Space-time Propagation Research Articles

Spin dynamics of 2-DEG Rashba-Dresselhaus spin-orbit systems: Quantum propagators and semi-analytical analysis in low electron density.

Abstract The spin dynamics in space and time for Dresselhaus and Rashba spin-orbit interaction 2-DEG systems can be studied for any value of their β and α coefficients by using quantum propagators. With the development of analytical expressions for the quantum propagators and numerical solutions of the wave function, it has been possible to simulate the spin propagation in space-time and analyze the spin dynamics for different α/β ratios. In the present paper, the effects of the spin diffusion for large collision time τp, was performed by using quantum propagators for different α/β ratios. It was found that the largest degree of spin polarization is achieved when |α| = |β|.

Kerr-MOG-(A)dS black hole and its shadow in scalar-tensor-vector gravity theory

The scalar-tensor-vector gravity (STVG) theory has attracted significant interest due to its ability to effectively address the issue of galaxy rotation curves and clusters of galaxies without considering the influence of dark matter. In this paper, we construct rotating black hole solutions with a cosmological constant in the STVG theory (i.e., Kerr-MOG-(A)dS black hole solutions), where the import of a gravitational charge as a source modifies the gravitational constant, determined by GG = G N(1+α). For Kerr-MOG-dS spacetime, the observer is situated at a specific location within the domain of outer communication, rather than being located infinitely far away. Since black hole shadows are shaped by light propagation in spacetime, the interaction between the MOG parameter and the cosmological constant is expected to produce novel effects on these shadows. As the cosmological constant Λ increases, the apparent size of the black hole shadow decreases. Additionally, the shadow expands with an increase in the MOG parameter α, reaching a maximum at a certain value, and its shape becomes more rounded under an arbitrary rotation parameter, which leads to degeneracy between different black hole parameters. However, by employing numerical ray-tracing techniques, we have found that gravitational lensing and the frame-dragging effect effectively distinguish this degeneracy. Our work contributes to a deeper understanding of black holes in modified gravity, their observational signatures, and constraints.

Majorana phase and matter effects in neutrino chiral oscillation

Due to finite masses and mixing, for neutrinos propagation in space-time, there is a chiral oscillation between left- and right- chiral neutrinos, besides the usual oscillation between different generations. The probability of chiral oscillation is suppressed by a factor of m2/E2 making the effect small for relativistic neutrinos. However, for non-relativistic neutrinos, this effect can be significant. In matter, the equation of motion is modified. When neutrinos produced in weak interaction pass through the matter, the eigen-energies are split into two different ones depending on the helicity of the neutrino. This results in different oscillation behavior for neutrinos with different helicity, in particular there is a new resonant effect related to the helicity state of neutrino different than the usual MSW effect. For Majorana neutrinos, chiral oscillation also depends on Majorana phases.

Spherical Gauss-Laguerre beam propagation in 4D space-time.

In this paper, what we believe to be a novel class of beams, which are referred to as the spherical Gauss-Laguerre beams, are proposed. The beams propagate stably in the anomalous dispersive media, within which the second order derivative with respect to t could be combined with the two-dimensional (2D) Laplacian operator in the transverse direction and forms a three-dimensional (3D) Laplacian operator, which describes the beam propagation in the z direction within the four-dimensional (4D) x-y-z-t space-time. The wave equation is solved by the variable separation method and the analytical expression for the spherical Gauss-Laguerre beams is derived. The beams have a 3D Gaussian field distribution with a variable beam waist with respect to the propagation distance. Unlike any 2D spatial vortex beams, the 3D beams could possess either the spatial vortex or the spatiotemporal optical vortex (STOV) by choosing the vortex plane in the 3D x-y-t space-time. The derived spherical Gauss-Laguerre beam expression in the 4D space-time is verified by the numerical simulations with excellent agreement.

Minimal quantum walk simulation of Dirac fermions in curved space-times

The problem of simulating through quantum walks the curved space-time propagation of Dirac fermions is revisited, taking the $$(1 + 1)$$ D case as an example. New quantum walks are introduced which encode the space-time geometry, not in the mixing operators, but in new unitary shift operators which carry out a position-dependent translation of the wave function components. These walks simulate Dirac fermions in arbitrary curved space-times and coordinates. Contrary to previously proposed general alternatives, the wave functions of the new walks have as many components as usual Dirac spinors, and not twice that number. In particular, in $$(1 + 1)$$ D space-times, only one qubit is needed at each lattice point, which makes it easier to perform quantum simulations of the Dirac dynamics on current NISQs quantum devices. Numerical simulations of the Dirac dynamics in the post Newtonian, so-called Gravitoelectromagnetism regime are presented as an illustration. The possible usefulness of the new shift operators and quantum walks in other more general contexts is also discussed.

Light propagation in Kerr spacetime

We explicitly solve the equations for the propagation of an electromagnetic wave up to the subleading order geometric optics expansion in the Kerr spacetime. This is done in two nontrivial steps. We first construct a set of parallel propagated null tetrad in Kerr spacetime. Two of the components of such tetrad give the propagation and polarization of an electromagnetic wave in geometric optics approximation. Then we use the parallel propagated tetrad to solve the modified trajectory equation in Kerr spacetime. We obtain the wavelength-dependent deviation of the trajectory of electromagnetic waves, which gives the mathematical description of the gravitational spin Hall effect in Kerr spacetime.

Adaptive analytical ray tracing of black hole photon rings

Recent interferometric observations by the Event Horizon Telescope have resolved the horizon-scale emission from sources in the vicinity of nearby supermassive black holes. Future space-based interferometers promise to measure the ''photon ring''--a narrow, ring-shaped, lensed feature predicted by general relativity, but not yet observed--and thereby open a new window into strong gravity. Here we present AART: an Adaptive Analytical Ray-Tracing code that exploits the integrability of light propagation in the Kerr spacetime to rapidly compute high-resolution simulated black hole images, together with the corresponding radio visibility accessible on very long space-ground baselines. The code samples images on a nonuniform adaptive grid that is specially tailored to the lensing behavior of the Kerr geometry and is therefore particularly well-suited to studying photon rings. This numerical approach guarantees that interferometric signatures are correctly computed on long baselines, and the modularity of the code allows for detailed studies of equatorial sources with complex emission profiles and time variability. To demonstrate its capabilities, we use AART to simulate a black hole movie of a stochastic, non-stationary, non-axisymmetric equatorial source; by time-averaging the visibility amplitude of each snapshot, we are able to extract the projected diameter of the photon ring and recover the shape predicted by general relativity.

Open superstring first mass level effective Lagrangian: Massive spin-3/2 fields in an electromagnetic background

We derive fully explicit equations of motion, and the associated set of constraints, describing the propagation in a flat space-time of a charged spin-3/2 massive state in a constant electromagnetic background. For this purpose, we provide the Lagrangian for the physical fermionic fields in the first massive level of the open superstring. We first write a compact Lagrangian, allowing a simple derivation of the equations of motion and constraints. Then another one is given that yields directly a decoupled system of equations, though the fields of different spins look coupled at the level of the Lagrangian.

NonReciprocal Wave Propagation in Space-Time Modulated Media

We show the possibility of achieving nonreciprocal wave propagation in space-time modulated media and give an asymptotic analysis of the nonreciprocity property in terms of the amplitude of the time modulation. Such modulation causes a folding of the band structure of the material, which may induce degenerate points. By breaking time-reversal symmetry, we show that these degeneracies may open into nonsymmetric, unidirectional band gaps. Finally, we illustrate our results by several numerical simulations.

Time delays, choice of energy-momentum variables, and relative locality in doubly special relativity

Doubly Special Relativity (DSR) theories consider (quantum-gravity motivated) deformations of the symmetries of special relativity compatible with a relativity principle. The existence of time delays for massless particles, one of their proposed phenomenological consequences, is a delicate question, since, contrary to what happens with Lorentz Invariance Violation (LIV) scenarios, they are not simply determined by the modification in the particle dispersion relation. While some studies of DSR assert the existence of photon time delays, in this paper we generalize a recently proposed model for time delay studies in DSR and show that the existence of photon time delays does not necessarily follow from a DSR scenario, determining in which cases this is so. Moreover, we clarify long-standing questions about the arbitrariness in the choice of the energy-momentum labels and the independence of the time delay on this choice, as well as on the consistency of its calculation with the relative locality paradigm of DSR theories. Finally, we show that the result for time delays is reproduced in models that consider propagation in a noncommutative spacetime.

Passive symmetry breaking of the space–time propagation in cavity dissipative solitons

Dissipative solitons are fundamental wave-pulses that preserve their form in the presence of periodic loss and gain. The canonical realization of dissipative solitons is Kerr-lens mode locking in lasers, which delicately balance nonlinear and linear propagation in both time and space to generate ultrashort optical pulses. This linear-nonlinear balance dictates a unique pulse energy, which cannot be increased (say by elevated pumping), indicating that excess energy is expected to be radiated in the form of dispersive or diffractive waves. Here we show that Kerr-lens mode-locked lasers can overcome this expectation. Specifically, by breaking the spatial symmetry between the forward and backward halves of the round-trip in a linear cavity, the laser can modify the soliton in space to incorporate the excess energy. Increasing the pump power leads therefore to a different soliton solution, rather than to dispersive/diffractive loss. We predict this symmetry breaking by a complete numerical simulation of the spatio-temporal dynamics in the cavity, and confirm it experimentally in a Kerr-lens mode-locked Ti:Sapphire laser with quantitative agreement to the simulation. The simulation opens a window to directly observe the nonlinear space-time dynamics that molds the soliton pulse, and possibly to optimize it.

Space-time propagation of photon pulses in dielectric media, illustrations with beam splitters

Photons are the elementary quantum excitations of the electromagnetic field. Quantization is usually constructed on the basis of an expansion in eigenmodes, in the form of plane waves. Since they form a basis, other electromagnetic configurations can be constructed by linear combinations. In this presentation we discuss a formulation constructed in the general formalism of bosonic Fock space, in which the quantum excitation can be constructed directly on localized pulses of arbitrary shape. Although the two formulations are essentially equivalent, the direct formulation in terms of pulses has some conceptual and practical advantages, which we illustrate with some examples. The first one is the passage of a single photon pulse through a beam splitter. The analysis of this formulation in terms of pulses in Fock space shows that there is no need to introduce ‘vacuum fluctuations entering through the unused port’, as is often done in the literature. Another example is the Hong–Ou–Mandel effect. It is described as a time dependent process in the Schrödinger representation in Fock space. The analysis shows explicitly how the two essential ingredients of the Hong–Ou–Mandel effect are the same shape of the pulses and the bosonic nature of photons. This formulation shows that all the phenomena involving linear quantum optical devices can be described and calculated on the basis of the time dependent solution of the corresponding classical Maxwell’s equations for pulses, from which the quantum dynamics in Fock space can be immediately constructed.

Social equity-based distribution networks design for the COVID-19 vaccine

This study aims to investigate the role of social equity in vaccine distribution network design problems. Inspired by the current COVID-19 vaccine allocation in-country context, we capture social equity-based distribution by modeling three theories: Rawls’ theory, Sadr’s theory, and utilitarianism. We consider various social groups based on degree of urbanization, including inhabitants of cities, towns and suburbs, and rural areas. The distribution problem is subject to, on the one hand, demand-side uncertainty characterized by the daily contamination rate and its space–time propagation that anticipate the in-need population. On the other hand, supply-side uncertainty characterized by the stochastic arrival of vaccine doses for the supply period. To tackle this problem, we propose a novel bi-objective two-stage stochastic programming model using the sample average approximation (SAA) method. We also develop a lexicographic goal programming approach where the social equity objective is prioritized, thereafter reaching an efficiency level. Using publicly available data on COVID-19 in-country propagation and the case of two major provinces in Iran as example of middle-income country, we provide evidence of the benefits of considering social equity in a model-based decision-making approach. The findings suggest that the design solution produced by each social equity theory matches its essence in social science, differing considerably from the cost-based design solution. According to the general results, we can infer that each social equity theory has its own merits. Implementing Rawls’ theory brings about a greater coverage percentage in rural areas, while utilitarianism results in a higher allocation of vaccine doses to social groups compared to the Sadr and Rawls theories. Finally, Sadr’s theory outperforms Rawls’ in terms of both the allocation and cost perspective. These insights would help decision-makers leverage the right equity approach in the COVID-19 vaccine context, and be better prepared for any pandemic crisis that the future may unfold.

Hydraulic behaviour and improving of water quality of the Chibayish Marshes

The Central Marshes are a rare and complete ecological system in southern Iraq that is of global and local significance, and Al-Chibayish Marsh makes up the major part of it. The water quality of these marshes suffers from salt accumulation, due to a restricted supply of water from sources, as well as a lack of sufficient outlets. Surface-water Modeling System (SMS) software was used to simulate the hydraulic behavior and the space-time propagation of water quality in the Central Marshes in general, with a focus on Al-Chibayish Marsh. Two types of field measurements were conducted to define the concentration of total dissolved solids (TDS) at nine sites, and water depths at 50 locations within the marsh. Also, samples were taken and examined for the physical properties of water. The defined hydrodynamic properties revealed the necessity of the need for one or more outlets to drain water of marshes, and also to perform a good distribution of TDS along the whole marshes area. Furthermore, results showed that the existence of these outlets will considerably improve water quality and decreasing TDS concentration. The numerical simulation revealed that the best site, taking into account the effect of drainage on neighboring lands, and the effective conditions for the drainage of stored water are case C that will result in a reduction of deterioration areas with high TDS concentration.

Space-time propagator and exact solution for wave equation in a layered system

Exact space-time propagator for the wave (second-order in time) equation in a layered ysstem, made up of a layer sandwiched between two other different semi-infinite layers, is obtained by means of the multiple scattering theory (MST) approach. The MST approach is made possible due to obtained effective potentials localized at interfaces and responsible for reflection from and propagation through them. The obtained spacetime propagator exactly solves the considered wave equation for any initial value and allows for following in time the processes of reflection and transmission. The solution for an initial Gaussian wave packet is obtained, analyzed, numerically visualized and discussed for the case of the perpendicular-to-interfaces incoming wave. In particular, the contribution of the backward-moving components of the wave packet is revealed.

Power density dynamics in a nuclear reactor with an extended in-core pulse-periodic neutron source based on a magnetic trap

The article examines the features of the spatial kinetics of an innovative hybrid nuclear power facility with an extended neutron source based on a magnetic trap. The fusion-fission facility under study includes a reactor plant, the core of which consists of an assembly of thorium-plutonium fuel blocks of the HGTRU reactor of a unified design and a long magnetic trap that penetrates the near-axial region of the core. The engineering solution for the neutron plasma generator is based on an operating gas-dynamic trap based on a fusion neutron source (GDT-FNS) developed at the Novosibirsk G.I. Budker Nuclear Physics Institute of the Siberian Branch of the Russian Academy of Sciences. The GDT-FNS high-temperature plasma pinch is formed in pulse-periodic mode in the investigated hybrid facility configuration, and, at a certain pulse rate, one should expect the formation of a fission wave that diverges from the axial part of the system and propagates throughout the fuel block assembly in a time correlation with the fast D-D neutron pulse source. In these conditions, it is essential to study the fission wave propagation process and, accordingly, the power density distribution formation within the facility blanket. The paper presents the results of a study on the steady-state and space-time performances of neutron fluxes and the power density dynamics in the facility under investigation. The steady-state neutronic performance and the space-time fission wave propagation were simulated using the PRIZMA software package developed at FSUE RFNC-VNIITF.

RAPTOR

Context. Accreting supermassive black holes are sources of polarized radiation that propagates through highly curved spacetime before reaching the observer. Accurate and efficient numerical schemes for polarized radiative transfer in curved spacetime are needed to help interpret observations of such polarized emission. Aims. We aim to extend our publicly available radiative transfer code RAPTOR to include polarized radiative transfer, so that it can produce simulated polarized observations of accreting black holes. The RAPTOR code must remain compatible with arbitrary spacetimes and it must be efficient in operation, despite the added complexity of polarized radiative transfer. Methods. We provide a brief review of various codes and methods for covariant polarized radiative transfer available in the literature and existing codes, and we present an efficient new scheme. For the spacetime propagation aspect of the computation, we developed a compact, Lorentz-invariant representation of a polarized ray. For the plasma-propagation aspect of the computation, we performed a formal analysis of the stiffness of the polarized radiative-transfer equation with respect to our explicit integrator. We also developed a hybrid integration scheme that switches to an implicit integrator in case of stiffness in order to solve the equation with optimal speed and accuracy for all possible values of the local optical/Faraday thickness of the plasma. Results. We performed a comprehensive code verification by solving a number of well-known test problems using RAPTOR and comparing its output to exact solutions. We also demonstrate convergence with existing polarized radiative-transfer codes in the context of complex astrophysical problems, where we found that the integrated flux densities for all Stokes parameters converged to excellent agreement. Conclusions. The RAPTOR code is capable of performing polarized radiative transfer in arbitrary, highly curved spacetimes. This capability is crucial for interpreting polarized observations of accreting black holes, which can yield information about the magnetic-field configuration in such accretion flows. The efficient formalism implemented in RAPTOR is computationally light and conceptually simple. The code is publicly available.

Space-Time Patterns, Change, and Propagation of COVID-19 Risk Relative to the Intervention Scenarios in Bangladesh.

The novel coronavirus (COVID-19) pandemic continues to be a significant public health threat worldwide, particularly in densely populated countries such as Bangladesh with inadequate health care facilities. While early detection and isolation were identified as important non-pharmaceutical intervention (NPI) measures for containing the disease spread, this may not have been pragmatically implementable in developing countries due to social and economic reasons (i.e., poor education, less public awareness, massive unemployment). Hence, to elucidate COVID-19 transmission dynamics with respect to the NPI status—e.g., social distancing—this study conducted spatio-temporal analysis using the prospective scanning statistic at district and sub-district levels in Bangladesh and its capital, Dhaka city, respectively. Dhaka megacity has remained the highest-risk “active” cluster since early April. Lately, the central and south eastern regions in Bangladesh have been exhibiting a high risk of COVID-19 transmission. The detected space-time progression of COVID-19 infection suggests that Bangladesh has experienced a community-level transmission at the early phase (i.e., March, 2020), primarily introduced by Bangladeshi citizens returning from coronavirus epicenters in Europe and the Middle East. Potential linkages exist between the violation of NPIs and the emergence of new higher-risk clusters over the post-incubation periods around Bangladesh. Novel insights into the COVID-19 transmission dynamics derived in this study on Bangladesh provide important policy guidelines for early preparations and pragmatic NPI measures to effectively deal with infectious diseases in resource-scarce countries worldwide.

In-building coverage of millimeter-wave wireless networks from channel measurement and modeling perspectives

To progress cost-effective deployment of millimeter-wave (mmWave) wireless networks for indoor users, the prediction of indoor-to-indoor (I2I) and outdoor-to-indoor (O2I) coverage based on field measurement studies is of great interest to the future generation mobile communication system. First, measurements in I2I and O2I scenarios, which have advantages in terms of achieving a fair comparison of channel characteristics across different mmWave bands and bandwidths, are performed. Next, the developed dual-slope path loss model with a break-point distance is found to well fit omnidirectional and directional measured I2I data, especially at 39.5 GHz, revealing that the transition from lit or shadow regions to totally blocked regions is abrupt. Combined with space-time propagation characteristics, the indoor blockage effect on path loss and angular spread is investigated, therein being essential for the design of beam-steering and tracking algorithms. Double-directional measurement results show that most dominant paths arrive along the line-of-sight path, and only a few in-building reflections can be detected in higher frequency bands. Based on the joint analysis of channel measurement and modeling results, several mmWave network design and in-building coverage enhancement insights are presented.

Perturbative polymer quantum field theory and high energy scalar propagator

We advance a proposal of perturbative polymer field theory motivated by the study of the high energy regime of scalar propagator in flat spacetime. To do so we revisit the model by Hossain, Husain and Seahra (HHS) with the field modes taken as polymer harmonic oscillators. In momentum basis, the mode Hamiltonian is a pendulum formed by a rotor plus a trigonometric potential which contains a discrete polymer scale. Mode frequencies much greater than the inverse squared of the polymer scale allow to treat the potential term as a perturbation. Using a Hamiltonian scheme we show the field two-point function acquires corrections over the mechanical rotors both through energy spectrum as well as wave functions. Then we implement an alternative, yet equivalent, path integral scheme for the same field quantity expressed in terms of the mechanical rotor propagator and its corresponding two-point function which also get perturbative corrections. Our approaches can be performed systematically to arbitrary order; previous results are regained at lowest non trivial (second) order. In this way our work provides a different interpretation of HHS model which was developed on the basis of Mathieu functions. Moreover, they pave the way to extensions beyond quadratic operators that can allow the study of interacting fields. These require further work not done here however. Finally we summarize our results.