering scheme is considered for the gravitational Hamiltonian. We study the implications of different ordering choices on the dynamics of the quantum universe. We demonstrate that the imprints of the operator ordering ambiguity are minimal, and quantum fluctuations are small in the case of sharply peaked states, leading to a consistent notion of a quantum-corrected spacetime defined via the expectation value of the scale factor. Surprisingly, the ordering imprints survive far away from the singularity through the quantum fluctuations in the quantum-corrected spacetime for broadly peaked states.

Аппроксимация статистических данных заболеваемости коронавирусной инфекцией с учетом расслоения по сопутствующим диагнозам

The article considers the stratification of concomitant diagnoses of Covid-19 recovery statistics for the city of Irkutsk for 2020-2021. The previous study was conducted without taking into account such stratification. Various options for approximating real statistics by Gaussian and Lorentz functions, gamma distribution, and Johnson curves are considered. It is shown that the stratification of recovery statistics improves the approximation of Gaussian and Lorentz functions in comparison with integral statistics, and the construction of an approximation based on the Lorentz function always describes the real statistics better. Estimates of mathematical expectation and variance based on statistical data are consistent with estimates of these values based on the Gaussian approximation of statistics by the least squares method, i.e. the approaches are equivalent. At the same time, calculations of the Pearson Chi-squared criterion reject the hypothesis that empirical data correspond to the assumed theoretical distribution. Therefore, we cannot talk about finding the distribution function, but only about approximating statistics by certain types of curves. The fitting of empirical data by Gaussian and Lorentz functions was carried out using the least squares method. In general, the approximation error due to the stratification of statistics on concomitant diagnoses decreases from 6% to 3%.

Density functional theory from spherically symmetric densities: Ground and excited states of Coulomb systems.

Recently, Theophilou [J. Chem. Phys. 149, 074104 (2018)] proposed a peculiar version of the density functional theory by showing that the set of spherical averages of the density around the nuclei determines uniquely the external potential in atoms, molecules, and solids. Here, this novel theory is extended to individual excited states. The generalization is based on the method developed in the series of papers by Ayers, Levy, and Nagy [Phys. Rev. A 85, 042518 (2012)]. Generalized Hohenberg-Kohn theorems are proved to the set of spherically symmetric densities using constrained search. A universal variational functional for the sum of the kinetic and electron-electron repulsion energies is constructed. The functional is appropriate for the ground state and all bound excited states. Euler equations and Kohn-Sham equations for the set are derived. The Euler equations can be rewritten as Schrödinger-like equations for the square root of the radial densities, and the effective potentials in them can be expressed in terms of wave function expectation values. The Hartree plus exchange-correlation potentials can be given by the difference of the interacting and the non-interacting effective potentials.

Reducing the negative impact of wildfire disasters through multi-scenario risk analysis of land investment

Natural meteorological and climatological hazards and vulnerable vegetation are frequent triggers of natural disasters, such as wildfires. These cause loss of life and significant economic damage, likely to increase due to climate and socio-economic changes. The increase in wildfires in recent decades has affected the decision-making of technocrats and policy experts and created the need for more sophisticated risk management. This paper develops a theoretical framework for reducing the economic impact of wildfire risk on forests. Also provides insight into land use decisions regarding losses that this increased risk of forest land management can cause. The impact of wildfire risk on economic land value is evaluated by comparing three scenarios, i.e. the deterministic risk-adjusted land expectation value with its risk-free counterparts calculated assuming the stationary risk and predicted increasing risk as time goes by. Also, for this purpose, we evaluate the economically optimal length rotation period pine stands and the risk premium. Fire risk is described as the probability of pine stands destruction due to their age and meteorological conditions in the experimental area Záhorská lowland (western Slovakia). Our findings highlight the importance of alerting forest policymakers to carefully incorporate assessment of the increasing risk of random natural disasters due to climate change into sustainable forest management. The study's results will also help current or future forest owners estimate and evaluate the economic/investing risk when buying or selling forest land.

Core concomitant symptoms reported by the patients with breast cancer in postoperative endocrine treatment and the demand for acupuncture therapy： a network-based cross-sectional study.

To investigate the most common concomitant symptoms and the urgent demand of solution in the breast cancer patients undergoing postoperative endocrine treatment, as well as the acceptance and expectation of acupuncture in the patients so as to provide the scientific data for promoting the application of acupuncture in the breast cancer patients. Breast cancer patients treated in Tianjin Medical University Cancer Institute and Hospital from January 2022 to March 2023 were randomly selected as the subjects. Using "questionnaire star" website, the questionnaire was conducted to investigate the relevant concomitant symptoms of the patients in postoperative endocrine treatment and the questions related to acupuncture treatment. In this study, 229 questionnaires were distributed and 211 valid ones were collected, with the response rate of 92.1%. Among these patients, the first three common symptoms were sleep disorders (157 cases, 74.4%), hot flashes (138 cases, 65.4%) and joint / muscle pain (118 cases, 55.9%)；the top three symptoms to be solved the most urgently were sleep disorders (131 cases, 62.1%), joint / muscle pain (62 cases, 29.4%) and hot flashes (45 cases, 21.3%). 79.1% of the patients (167 cases) were willing to receive acupuncture treatment because of the high expectations on its potential effect (93%). 20.9% of them (44 cases) refused acupuncture because they were worried not to be treated by the experienced physicians of TCM (52%) or afraid of needling feelings (48%). The average expectation value of acupuncture treatment was 4.02 points (5 points for the total score) among patients willing to receive acupuncture treatment. The main purposes of receiring acupuncture for the patients undergoing endocrine treatment were to strengthen the immune function (92%), reduce the adverse reactions (83%), and improve the physical condition (75%), et al. Sleep disorder is one of the most concerned symptoms in endocrine treatment for the patients after breast cancer surgery. The patients highly expect for acupuncture treatment even though some patients dislike the needling sensation. How to provide the acceptable and high-quality acupuncture services for cancer patients will be one of the major directions of acupuncture research in the future.

Thermometry with a dissipative heavy impurity

Improving the measurement precision of low temperature is significant in fundamental science and advanced quantum technology application. However, the measurement precision of temperature T usually diverges as T tends to zero. Here, by utilizing a heavy impurity to measure the temperature of a Bose gas, we obtain the Landau bound to precision δ2T∝T2 to avoid the divergence. When the initial momentum of the heavy impurity is close to be fixed and nonzero, the measurement precision can be δ2T∝T3 to break the Landau bound. We derive the momentum distribution of the heavy impurity at any moment and obtain the optimal measurement precision of the temperature by calculating the Fisher information. As a result, we find that increasing the expectation value P0 and reducing the variance Δ/2 of the initial momentum can help to improve the measurement precision. Moreover, under certain conditions, Δ/P0 is a relevant parameter, the smallness of which helps improve the thermometric precision of the probe. In addition, the momentum measurement is the optimal measurement of the temperature in the case that the initial momentum is close to be fixed and not equal to zero. The kinetic energy measurement is the optimal measurement in the case that the expectation value of the initial momentum is close to zero. Finally, we obtain that the temperatures of two Bose gases can be measured simultaneously. The simultaneous measurement precision is proportional to T2 when two temperatures are close to T. Published by the American Physical Society 2024

On the addition of a large scalar multiplet to the Standard Model

Abstract We consider the addition of a single SU(2) multiplet of complex scalar fields to the Standard Model (SM). We explicitly consider the various possible values of the weak isospin J of that multiplet, up to and including J = 7/2. We allow the multiplet to have arbitrary weak hypercharge. The scalar fields of the multiplet are assumed to have no vacuum expectation value; the mass differences among the components of the multiplet originate in its coupling, present in the scalar potential (SP), to the Higgs doublet of the SM. We derive exact bounded-from-below and unitarity conditions on the SP, thereby constraining those mass differences. We compare those constraints to the ones that may be derived from the oblique parameters.

Integrable structure of higher spin CFT and the ODE/IM correspondence

We study two dimensional systems with extended conformal symmetry generated by the W\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{W} $$\\end{document}3 algebra. These are expected to have an infinite number of commuting conserved charges, which we refer to as the quantum Boussinesq charges. We compute the eigenvalues of the quantum Boussinesq charges in both the vacuum and first excited states of the higher spin module through the ODE/IM correspondence. By studying the higher spin conformal field theory on the torus, we also calculate thermal correlators involving the energy-momentum tensor and the spin-3 current by making use of the Zhu recursion relations. By combining these results, we show that it is possible to derive the current densities, whose integrals are the quantum Boussinesq charges. We also evaluate the thermal expectation values of the conserved charges, and show that these are quasi-modular differential operators acting on the character of the higher spin module.

Employability and motivation: which motivational theories are most appropriate?

PurposeA range of models of employability implicitly or directly identify potential drivers of motivated behaviour related to engaging in employment-related outcomes whilst acknowledging that employability is also about developing life skills. Motivational theorists suggest that tasks engaged for external purposes, e.g. working towards an employment-related goal, are experienced differently than (those same) tasks engaged in for less external reasons, e.g. the desire for knowledge. Whilst there are excellent examples of the use of motivational theory in some models of employability, sometimes the evidence is either outdated, incorrectly interpreted or fails to use the most appropriate motivational theory. The aim of this paper is to bring to attention several prominent motivational theories and some key evidence that seems most pertinent across models of employability.Design/methodology/approachAs this was a non-empirical design, the approach did not fit any research design methodology or structured, systematic or meta-analysis review. The paper outlines a series of arguments by reviewing in detail several theories of motivation and mapping them against current models of employability.FindingsFrom a theoretical point of perspective, it is suggested that Expectancy Value Theory needs to be considered when creating models of employability. It is also suggested that motivation for employment-related tasks is probably extrinsic, though evidence suggests that forms of extrinsic motivation can also be motivationally adaptive. Several models posit self-efficacy as a driver of motivated behaviour, but the evidence suggests a clear and consistent interactive relationship between subjective task value and self-efficacy, suggesting that self-efficacy is only a useful predictor when value is high.Practical implicationsWhilst the aim of models of employability is to improve our understanding of the predictors of employability behaviours, the practical consequence is the development of appropriate curriculum. Understanding which features of employability create adaptive and maladaptive motivation should help educators create curriculum that produces optimal engagement and performance.Originality/valueModels of employability are mostly created using bodies of extant evidence. In this paper, we have tried to identify where some of the interpretation of the evidence has been more or less appropriate. We hope that ideas and evidence in this paper will allow theorists, where appropriate, to re-develop their models.

Probing bad theories with the dualization algorithm. Part II.

We continue our analysis of bad theories initiated in [1], focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver.