Field Operators Research Articles

Nonclassical properties of a deformed atom-cavity field state

We analyse here a nonclassical state produced by an atom-cavity field interaction. The two-level atom is passed through the single-mode electromagnetic cavity field. By deforming the field operators and introducing nonlinearity to the classic Jaynes–Cummings model, we explore the system in respect of a nonlinear Hamiltonian. Assuming that the atom is in an excited state and the field is in a coherent state initially, the analytic expression for the state vector of the entire system state vector is obtained. With the help of the derived state vector, we calculate the photon number distribution, Mandel's parameter, Wigner function, anti-bunching, squeezing properties and Q function etc.

How can quantum field operators encode entanglement?

We present techniques to construct the Deutsch–Hayden representation for quantum field operators and apply them to an entangled state of identical nonrelativistic spin-1/2 fermions localized in well-separated spatial regions. Using these entangled field operators we construct operators measuring spin in localized spatial regions, and verify that matrix elements of the spin-measurement operators in the information-free Deutsch–Hayden state yield the expected correlations between pairs of both entangled and unentangled particles. The entangled Deutsch–Hayden representation field operators furnish an explicitly separable description of the entangled system.

Phonon and Optical-roton Branches of Excitations of the Bose System

For a system of a large number of Bose particles, a chain of coupled equations for the averages of field operators is obtained. In the approximation where only the averages of one field operator and the averages of products of two operators at zero temperature are taken into account, there is derived a closed system of dynamic equations. Taking into account the finite range of the interaction potential between particles, the spectrum of elementary excitations of a many-particle Bose system is calculated, and it is shown that it has two branches: a sound branch and an optical branch with an energy gap at zero momentum. At high density, both branches are nonmonotonic and have the roton-like minima. The dispersion of the phonon part of the spectrum is considered. The performed calculations and analysis of experiments on neutron scattering allow to make a statement about the complex structure of the Landau dispersion curve in the superfluid $$^4$$ He.

Using pressure changes in offset wells for interpreting fracture driven interactions (FDI)

Infill completions have been used in the field to enhance ultimate recovery of unconventional low permeability reservoirs. The stimulation of the infill wells can cause pressure increase in nearby wells. Most available studies have focused on the propagation of fractures from infill wells and pressure changes in treatment wells rather than offset wells which their pressure data may reveal important signatures of fracture-driven interactions (FDI). In this study, we looked at different signatures of FDI data collected in the field and then used a numerical approach to model the pressure fluctuations in offset wells induced by fracturing infill wells and provide insight into how field operators can use the pressure data from nearby wells to identify different forms of FDI, including frac/frac connections and fracture shadowing. The trajectory of a fracture propagating from an infill well is modeled using the extended finite element methods (XFEM). This method allows us to model change of fracture propagation direction due to the rotation of stress field caused by the production of the offset wells. Then, we calculate the pressure response after the fracture intersection using a multi-phase flow model. We investigate the effect of several parameters on the pressure behavior such as the fracture intersection location, the vertical well offset and the fluid compressibility. Typically, a sudden increase in the offset well pressure over a short period is interpreted as a fracture intersection. However, our numerical examples reveal that a gradual increase in the offset well pressure may also indicate a frac/frac connection, especially if the offset well is initially pressurized by injection of fluid before stimulating the infill well. Therefore, only looking at the magnitude of the pressure increase may not be very definitive to make a judgement. Thus, we propose to use diagnostic pressure plots to differentiate fracture connection and fracture shadowing. The proposed analytical model for frac/frac connection pressure threshold and the pressure diagnostic plots can be combined to quickly assess fracture's connections.

The Effect of Capital Structure on the Performance of Marginal Oil Fields in Nigeria

Marginal fields are pivotal to wealth creation and indigenous participation in the oil and gas industry. Despite the potential role of marginal fields in economic growth, indigenous operators are confronted with financing fields development. This study examined the relationship between capital structure and performance of producing marginal oil fields in Nigeria. Ten fields operated by five companies were empirically investigated between 2011 and 2021. Firm’s performance indicators are accounting-based measurement namely, Return on Asset (ROA) and Return on Equity (ROE). Capital structure measures are equity, long term debt and short-term debt. Panel Corrected standard errors regression technique was employed to analyse time series cross sectional data. Findings indicate that there was a significant positive relationship between equity and performance of Marginal fields in Nigeria. These corroborate Pecking order theory that firms use retained earnings first, then debts. Long term debt and short-term debt show negative relationship with marginal field operators’ performance. This could be attributed to the high cost of borrowing in Nigeria and the unwillingness of local banks to grant loans without adequate collateral.

E&P Notes (October 2022)

E&P Notes (October 2022)

Vacuum densities and the Casimir forces for branes orthogonal to the AdS boundary

For a massive scalar field with general curvature coupling we evaluate the Wightman function in the geometry of two parallel branes perpendicular to the AdS boundary. On the separate branes, the field operator is constrained by Robin boundary conditions, in general, with different coefficients. In the region between the branes their contribution to the Wightman function is explicitly separated. By using this decomposition, the brane-induced effects on the vacuum expectation values (VEVs) for the field squared and energy-momentum tensor are investigated. The behavior of those expectation values is studied in various asymptotic regions of the parameters. The vacuum energy-momentum tensor in addition to the diagonal components has a nonzero off-diagonal stress. Depending on the boundary conditions and also on the distance from the branes, the vacuum energy density can be either positive or negative. The Casimir forces acting on the branes have two components. The first one corresponds to the standard normal force and the second one is parallel to the branes and presents the vacuum shear force. Unlike to the problem of parallel plates in the Minkowski bulk, the normal Casimir forces acting on separate branes differ if the boundary conditions on the branes are different. They can be either repulsive or attractive. In a similar way, depending on the coefficients in the boundary conditions, the shear force is directed toward or from the AdS boundary. The separate components may also change their signs as functions of the interbrane separation. At large proper separations between the branes, compared to the AdS curvature radius, both the components of the Casimir forces exhibit a power-law decay. For a massive scalar field this behavior is in contrast to that for the Minkowski bulk, where the decrease is exponential.

Fundamental asymmetry between space and time in quantum field theory

In 1 + 1 dimensions, space and time are geometrically interchangeable. The reason is that, if we switch the roles of the spacelike and the timelike dimensions, this only amounts to redefining the signature convention of the metric tensor. This establishes a mathematical duality between classical Klein–Gordon fields and classical tachyonic fields: one is the ‘space/time swapped’ version of the other. Here, we show that this duality breaks down completely in a quantum world. In quantum field theory, if we exchange space with time, we end up with non-canonical field theories that exhibit all sorts of paradoxical behaviours. Theories that should be stable are, instead, unstable, while theories that should be unstable are stable. Theories that should be causal are, instead, acausal. This formalizes a widespread (but often neglected) intuition: there is a fundamental (non-geometrical) asymmetry between space and time, which has a purely quantum origin, and does not exist in a classical world. Such asymmetry exists independently from the measurement problem, as it is encoded directly in the algebraic properties of the field operators.

The massless thermal field and the thermal fermion bosonization in two dimensions

We come back to the issue of bosonization of fermions in two spacetime dimension and give a new costruction in the steady state case where left and right moving particles can coexist at two different temperatures. A crucial role in our construction is played by translation invariant infrared states and the corresponding field operators which are naturally linked to the infrared behaviour of the correlation functions. We present two applications: a simple new derivation in the free relativistic case of a formula by Bernard and Doyon and a full operator solution of the massless Thirring model in the steady state case where the left and right movers have two distinct temperatures.

Entanglement and Fisher information for a two-atom system interacting with deformed fields in correlated two-mode states

Based on the deformed Heisenberg algebra, we propose a nonlinear Tavis–Cummings model (TCM) which is obtained from the usual TCM by using deformed operators of a two-mode field. Such a generalization of the TCM considers the interaction of a two-atom system with a correlated two-mode field in the presence of time-dependent coupling. We show the effect of the deformation and interaction process between the two modes and atoms on the time variation of current interest quantum phenomena, such as entanglement and parameter estimation. The obtained results provide a new approach to manipulate the interaction between the atoms and fields that can be useful for considerable applications in quantum optics and information.

Experimental evaluation of enhanced oil recovery in unconventional reservoirs using cyclic hydrocarbon gas injection

The significant amount of gas produced from unconventional reservoirs in the US in recent years has reduced market prices for hydrocarbon gas and created an opportunity for using low-cost gas in enhanced oil recovery (EOR) projects. In addition to its availability in large quantities and at low cost, injecting produced gas back into the reservoir prevents flaring the gas, reducing environmental concerns associated with greenhouse gas emissions to the atmosphere. Furthermore, while CO2 has shown tremendous success as an EOR injectant in huff-and-puff operations in tight liquid-rich shales, the lack of sufficient pipeline infrastructure supplying low-cost CO2 as well as operational issues (e.g., corrosion) has forced field operators to consider other gas options, such as produced gas, to substitute for or mix with CO2.While limited, experimental and numerical studies conducted on produced gas huff-and-puff in unconventional resources have shown promising results and highlighted the great potential of this technique for enhanced oil recovery from ultra-tight shale resources. The objective of the current work is to investigate the feasibility of produced gas huff-and-puff operations in one of the major oil-producing shale formations in North America further by performing several flow experiments using various mixtures of hydrocarbon gases. Three reservoir-condition core-flooding experiments are carefully designed and executed on shale core plugs in the absence and presence of proppant-filled fractures. After establishing initial two-phase brine-oil conditions in the core samples, hydrocarbon gas is injected into the medium through a huff-and-puff approach. The cycle of injection-soaking-production is repeated multiple times in each experiment. The results show that the use of hydrocarbon gas in huff-and-puff operations has great potential similar to CO2 for enhanced oil recovery from tight shale rocks and can lead to remarkable oil recovery. The hydrocarbon gas mixture in the fracture penetrates the matrix due to pressure and concentration gradients during the injection and soaking periods and forces the oil to leave the matrix during the depressurization process. It is observed that the rate of oil production is high in the first cycle and decreases in subsequent cycles as the rate of mass transfer and the amount of oil remaining in the matrix decrease. The average oil production due to the cyclic gas injection process in an intact and fractured composite rock sample was more than 48 and 21%, respectively. The results show that even though the ultratight formations could be heavily fractured, a proper cyclic gas injection EOR scheme could potentially improve oil recovery from the shale oil reservoirs, significantly.

Development of a Remote Collaboration System for Interactive Communication with Building Information Model in Mixed Reality

Remote collaboration for construction site management is challenging. Building Information Modeling (BIM) provides the potential for remote collaboration based on its powerful data compatibility. Furthermore, the recently evolving Mixed Reality technology improves visual perception by superimposing 3D virtual BIM objects on real-world artifacts. This study proposes a remote collaboration system based on BIM in Mixed Reality. This system consists of three-unit systems: (1) Field Operator System (FOS), (2) Communication Server, and (3) Office Manager System (OMS). FOS was developed based on MR smart glasses for a field operator. The field operator can manipulate virtual BIM objects with finger-pointing cues and share the view with an office manager. FOS creates Mixed Reality Capture (MRC) video, the combined image of real-world images of existing artifacts in the construction site with virtual BIM elements superimposed on them, and sends it through the Communication Server to OMS. Thus, the office manager can see the field operator’s view through OMS based on a desktop or tablet PC. The office manager can give instructions to a field operator by voice through OMS. A user test was conducted to evaluate the applicability of the developed prototype system. As a result of the test, it was found that most of the testers had a positive evaluation of the developed system. This paper discusses the development of the BIM and MR-based remote collaboration and the test results.

Super-Operator Linear Equations and Their Applications to Quantum Antennas and Quantum Light Scattering

In this paper, we develop a resolvent method for super-operator equations with applications in quantum optics. Our approach is based on the novel concept of a linear super-operator acting on the Hilbert subspace of vector or scalar linear operators satisfying physically reasonable commutation relations. The super-operator equations for the electromagnetic (EM) field operators are formulated for the problems of quantum antenna emission and quantum light scattering by a dielectric body. The general solution of super-operator equation is presented in terms of the classical resolvent. In contrast to the classical case, it includes the ancillary components associated with the quantum noise even in the absence of absorption. The reason for this lies in the energy exchange between different spatial regions with various bases for the field presentation (which looks like losses or gain from the point of view of the correspondent region). A number of examples (a two-element dipole antenna, a plane dielectric layer, and a dielectric cylinder with a circular cross section) which demonstrate the physical mechanism of the appearance of noise are considered. It is shown that antenna emission or scattering transforms the coherent properties of quantum light. This leads to a new way of controlling coherence in a direction-dependent manner, a feature that can be useful in various applications of quantum technologies, including quantum radars and lidars, and quantum antennas.

Quantum metrology with multimode Gaussian states of multiple point sources

A unified theoretical framework is developed for measuring multimode Gaussian states of multiple point sources. The spatial and temporal mode functions are found analytically by aid of the circular symmetry of the object plane and aperture, as well as by the rectangular spectral density function of the background. They relate the modal operators and statistical moments to the locations of the point sources through the prolate spheroidal functions. An experimentally straightforward implementation is proposed, which consists of a nonabsorptive polarization- and phase-modulating spatial light modulator (SLM), three lenses, and a polarization beam splitter. Interestingly, it is found that the spatial modal annihilation operators are related to the modal field operators in the image plane by a simple complex-valued scale factor. The quantum Fisher information matrix and quantum Cram\'er-Rao bound (QCRB) are also discussed. The numerical calculation of QCRB is completed for the case where the spatially multimode aperture fields are prepared by the spatial propagation from temporally single-mode thermal states, coherent states, or quadrature squeezed states of the point sources in the object plane. The results show that the Rayleigh limit can always be surpassed by means of increasing the mean photon rate or the squeeze parameter.

Experimental investigation of proppant transport in hydraulically fractured wells using supercritical CO2

Supercritical CO2 fracturing is a promising waterless stimulation technology, and pumping proppant during fracturing is an essential part of the frac job design to obtain a high-conductivity flow channel after the artificial fracture is created. To date, only a few laboratory experiments have been conducted using supercritical CO2 directly to carry the proppant. In this study, an experimental system was designed to allow investigation of supercritical CO2 transport of proppants within a fracture. To determine the supercritical CO2 transport proppant mechanism and the impact of key operational variables, a series of laboratory experiments were performed considering various pumping schemes. The results demonstrate that the mechanism of supercritical CO2 transport proppant includes various flow patterns such as scouring, throwing and fluidization, among which fluidization is the key to the further migration of proppant. Continued injection of clear-fluid after the addition of proppant is complete, will help the dunes extend deeper into the fracture. Fluid velocity has a significant effect on supercritical CO2 transport proppant. While under the premise of constant mass flow rate, increasing the injection temperature, decreasing the injection pressure or reducing the proppant concentration will make the dune equilibrium height lower and the dune laying distance longer. Meanwhile, small-sized proppant particles can still be easily lifted and suspended in supercritical CO2, and reducing proppant size significantly increases the transportability. Furthermore, dune equilibrium height correlates significantly with the variation of the Reynolds number of the fluid flow. Therefore, from a practical field operation point of view, using Reynolds number as a controlling parameter seems to be a viable option for selection of optimum pumping operational variables and prediction of proppant migration within the fracture. The results of this study are expected to provide guidance for field operators to better design operational variables (e.g. CO2 injection rates, proppant load and pumping schedule, etc.) used for supercritical CO2 fracturing.

Agricultural Land Conversion and Human Trafficking in Northern Java Island, Indonesia

This study examines human trafficking, its causes, and the survival abilities of victims using qualitative interpretive methods and thematic data analysis. Previous studies have not linked human trafficking with agricultural land conversion; however, in Indonesia, this problem is mainly caused by agricultural land conversion, which resulted in a floating mass comprising farmers and their families when this process was not carried out carefully, involving local officials and capital owners. The cooperation between the two forces was assisted by field operators who suppressed landowners in various ways. The owners of large pieces of land managed to reinvest the money from the sale of the land. On the other hand, owners of less than 0.5 hectares tended to share the proceeds from the sale of their land with relatives, as a provision for finding work in other cities or countries. Consequently, they are easily persuaded by the promises of brokers to be trafficked as plantation or sex workers. There are no significant differences in the characteristics of labor and sex trafficking victims. For instance, they both come from economically unstable families with little education. The former farmers do not participate in the industrial sector but work in the informal sector with long working hours and low wages. Nevertheless, they act as the backbone of the family's economy. Therefore, agricultural land conversion policies in developing countries should protect farmers from poverty and vulnerability.

Tripability Analysis of Casing Strings in Directional Wells Using the Continuous Beam-Column and Buckling Theory

Hindered casing strings are often encountered in unconventional oil and gas exploration during the casing running process. This not only increases the operating costs and time but can also lead to downhole accidents and even abandonment in serious cases. Due to various assumptions, the calculation results of the existing soft models and hard models are different, which causes confusion for field operators when taking friction reduction measures. Moreover, a lowering force is often applied to assist hindered casing string running in a drilling field. However, its application is mainly based on work experience and lacks mechanistic analysis and theoretical guidance. Thus, in this study, a simulation model for the analysis of casing string tripability in a directional well was established and the model was combined with the continuous beam-column theory and buckling theory. The model was used to study how various factors including the friction coefficient, drilling fluid density, and casing diameter could affect the lowering force required when a casing string was hindered by buckling. The results showed that the maximum lowering force and the maximum effective lowering force decreased with the increase in the friction coefficient and the performance of the drilling fluid could be adjusted rapidly, which would be beneficial for ensuring that the casing string could be tripped smoothly by applying a lowering force. The increase in the drilling fluid density caused the maximum lowering force and the maximum effective lowering force to decrease, which was not conducive to hindered casing string running. The larger the casing diameter was, the greater the maximum lowering force and the maximum effective lowering force were. It was more convenient to apply a lowering force for a casing with a large diameter. In addition, the improved model could identify whether the casing string was in contact with the upper or lower borehole walls. Through finite element method verification, the prediction was in line with the actual casing running operation and the improved model has the smallest prediction error, i.e., 6.58%, compared with the existing models. Therefore, the improved model might provide necessary theoretical guidance for casing running operations in directional wells.

Experimental test of the third quantization of the electromagnetic field

Each mode $j$ of the electromagnetic field is mathematically equivalent to a harmonic oscillator with a wave function ${\ensuremath{\psi}}_{j}({x}_{j})$ in the quadrature representation. An approach was recently introduced in which ${\ensuremath{\psi}}_{j}({x}_{j})$ was further quantized to produce a field operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j})$ [J. D. Franson, Phys. Rev. A 104, 063702 (2021)]. This approach allows a generalization of quantum optics and quantum electrodynamics based on an unknown mixing angle $\ensuremath{\gamma}$ that is somewhat analogous to the Cabibbo angle or the Weinberg angle. The theory is equivalent to conventional quantum electrodynamics for $\ensuremath{\gamma}=0$, while it predicts an inelastic photon scattering process for $\ensuremath{\gamma}\ensuremath{\ne}0$. Here we report the results of an optical scattering experiment that set an upper bound of $|\ensuremath{\gamma}|\ensuremath{\le}1.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ rad at the 99% confidence level, provided that the particles created by the operator ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\psi}}}_{j}({x}_{j})$ have negligible mass. High-energy experiments would be required to test the theory if the mass of these particles is very large.

Inverse Source Problems for the Stochastic Wave Equations: Far-Field Patterns

This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally isotropic Gaussian random field, whose covariance and relation operators are classical pseudodifferential operators. Given the random source, the direct problems are shown to be well-posed in the sense of distributions and the regularity of the solutions are given. For the inverse problems, we demonstrate by ergodicity that the principal symbols of the covariance and relation operators can be uniquely determined by a single realization of the far-field pattern averaged over the frequency band with probability one.

Dynamic roll instability of liquid natural gas carrier during offloading operations and prediction of downtime cost in Malaysian waters

The loss of revenue or global loss in term of cost due to downtime conditions is always a concern for field operators. Prevailing wave conditions may suddenly appear during offloading operations, which will influence the overall process and may lead to downtime of operations. Severe weather can significantly impact downtime costs of offloading operations and cause a huge loss of revenue. This research work integrates the dynamic stability with downtime cost for LNG carrier in different location of Malaysian waters using real time metocean data. This study on downtime cost utilizes the real time and location-specific wave scatters, as well as limiting criteria of offloading in Malaysian waters. The dynamic roll stability of LNG carrier was investigated for ABS criteria in two depths of water at three real-time locations. Susceptible wave conditions had been identified along with downtime cost analysis. This domain of downtime cost study was further rendered into mathematical package in the form of graphical interfaces for field operators. This mathematical based graphical interface facilitates in predicting location-specific downtime cost charts and allows operator companies to determine the fiscal losses for different range of downtime days and various capacities of LNG carrier. Overall, this research contributes by linking dynamic stability with operating costs through real time metocean data in Malaysian waters.