Expected Value Research Articles

Floquet systems with continuous dynamical symmetries: characterization, time-dependent noether charge, and solvability

We study quantum Floquet (periodically-driven) systems having continuous dynamical symmetry (CDS) consisting of a time translation and a unitary transformation on the Hilbert space. Unlike the discrete ones, the CDS strongly constrains the possible Hamiltonians H(t) and allows us to obtain all the Floquet states by solving a finite-dimensional eigenvalue problem. Besides, Noether’s theorem leads to a time-dependent conservation charge, whose expectation value is time-independent throughout evolution. We exemplify these consequences of CDS in the seminal Rabi model, an effective model of a nitrogen-vacancy center in diamonds without strain terms, and Heisenberg spin models in rotating fields. Our results provide a systematic way of solving for Floquet states and explain how they avoid hybridization in quasienergy diagrams.

Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function Cmn(t)=〈ψ(t)∣cm†cn∣ψ(t)〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn (t) = C mn (t) − C mn (∞) decays with time following the power law behavior t −μ , where the exponent μ depends on whether the quench is to the commensurate phase (μ = 1) or incommensurate phase ( μ=12 ). This decay of δ C mn (t) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

Behavior and damage potential of the newly emerged pest Myochrous armatus (Chrysomelidae: Eumolpinae) on soybean plants in Brazil

AbstractMyochrous armatus Baly, 1865 (Coleoptera: Chrysomelidae) has expanded its occurrence significantly into soybean‐growing areas of Brazilian Cerrado and became an important early‐season soil pest. Experiments were performed under field conditions from 2020 to 2023 to assess several aspects: (1) population behaviour over crop season and offseason; (2) day/night behaviour during the early stages of soybean plants and (3) injury to plants and potential damage to soybean yield to establish the Economic Injury Level (EIL). Adults of the M. armatus population presented a season‐long abundance during the specific period from late October to January, with major captures in November and December (end of Spring), either inside or on the edge of soybean fields. Weeds and volunteer plants of corn and cotton hosts adults and eggs. These findings suggest an univoltine life cycle. Behavioural assessments revealed that M. armatus does not exhibit a specific day, night or crepuscular behaviour, performing deeds at any time. The majority of insects (40% to 70%) were found in the soil throughout the day and night. Adults feed on soybean plants by scraping or cutting the stem, cotyledon, petiole and apical sprouting. Their preference is initially for the stem and cotyledon (up to 14 days after emergence), and later for the petiole (after 21 days of emergence). After 7 days of coexistence at V1‐V3 soybean stages, we observed a potential yield reduction of 35% for each insect per plant. Dynamic EIL estimations are between 0.4 and 1.9 adults per row metre, depending on the grower productivity expectation, control costs and soybean market value. Our results are fundamental for establishing Integrated Pest Management for M. armatus in soybean and other crop systems.

Analysis of the acceptance of E-learning platform (SIDEK-Edu) among high school students with UTAUT2-TOE approach: implications for digital learning

PurposeThe purpose of this study is to examine the acceptance factors of e-learning among students in high schools. In this study, researchers used a combination of system acceptance models, namely UTAUT2 and TOE. The UTAUT2 framework is used to explore technology acceptance from the context of individual behavior, while TOE is used to understand technology acceptance from the organizational context based on the perspective of students, as it results in a better choice to anticipate the relationship between the acceptance of technological innovation in high schools.Design/methodology/approachThis study used quantitative methods. The sample in this study amounted to 212 people who were high school students who had just tried using SIDEK-Edu. This study uses Partial Least Square-Structural Equation Modeling (PLS-SEM) to analyze the measurement model and structural model with WarpPLS version 6 software.FindingsBased on the results of the tests carried out, out of a total of 16 hypotheses, 6 hypotheses were accepted and 10 hypotheses were rejected. Research findings from the individual context show that performance expectancy, social influence, and learning value have a positive and significant effect on behavioral intention to use SIDEK-Edu innovation technology. Furthermore, judging from students' perceptions in the organizational context, only relative advantage has a positive and significant effect on behavioral intention, while compatibility, ICT resources, and competitive pressure do not.Research limitations/implicationsThe limitations of this research are that this research uses a homogeneous sample of high school students, this research only focuses on the high school level, this research is limited to the dominant variables in measuring the acceptance of SIDEK-Edu innovation technology.Practical implicationsInput to the high school, both the organization, teachers, and also decision makers in the organization. This makes it easier for all parties to design and implement the system they have so that it is as expected, In addition, the existence of SIDEK-Edu also provides a new learning method experience in learning accounting which is very beneficial for high school students, especially vocational high school.Originality/valueSIDEK-Edu is a new innovative technology to research and is an LMS that focuses on accounting learning (theory room and practice room in one learning media). In addition, the model used in the study is a combination of models (UTAUT2-TOE) to indentify e-learning acceptance.

Synergy between noisy quantum computers and scalable classical deep learning for quantum error mitigation

We investigate the potential of combining the computational power of noisy quantum computers and of classical scalable convolutional neural networks (CNNs). The goal is to accurately predict exact expectation values of parameterized quantum circuits representing the Trotter-decomposed dynamics of quantum Ising models. By incorporating (simulated) noisy expectation values alongside circuit structure information, our CNNs effectively capture the underlying relationships between circuit architecture and output behaviour, enabling, via transfer learning, also predictions for circuits with more qubits than those included in the training set. Notably, thanks to the quantum information, our CNNs succeed even when supervised learning based only on classical descriptors fails. Furthermore, they outperform a popular error mitigation scheme, namely, zero-noise extrapolation, demonstrating that the synergy between quantum and classical computational tools leads to higher accuracy compared with quantum-only or classical-only approaches. By tuning the noise strength, we explore the crossover from a computationally powerful classical CNN assisted by quantum noisy data, towards rather precise quantum computations, further error-mitigated via classical deep learning.

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.

The Influence of Correlation between Observations on the Probabilistic Characteristics of the MA-Algorithm for Detecting a Gaussian Time Series Disorder from Mathematical Expectation

The Influence of Correlation between Observations on the Probabilistic Characteristics of the MA-Algorithm for Detecting a Gaussian Time Series Disorder from Mathematical Expectation

Time-bin entanglement in the deterministic generation of linear photonic cluster states

We theoretically investigate strategies for the deterministic creation of trains of time-bin entangled photons using an individual quantum emitter described by a Λ-type electronic system. We explicitly demonstrate the theoretical generation of linear cluster states with substantial numbers of entangled photonic qubits in full microscopic numerical simulations. The underlying scheme is based on the manipulation of ground state coherences through precise optical driving. One important finding is that the most easily accessible quality metrics, the achievable rotation fidelities, fall short in assessing the actual quantum correlations of the emitted photons in the face of losses. To address this, we explicitly calculate stabilizer generator expectation values as a superior gauge for the quantum properties of the generated many-photon state. With widespread applicability in other emitter and excitation–emission schemes also, our work lays the conceptual foundations for an in-depth practical analysis of time-bin entanglement based on full numerical simulations with predictive capabilities for realistic systems and setups, including losses and imperfections. The specific results shown in the present work illustrate that with controlled minimization of losses and realistic system parameters for quantum-dot type systems, useful linear cluster states of significant lengths can be generated in the calculations, discussing the possibility of scalability for quantum information processing endeavors.

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.

Probing the quantum nature of gravity using a Bose-Einstein condensate

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The general complex scalar field theory with a quadratic self-interaction term has been considered in the presence of a gravitational wave. The gravitational wave perturbation is then considered as a sum of discrete Fourier modes in the momentum space. Varying the action and making use of the principle of least action, one obtains two equations of motion corresponding to the gravitational perturbation and the time-dependent part of the pseudo-Goldstone boson. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonical commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. The entries of the covariance matrix now involves a stochastic contribution which results in an operatorial stochastic structure of the quantum Fisher information. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. It always has a finite value if the gravitons are initially in a squeezed state with high enough squeezing. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in a decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing. Published by the American Physical Society 2024

Managing ecosystem services in oleaginous forests for bioenergy provision and climate change mitigation

Oleaginous forests provide diverse ecosystem services, including timber, seed yield (a vital feedstock for biodiesel production), and substantial carbon savings. These carbon savings encompass carbon sequestration related to timber growth and carbon savings resulting from substituting fossil fuel with biodiesel. However, oleaginous forests are vulnerable to seed wasp attacks (disservice), which significantly threaten both seed yield and carbon savings. Using an integrated ecological-economic model that includes Faustmann's Land Expectation Value model and a pest damage control model, we aim to understand the intricate relationship among multiple ecosystem services and disservices of oleaginous forests. The results reveal four distinct phases contingent on varying pesticide application rates: the pesticide under-use phase, substitution phase, complementary phase, and over-use phase. Notably, a potential avenue to minimize pest damage is identified during the complementary phase by reducing the optimal rotation age at the expense of decreased carbon sequestration and bioenergy provision, posing a challenge to climate change mitigation. These findings have implications for formulating policies to manage conflicting ecosystem services of energy forests, offering valuable insights into the intersection of sustainable forest management and climate policy.

The Radiation Field, at the Origin of the Quantum Canonical Operators

We show that the electromagnetic radiation field, conventionally introduced as a perturbation in quantum mechanics, is actually at the basis of the operator formalism. We first analyze the linear resonant response of the (continuous) variables x(t), p(t) of a harmonic oscillator to the full radiation field, i.e. the zero-point field plus an applied field playing the role of the driving force, and then extend the analysis to the response of a charged particle bound by a non-linear force, typically an atomic electron. This leads to the establishment of a one-to-one correspondence between the response functions and the respective quantum operators, and to the identification of the quantum commutator with the Poisson bracket of the response functions with respect to the normalized variables of the driving field. To complete the quantum description, a similar procedure is used to obtain the field operators as the response functions to the same normalized variables. The results allow us to draw important conclusions about the physical content of the quantum formalism, in particular about the meaning of the quantum expectation values and the coarse-grained nature of the quantum-mechanical description.

Structured electrons with chiral mass and charge.

Chirality is a phenomenon with widespread relevance in fundamental physics, material science, chemistry, optics, and spectroscopy. In this work, we show that a free electron can be converted by the field cycles of laser light into a right-handed or left-handed coil of mass and charge. In contrast to phase-vortex beams, our electrons maintained a flat de Broglie wave but obtained their chirality from the shape of their expectation value in space and time. Measurements of wave function densities by attosecond gating revealed the three-dimensional shape of coils and double coils with left-handed or right-handed pitch. Engineered elementary particles with such or related chiral geometries should be useful for applications in chiral sensing, free-electron quantum optics, particle physics or electron microscopy.

Economic evaluation of reopening a dormant tree improvement programme: a case study with Scots pine in Scotland

Abstract The deployment of improved forest reproductive material (FRM) selected to yield greater timber volume and quality than unimproved material could help to maintain productive, sustainable, and resilient forests and increase resistance to abiotic and biotic threats under extreme climate change events. In Scotland, Scots pine (Pinus sylvestris L.) is a productive species that aligns with these objectives. However, confidence in Scots pine has been low in recent years due to damage caused by the needle blight Dothistroma septosporum. Recent provenance/progeny trials using native Scots pine material from the Caledonian pine woods indicate a favourable genetic correlation between growth and resistance to D. septosporum, suggesting that simultaneous improvements are possible. The Scots pine breeding programme in Scotland was closed in 2002. Here, we present an economic case for reopening the breeding programme to further improve Scots pine FRM. Specifically, we evaluate the costs and potential benefits of supporting a new programme. We conduct an analysis using three improvement scenarios using a Faustmann formula (amended with thinnings) to maximize the land expectation value. Our results indicate that further improvement of Scots pine FRM would be cost-effective, outperforming the current Scots pine timber production and financial outcomes. The analysis shows that the Central scenario’s land expectation value rises by £883 ha−1 compared to the baseline of £79 ha−1, assuming a 3.5% interest rate. We employed both annuity calculations and a break-even analysis to show improved FRM could maintain a breeding programme investment of £3.5 million per year over a 30-year period with a break-even cost threshold increase of ~52% for purchasing improved planting materials from £0.33 to £0.50 per seedling. In conclusion, the study provides economic evidence of the commercial benefits for reopening the Scots pine breeding programme to increase timber production and financial returns.

Exponentiation of soft quark effects from the replica trick

In this paper, we show that multiple maximally soft (anti-)quark and gluon emissions exponentiate at the level of either the amplitude or cross-section. We first show that such emissions can be captured by introducing new soft emission operators, which serve to generalise the well-known Wilson lines describing emissions of maximally soft gluons. Next, we prove that vacuum expectation values of these operators exponentiate using the replica trick, a statistical-physics argument that has previously been used to demonstrate soft-gluon exponentiation properties in QCD. The obtained results are general, i.e. not tied to a particular scattering process. We illustrate our arguments by demonstrating the exponentiation of certain real and virtual corrections affecting subleading partonic channels in deep-inelastic scattering.

Multiparton Cwebs at five loops

Scattering amplitudes involving multiple partons are plagued with infrared singularities. The soft singularities of the amplitude are captured by the soft function which is defined as the vacuum expectation value of Wilson line correlators. Renormalization properties of soft function allows us to write it as an exponential of the finite soft anomalous dimension. An efficient way to study the soft function is through a set of Feynman diagrams known as Cwebs (webs). We present the mixing matrices and exponentiated colour factors (ECFs) for the Cwebs at five loops that connect six Wilson lines, except those that are related by relabeling of Wilson lines. Further, we express these ECFs in terms of 29 basis colour factors. We also find that this basis can be categorized into two colour structures. Our results are the first key ingredients for the calculation of the soft anomalous dimension at five loops.

Flavon vacuum alignment beyond SUSY

In flavor models the vacuum alignment of flavons is typically achieved via the F-terms of certain fields in the supersymmetric limit. We propose a method for preserving such alignments, up to a rescaling of the vacuum expectation values, even after softly breaking supersymmetry (and the flavor symmetry). This facilitates the vacuum alignment in models which are nonsupersymmetric at low energies. Examples of models with different flavor groups, namely, A4, T7, S4, and Δ(27), are discussed. Published by the American Physical Society 2024

Relaxation dynamics in the alternating XY chain following a quantum quench

Abstract We investigate the relaxation dynamics of the fermion two-point correlation function $C_{mn}(t)=\langle\psi(t)|c_{m}^{\dag}c_{n}|\psi(t)\rangle$ in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation $\delta C_{mn}(t)=C_{mn}(t)-C_{mn}(\infty)$ decays with time following the power law behavior $t^{-\mu}$, where the exponent $\mu$ depends on whether the quench is to the commensurate phase ($\mu=1$) or incommensurate phase ($\mu=\frac{1}{2}$). This decay of $\delta C_{mn}(t)$ arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value $C_{mn}(\infty)$ only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value $C_{mn}(\infty)$ for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

Multifield stochastic dynamics in GUT hybrid inflation without monopole problem and with gravitational wave signatures of GUT Higgs representation

We revisit the hybrid inflation model within the framework of the Grand Unified Theory (GUT), focusing on cases where the waterfall phase transition extends over several e-foldings to dilute monopoles. Considering the stochastic effects of quantum fluctuations, we demonstrate that the waterfall fields (i.e., GUT Higgs) maintain a nonzero vacuum expectation value around the waterfall phase transition. By accurately accounting for the number of degrees of freedom of the GUT Higgs field, we establish that these fluctuations can produce observable gravitational waves without leading to an overproduction of primordial black holes. The amplitude of these gravitational waves is inversely proportional to the degrees of freedom of the waterfall fields, thereby providing a unique method to probe the representation of the GUT Higgs.

Brief theory of multiqubit measurement

Peculiarities of multiqubit measurement are for the most part similar to peculiarities of measurement for qudit — quantum object with finite-dimensional Hilbert space. Three different interpretations of measurement concept are analyzed. One of those is purely quantum and is in collection, for a given state of the object to be measured, of incompatible observable measurement results in amount enough for reconstruction of the state. Two others make evident the difference between the reduced density matrix and the density matrices of physical objects involved in the measurement. It is shown that the von Neumann projectors, in combination with the concept of qudit phase space, produce an idea of a phase portrait of qudit state as a set of mathematical expectations for projectors on the possible pure states. The phase portrait is not a probability distribution since the projectors on nonorthogonal states are incompatible observables. Along with that, the phase portrait includes probability distributions for all the resolutions of identity of the qudit observable algebra. Additional peculiarities of measurement of the qudit degenerated observables, caused by the possibility of independent measurement of the observables for the particles, make possible to distinguish the local reduction of the qudit particle states from the entanglement of the local measurement results. The phase portrait of a composite system comprised by a qudit pair generates local and conditional phase portraits of particles. The entanglement is represented by the dependence of the shape of conditional phase portrait on the properties of the observable used in the measurement for the other particle. Analysis of the properties of a conditional phase portrait of a multiqubit qubits shows that absence of the entanglement is possible only in the case of substantial restrictions imposed on the method of multiqubit decomposition into qubits. Such a special method for determination of particles exists for each multiqubit state.