Real-time Formalism Research Articles

Wigner functions and quantum kinetic theory of polarized photons

We derive the Wigner functions of polarized photons in the Coulomb gauge with the ħ expansion applied to quantum field theory, and identify side-jump effects for massless photons. We also discuss the photonic chiral vortical effect for the Chern-Simons current and zilch vortical effect for the zilch current in local thermal equilibrium as a consistency check for our formalism. The results are found to be in agreement with those obtained from different approaches. Moreover, using the real-time formalism, we construct the quantum kinetic theory (QKT) for polarized photons. By further adopting a specific power counting scheme for the distribution functions, we provide a more succinct form of an effective QKT. This photonic QKT involves quantum corrections associated with self-energy gradients in the collision term, which are analogous to the side-jump corrections pertinent to spin-orbit interactions in the chiral kinetic theory for massless fermions. The same theoretical framework can also be directly applied to weakly coupled gluons in the absence of background color fields.

Real time ultrasoft fermion self energy at next to-leading order in hot QED

Subsequent studies of the behavior of the gluon and quark damping rates in the imaginary-time formalism have indicated that there are difficulties in the infrared sector [1, 2, 3, 4, 5, 6, 7]. To look further into the infrared behavior, we propose to calculate the next-to-leading order dispersion relations for slow-moving Fermions at high-temperature quantum electrodynamics (QED) in real-time formalism. We determine a compact analytic expression for the complete next-to-leading contribution to the retarded fermion self-energy with ultrasoft momentum in the framework of hard-thermal-loop (HTL)-summed perturbation of massless QED at high temperature. The calculation is done using real-time formalism. The next-to-leading order fermion self-energy is written in terms of three and four HTL-dressed vertex functions. The real part and the opposite of the imaginary part of the retarded fermion self-energy are related to the next-to-leading order contributions of energy and damping rate respectively.

A Two-stage Robust Optimal Allocation Model of Distributed Generation Considering Capacity Curve and Real-time Price Based Demand Response

Demand response, the reactive power output of distributed generation (DG), and network reconfiguration have significant impacts on a DG allocation strategy. In this context, a novel real-time price-based demand response formulation is integrated into the allocation model of DG. The tariff is regulated by the difference between the load and active power of renewable energy. Meanwhile, network reconfiguration and the capacity curve describing the active and reactive power limits of DG are included in the optimization model for promoting the allocation of DG. With these measures, the optimal allocation model of DG is established with the goal of maximizing the net annual profit while guaranteeing the efficient utilization of renewable energy. In addition, the uncertainties of renewable energy are considered on the basis of a two-stage robust optimization method. Finally, the entire optimization model is solved by the column and constraint generation algorithm in the IEEE 33-bus distribution system and a practical 99-bus distribution system. Numerical simulations show that the proposed model is effective in terms of improving both the usage of renewable energy and net annual profit.

Probing the molecular frame of uracil and thymine with high-harmonic generation spectroscopy.

In this work, we present the computed high-harmonic generation (HHG) spectra of uracil and thymine molecules, by means of the real-time time-dependent formulation of Gaussian-based configuration interaction with single excitations (RT-TD-CIS). According to the experimental work [Hutchison et al., Comparison of high-order harmonic generation in uracil and thymine ablation plumes, Phys. Chem. Chem. Phys., 2013, 15, 12308], a pulse wavelength of 780 nm has been used, together with an intensity of 1014 W cm-2 and a pulse duration of 23 optical cycles. In order to examine the effect of pulse polarisation, rotationally averaged (to mimic the gas-phase sample) and single-polarisations have been computed for both molecules. Our results show that the HHG signal for both molecules possibly originates from different ionisation channels, involving HOMO, HOMO-1, HOMO-2 and HOMO-3 orbitals, which lie within 4 eV. We characterize the HHG spectrum of thymine, supporting the idea that the absence of the thymine signal in the original work does not depend on the single-molecule behaviour. Present results for uracil are consistent with the experimental data. Moreover, we have observed that states below and above the chosen ionisation threshold provide different contributions to the HHG spectrum in averaged and single-polarisation calculations.

Reduction of COVID-19 Incidence and Nonpharmacologic Interventions: Analysis Using a US County-Level Policy Data Set.

BackgroundWorldwide, nonpharmacologic interventions (NPIs) have been the main tool used to mitigate the COVID-19 pandemic. This includes social distancing measures (closing businesses, closing schools, and quarantining symptomatic persons) and contact tracing (tracking and following exposed individuals). While preliminary research across the globe has shown these policies to be effective, there is currently a lack of information on the effectiveness of NPIs in the United States.ObjectiveThe purpose of this study was to create a granular NPI data set at the county level and then analyze the relationship between NPI policies and changes in reported COVID-19 cases.MethodsUsing a standardized crowdsourcing methodology, we collected time-series data on 7 key NPIs for 1320 US counties.ResultsThis open-source data set is the largest and most comprehensive collection of county NPI policy data and meets the need for higher-resolution COVID-19 policy data. Our analysis revealed a wide variation in county-level policies both within and among states (P<.001). We identified a correlation between workplace closures and lower growth rates of COVID-19 cases (P=.004). We found weak correlations between shelter-in-place enforcement and measures of Democratic local voter proportion (R=0.21) and elected leadership (R=0.22).ConclusionsThis study is the first large-scale NPI analysis at the county level demonstrating a correlation between NPIs and decreased rates of COVID-19. Future work using this data set will explore the relationship between county-level policies and COVID-19 transmission to optimize real-time policy formulation.

Integrating Net Benefits Test for Demand Response Into Optimal Power Flow Formulation

In 2011, the Federal Energy Regulatory Commission (FERC) mandated that demand response (DR) procurement pass a net benefits test (NBT) in Order 745 to ensure that the benefits outweighed the costs. Without NBT, DR procurement could result in losses to consumers considering payments for energy and DR services. Current NBT implementations are monthly. However, this neglects to consider two important issues: (a) generator supply curve and demand changes on an hourly basis thus altering the maximum DR quantity that can be dispatched considering NBT; and (b) system-wide implementations don't consider locational marginal prices, line flow limits, and network congestion. Both of these issues can severely distort proper implementation of the NBT. However, FERC allowed the NBT be applied monthly and system-wide in recognition of computational difficulties and lack of methods, and FERC called for research in real-time implementations of NBT. Our work responds to this call. To address these two shortcomings, we propose a new optimal power flow (OPF) formulation in which NBT is implemented into a real-time or near real-time dispatch OPF model and considers the network model in its entirety. Our proposed methodology is applied to a 4-bus test system, a 118-bus modified IEEE system, and a real Ontario system. We demonstrate that the embedding of NBT into real-time OPF formulation yields maximum benefits to remaining consumers when compared to conventional DR formulations.

Quark mass function at finite density in real-time formalism

Abstract Chiral symmetry restoration of quarks is investigated at finite density in quantum chromodynamics. The critical chemical potentials at zero temperature, in which the chiral symmetry is restored, are calculated with the Schwinger-Dyson equation in the real-time formalism without the instantaneous exchange approximation. We present some properties of the quark mass functions and the quark propagators.

The HTL Lagrangian at NLO: The photon case

We calculate the two loop hard correction to the photon self-energy in an electron-positron plasma (EPP) for arbitrary soft momenta. This provides the only missing ingredient to obtain the Hard Thermal Loop (HTL) effective Lagrangian at next-to-leading order (NLO), and the full photon propagator at the same order. This result can be easily extended to obtain the soft photon propagator in a quark gluon plasma. We use the Keldysh representation of the real time formalism in the massless fermion limit, and dimensional regularization (DR) to regulate any ultraviolet (UV), infrared (IR) or collinear divergences that appear in the intermediate steps of the calculation. In the limit of soft photon momenta, our result is finite. It not only provides an O(α) correction to the Debye mass, but also a new non-local structure. A consistent regularization of radial and angular integrals is crucial to get this new structure. As an application we calculate the plasmon dispersion relations at NLO.

Validation of a Real-Time Capable Multibody Vehicle Dynamics Formulation for Automotive Testing Frameworks Based on Simulation

The growing functionalities implemented on vehicles have increased the importance of simulation in the design process. This complexity is mainly driven by the introduction of electrified powertrains, Advanced Driver Assistance Systems (ADAS) and Automated Driving Systems (ADS). Additionally, the automotive industry must reduce development times and cost, while keeping flexible development capabilities and fulfilling demanding regulation standards for safety-critical systems. Existing testing frameworks based on simulation implement typically analytical models to ensure real-time performance, and provide limited flexibility to perform Hardware in the Loop (HiL) setup based tests. In this work a vehicle modelling approach which guarantees high accuracy and real-time capabilities is proposed. Moreover, the proposed approach is validated firstly with real vehicle data, demonstrating that it can fairly reproduce the behaviour of the vehicle tested; and secondly, in a HiL setup to demonstrate the real-time execution capabilities of the approach.

Landau damping in a strong magnetic field: Dissociation of quarkonia

In this article we have investigated the effects of strong magnetic field on the properties of quarkonia immersed in a thermal medium of quarks and gluons and then studied the quasi-free dissociation of quarkonia due to the Landau-damping. Thermalising the Schwinger propagator for quarks in the lowest Landau levels and the Feynman propagator for gluons in real-time formalism, we have calculated the resummed retarded and symmetric propagators, which in turn give the real and imaginary components of dielectric permittivity, respectively. Finally the inverse Fourier transform of the permittivities encrypt the effect of hot QCD medium in the presence of strong magnetic field into both real and imaginary parts of heavy quark potential. We have found that the magnetic field largely affects the large-distance interaction, as a result, the real part of potential becomes more attractive and the magnitude of imaginary part too becomes larger, compared to its counterpart in the absence of magnetic field. The real part of the potential is thereafter solved numerically by the Schrödinger equation to obtain the energy eigenvalues and energy eigenfunctions of the charmonium states. We have noticed that in the presence of strong magnetic field, the size (r2) of J/ψ and ψ′ are swelled whereas χc gets shrunk, unless the temperature is very high. Similarly the magnetic field affects the binding of J/ψ and χc differently, i.e. it decreases the binding of J/ψ but increases for χc. On contrary the magnetic field increases the width of the resonances, unless the temperature is sufficiently high. We have finally studied the dissociation due to the Landau damping and found that the dissociation temperatures become higher in the presence of magnetic field. For example, with eB=6mπ2 the J/ψ is dissociated at 2Tc, and with eB=4mπ2 the χc is dissociated at 1.1Tc in comparison, with eB = 0 the J/ψ is dissociated at T=1.6Tc and χc is dissociated at T=0.8Tc. However, with the further increase of magnetic field the dissociation temperatures decrease.

Equilibrium States in Thermal Field Theory and in Algebraic Quantum Field Theory

In this paper we compare the construction of equilibrium states at finite temperature for self-interacting massive scalar quantum field theories on Minkowski spacetime proposed by Fredenhagen and Lindner with results obtained in ordinary thermal field theory, by means of real time and Matsubara formalisms. In the construction of this state, even if the adiabatic limit is considered, the interaction Lagrangian is multiplied by a smooth time cut-off. In this way the interaction starts adiabatically and the correlation functions are free from divergences. The corresponding interaction Hamiltonian is a local interacting field smeared over the interval of time where the chosen cut-off is not constant. In order to cope with this smearing, the Matsubara propagator needs to be modified. We obtain an expansion of the correlation functions of the interacting equilibrium state as a sum over certain type of graphs with mixed edges, some of them correspond to modified Matsubara propagators and others to propagators of the real time formalism. An integration over the adiabatic time cut-off is present in every vertex. However, at every order in perturbation theory, the final result does not depend on the particular form of the cut-off function. The obtained graphical expansion contains in it both the real time formalism and the Matsubara formalism as particular cases. Finally, we show that a particular factorisation which is used to derive the ordinary real time formalism holds only in special cases and we present a counterexample. We conclude with the analysis of certain correlation functions and we notice that corrections to the self-energy in a $\lambda\phi^4$ at finite temperature theory are expected.

Effective coupling constant of plasmons

We study an ultrarelativistic QED plasma in thermal equilibrium. Plasmons - photon collective excitations - are postulated to correspond not to poles of the retarded photon propagator but to poles of the propagator multiplied by the fine structure constant. This product is an invariant of the renormalization group that is independent of an arbitrarily chosen renormalization scale. In addition, our proposal is physically motivated since one needs to scatter a charged particle off a plasma system to probe its spectrum of collective excitations. We present a detailed calculation of the QED running coupling constant at finite temperature using the Keldysh-Schwinger representation of the real-time formalism. We discuss the issue of how to choose the renormalization scale and show that the temperature is a natural choice which prevents the breakdown of perturbation theory through the generation of potentially large logarithmic terms. Our method could be applied to anisotropic systems where the choice of the renormalization scale is less clear, and could have important consequences for the study of collective modes.

Saha Ionization Equation in the Early Universe

Abstract The Saha equation follows from thermal equilibrium of matter and radiation. We discuss this problem of equilibrium in the early universe, when matter consists mostly of electrons, protons, and hydrogen atoms. Taking H atoms in their ground state only and applying the real-time formulation of thermal field theory, we calculate the difference of ionization and recombination rates, which controls the equilibration of H atoms. By comparing with realistic calculations including the excited states of the H atom, we conclude that the presence of excited states lowers the equilibrium temperature from 5000 to 4000 K.

Vacuum decay in real time and imaginary time formalisms

We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation. In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field operator, imposes Dirichlet boundary conditions on the initial field value, and evolves in imaginary time. This approach does not have an obvious physical interpretation. However, an alternative approach does have a physical interpretation: in quantum field theory, tunneling can happen via classical dynamics, seeded by initial quantum fluctuations in both the field and its momentum conjugate, which was recently implemented in Ref. [1]. We show that the Wigner representation is a useful framework to calculate and understand the relationship between these two approaches. We find there are two, related, saddle point approximations for the path integral of the tunneling process: one corresponds to the instanton solution in imaginary time and the other one corresponds to classical dynamics from initial quantum fluctuations in real time. The classical approximation for the dynamics of the latter process is justified only in a system with many degrees of freedom, as can appear in field theory due to high occupancy of nucleated bubbles, while it is not justified in single particle quantum mechanics, as we explain. We mention possible applications of the real time formalism, including tunneling when the instanton vanishes, or when the imaginary time contour deformation is not possible, which may occur in cosmological settings.

Modeling and velocity-field control of autonomous excavator with main control valve

We propose a novel modeling and control framework for the autonomous excavator with main control valve (MCV), which distributes fluid from pumps to hydraulic actuators with the number of the pumps less than that of the actuators and whose internal hydraulic circuitry switches depending on operating conditions and internal pressures. We first derive the mathematical model of the MCV, including the switching components and supply pump flow constraint. We then design a novel velocity-field control for the bucket position/orientation, which, by relying on a constrained-optimization formulation, can adjust the velocity-field following speed reflecting the physical constraints imposed by the MCV in such a way that the bucket fully follows the desired velocity-field when the constraints are inactive or still preserves the desired direction (or automatic stopping) while slowing down when the constraints become active (e.g. flow saturation). We further show that this optimization can be reduced to simple real-time solvable formulation with its solution existence/optimality (or suboptimality) guaranteed. Simulation is also performed to verify the theory by using a detailed Simulink/Sim-Hydraulics model.

Quark mass function at finite temperature in real-time formalism

We investigate properties of quark mass functions at finite temperature in quantum chromodynamics calculated by Schwinger-Dyson equation in real-time formalism without the instantaneous exchange approximation, in which one-loop integration is performed in Minkowski space. In our model, an imaginary part of the mass function is directory evaluated.

Axial Ward Identity and the Schwinger Mechanism: Applications to the Real-Time Chiral Magnetic Effect and Condensates.

We elucidate chirality production under parity breaking constant electromagnetic fields, with which we clarify qualitative differences in and out of equilibrium. For a strong magnetic field the pair production from the Schwinger mechanism increments the chirality. The pair production rate is exponentially suppressed with mass according to the Schwinger formula, while the mass dependence of chirality production in the axial Ward identity appears in the pseudoscalar term only. We demonstrate that, in a real-time formulation with in and out states, the axial Ward identity with an in-in expectation value leads to a chirality production rate consistent with the Schwinger formula, while the axial anomaly with an in-out expectation value is canceled by the pseudoscalar condensate for any mass. We illuminate that such an in- and out-state formulation clarifies subtleties in the chiral magnetic effect in and out of equilibrium, and we discuss further applications to real-time condensates.

Identifying Electronic Modes by Fourier Transform from δ-Kick Time-Evolution TDDFT Calculations

Time-dependent density-functional theory (TDDFT) is widely used for calculating electron excitations in clusters and large molecules. For optical excitations, TDDFT is customarily applied in two distinct approaches: transition-based linear-response TDDFT (LR-TDDFT) and the real-time formalism (RT-TDDFT). The former directly provides the energies and transition densities of the excitations, but it requires the calculation of a large number of empty electron states, which makes it cumbersome for large systems. By contrast, RT-TDDFT circumvents the evaluation of empty orbitals, which is especially advantageous when dealing with large systems. A drawback of the procedure is that information about the nature of individual spectral features is not automatically obtained, although it is of course contained in the time-dependent induced density. Fourier transform of the induced density has been used in some simple cases, but the method is, surprisingly, not widely used to complement the RT-TDDFT calculations; although the reliability of RT-TDDFT spectra is now widely accepted, a critical assessment for the corresponding transition densities and a demonstration of the technical feasibility of the Fourier-transform evaluation for general cases is still lacking. In the present work, we show that the transition densities of the optically allowed excitations can be efficiently extracted from a single δ-kick time-evolution calculation even in complex systems like noble metals. We assess the results by comparison with the corresponding LR-TDDFT ones and also with the induced densities arising from RT-TDDFT simulations of the excitation process.

Electromagnetic spectral function and dilepton rate in a hot magnetized QCD medium

The dilepton production rate in hot QCD medium is studied within a effective description of the medium in the presence of magnetic field. This could be done by obtaining the one-loop self energy of photon due to the effective (quasi-) quark loop at finite temperature under an arbitrary external magnetic field while employing the real time formalism of Thermal Field Theory. The effective quarks and gluons encode hot QCD medium effective in terms of their respective effective fugacities. The magnetic field enters in the form of landau level quantization, in the matter sector (quarks, antiquarks). The full Schwinger proper time propagator including all the Landau levels is considered for the quasi quarks while calculating the photon self energy. The electromagnetic Debye screening (in terms of the self-energy) has seen to be influenced both by the hot QCD medium effects and magnetic field. Analogous results are also obtained from the semi classical transport theory. The imaginary part of the photon self energy function is obtained from the discontinuities of the self energy across the Unitary cuts which are also present at zero magnetic field and the Landau cuts which are purely due to the magnetic field. The dilepton production rate is then obtained in terms of the product of electromagnetic spectral functions due to quark loop and lepton loop. The modifications of both the quarks/antiquarks as well as leptons in presence of an arbitrary external magnetic field have been considered in the formalism. Significant enhancement of the low invariant mass dileptons due the appearance of the Landau cuts in the electromagnetic spectral function at finite external magnetic field has been observed. A substantial enhancement of dilepton rate is also found when the EOS effects are considered through the effective quarks/antiquraks.

Microfluidic device for real-time formulation of reagents and their subsequent encapsulation into double emulsions

Emulsion drops are often employed as picoliter-sized containers to perform screening assays. These assays usually entail the formation of drops encompassing discrete objects such as cells or microparticles and reagents to study interactions between the different encapsulants. Drops are also used to screen influences of reagent concentrations on the final product. However, these latter assays are less frequently performed because it is difficult to change the reagent concentration over a wide range and with high precision within a single experiment. In this paper, we present a microfluidic double emulsion drop maker containing pneumatic valves that enable real-time formulation of different reagents using pulse width modulation and consequent encapsulation of the mixed solutions. This device can produce drops from reagent volumes as low as 10 µL with minimal sample loss, thereby enabling experiments that would be prohibitively expensive using drop generators that do not contain valves. We employ this device to monitor the kinetics of the cell-free synthesis of green fluorescent proteins inside double emulsions. To demonstrate the potential of this device for real-time formulation, we perform DNA titration experiments to test the influence of DNA concentration on the amount of green fluorescence protein produced in double emulsions by a coupled cell-free transcription / translation system.