Field In Spacetime Research Articles

Revisiting vacuum energy in compact spacetimes

We revisit the calculation of vacuum energy density in compact spacetimes. For the general case of k compact spatial dimensions in p+k dimensional Minkowski spacetime, we calculate the Casimir force on a piston placed in the presence of external electromagnetic fields. We observe that while the presence of a strong external magnetic field reduces the intensity of the Casimir force, the presence of an electric field enhances it instead. We discuss various physical cases and also derive the particle production rate in the presence of such external fields in compact spacetimes. We observe that the pair production rate is enhanced in the presence of a piston.

Perturbative path-integral of string fields and the A∞ structure of the BV master equation

Abstract The perturbative path-integral gives a morphism of the (quantum) A∞ structure intrinsic to each quantum field theory, which we show explicitly on the basis of the homological perturbation. As is known, in the Batalin–Vilkovisky (BV) formalism, any effective action also solves the BV master equation, which implies that the path-integral can be understood as a morphism of the BV differential. Since each solution of the BV master equation is in one-to-one correspondence with a quantum A∞ structure, the path-integral preserves this intrinsic A∞ structure of quantum field theory, where A∞ reduces to L∞ whenever multiplications of space-time fields are graded commutative. We apply these ideas to string-field theory and (re-)derive some quantities based on the perturbative path-integral, such as effective theories with finite α′, reduction of gauge and unphysical degrees, the S-matrix, and gauge-invariant observables.

Mode-sum prescription for the renormalized stress energy tensor on black hole spacetimes

In this paper, we describe an extremely efficient method for computing the renormalized stress-energy tensor of a quantum scalar field in spherically-symmetric black hole spacetimes. The method applies to a scalar field with arbitrary field parameters. We demonstrate the utility of the method by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime, applying our results to discuss the null energy condition and the semi-classical backreaction.

Holographic reconstruction of asymptotically flat spacetimes

Here, we present a “holographic” reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the “future boundary” of the spacetime, namely future null infinity [Formula: see text]. It is holographic in the sense that there exists a one-to-one correspondence between correlation functions of a massless field in four-dimensional spacetime [Formula: see text] and those of another massless field living in three-dimensional null boundary [Formula: see text]. The idea is to first reconstruct the bulk metric [Formula: see text] by “inverting” the bulk correlation functions and re-express the latter in terms of boundary correlators via the correspondence. This effectively allows asymptotic observers close to [Formula: see text] to reconstruct the deep interior of the spacetime using only correlation functions localized near [Formula: see text].

Renormalization group improvement of the effective potential in a (1 + 1) dimensional Gross-Neveu model

In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective potential and the study of Dynamical Symmetry Breaking (DSB) in an Gross-Neveu (GN) model with N fermions fields in (1+1) dimensional space-time, which can be applied as a model to describe certain properties of the polyacetylene. The classical Lagrangian of the model is scale invariant, but radiative corrections to the effective potential can lead to dimensional transmutation, when a dimensionless parameter (coupling constant) of the classical Lagrangian is exchanged for a dimensionful one, a dynamically generated mass for the fermion fields. For the model we are considering, perturbative calculations of the effective potential and renormalization group functions up to three loops are available, but we use the RGE and the leading logs approximation to calculate an improved effective potential, including contributions up to six loops orders. We then perform a systematic study of the general aspects of DSB in the GN model with finite N, comparing the results we obtain with the ones derived from the original unimproved effective potential we started with.

A Note for Estimation About Average Differential Entropy of Continuous Bounded Space‐Time Random Field

In this paper, we mainly study the discrete approximation about average differential entropy of continuous bounded space-time random field. The estimation of differential entropy on random variable is a classic problem, and there are many related studies. Space-time random field is a theoretical extension of adding random variables to space-time parameters, but studies on discrete estimation of entropy on space-time random field are relatively few. The differential entropy forms of continuous bounded space-time random field and discrete estimations are discussed, and three estimation forms of differential entropy in the case of random variables are generated in this paper. Furthermore, it is concluded that under the condition that the entropy estimation formula after space-time segmentation converges with probability 1, the average entropy in the bounded space-time region can also converge with probability 1, and three generalized entropies are verified respectively. In addition, we also carried out numerical experiments on the convergence of average entropy estimation based on parameters, and the numerical results are consistent with the theoretical results, which indicting further study of the average entropy estimation problem of space-time random fields is significant in the future.

Almost Price's law in Schwarzschild and decay estimates in Kerr for Maxwell field

We consider the asymptotics of a Maxwell field in Schwarzschild and Kerr spacetimes. In a Kerr spacetime, we utilize the basic energy and Morawetz estimates proven in earlier work to derive pointwise estimates where the total power of decay rate for all components of the Maxwell field towards a stationary solution is −7/2. Moreover, on a Schwarzschild background, if the constructed Newman–Penrose constant vanishes (or does not vanish), we prove almost sharp Price's law decay v−2−sτ−3+s+ (or v−2−sτ−2+s+) for Maxwell field and v−2−sτ−2+s−ℓ0+ (or v−2−sτ−1+s−ℓ0+) for the ℓ≥ℓ0 modes of the field towards a static solution, with s being the spin weight of the Newman–Penrose components of Maxwell field. All estimates are uniform in the exterior of the black hole.

On the concept of infinitesimal position vector fields in Galilean spacetimes

We introduce two different ways to establish the concept of infinitesimal position vector field between “infinitesimally nearby” observers in a Galilean spacetime as well as show their mathematical equivalence. We also use this concept to characterize the family of spatially conformally Leibnizian spacetimes.

Quantum vortex instability and black hole superradiance

Vortices and black holes set the scene for many interesting dynamical processes in physics. Here, we study the dynamical instability of quantized vortices and rotational superradiance around rotating black holes, illustrating in the process that the same physics is at play in these two seemingly disparate phenomena. We also compare the instability of the vortex to the black hole bomb instability, which occurs for massive scalar fields in the Kerr spacetime. Taking inspiration from the analogy between black hole bomb modes and the hydrogen spectrum, the vortex instability is compared with nuclear resonances involved in $\ensuremath{\alpha}$ decay.

The self-interacting Dirac fields in FLRW spacetime

We prove the existence of global in time solution with the small initial data for the semilinear equation of the spin-\(\frac{1}{2}\) particles in the Friedmann–Lemaître–Robertson–Walker spacetime. Moreover, we also prove that if the initial function satisfies the Lochak–Majorana condition, then the global solution exists for arbitrary large initial value. The solution scatters to free solution for large time. The mass term is assumed to be complex-valued. The conditions on the imaginary part of mass are discussed by proving nonexistence of the global solutions if certain relation between scale function and the mass are fulfilled.

Fluctuations in the stress energy tensor of spinor fields evolving in general FRW spacetimes

In this work, we study quantum fluctuations in the stress energy tensor of spinor fields evolving in general FRW spacetimes. We quantify these fluctuations by the noise kernel of spinor fields. For the particular case of de Sitter spacetime, we place the spinor field in what is called the fermionic Bunch Davies vacuum and study the variation of the noise kernel with the mass of the field. We then make use of the conformal invariance of massless spinor fields and employ an equivalence that relates a massless spinor field in any given FRW spacetime with a corresponding massless spinor field in de Sitter spacetime. Using this equivalence, we study the behaviour of the noise kernel of massless spinor fields in general FRW spacetimes while placing the fields in the Bunch Davies vacuum of the corresponding massless spinor field of the de Sitter spacetime. We extend this analysis to the coordinate invariant quantity of the energy energy correlator. We compare these results for spinor fields in considered spacetimes with the analogous results for scalar fields. This study helps us better understand whether the spin 1/2 fermionic matter remains strongly correlated in considered spacetimes leading to considerable backreaction or not.

A discrete-adjoint framework for optimizing high-fidelity simulations of turbulent reacting flows

An adjoint-based framework is presented that measures exact sensitivity from high-fidelity simulations of turbulent reacting flows. The framework leverages and extends state-of-the-art numerical methods in a manner that is compatible with a discrete adjoint solver. To ensure energy stability and accuracy, high-order narrow-stencil finite-difference operators satisfying the summation-by-parts (SBP) property are combined with simultaneous-approximation-term boundary treatment. An adaptive SBP dissipation operator and its corresponding adjoint are formulated in a way to dampen unresolved modes and preserve scalar boundedness. A flamelet/progress variable approach is employed to handle chemical reactions using tabulated chemistry. The utility of using pre-computed lookup tables is that discrete adjoint sensitivity can be computed efficiently for arbitrary chemical mechanisms. Gradient-based optimization utilizing the sensitivity obtained from the adjoint solution is demonstrated on two configurations. First, momentum actuation is applied upstream in a spatial mixing layer to control the evolution of a passive scalar in a target region downstream. Then, the framework is used to optimize an acoustic actuator in a three-dimensional turbulent jet with the aim of anchoring an H2 lifted flame at a target location. Both cases involve manipulating discrete space-time fields with O(108)−O(109) degrees of freedom, which would not be possible via a brute-force trial-and-error approach.

Two-color laser PEEM imaging of horizontal and vertical components of femtosecond surface plasmon polaritons

Explicit visualization of different components of surface plasmon polaritons (SPPs) propagating at dielectric/metal interfaces is crucial in offering chances for the detailed design and control of the functionalities of plasmonic nanodevices in the future. Here, we reported independent imaging of the vertical and horizontal components of SPPs launched from a rectangular trench in the gold film by a 400-nm laser-assisted near-infrared (NIR) femtosecond laser time-resolved photoemission electron microscopy (TR-PEEM). The experiments demonstrate that distinct imaging of different components of SPPs field can be easily achieved by introducing the 400-nm laser. It can circumvent the risk of sample damage and information loss of excited SPPs field that is generally confronted in the usual NIR laser TR-PEEM scheme. The underlying mechanism for realizing distinct imaging of different components of the SPPs field with two-color PEEM is revealed via measuring the double logarithmic dependence of photoemission yield with the 800-nm and 400-nm pulse powers of different polarizations. Moreover, it is found that the PEEM image quality of the vertical and horizontal components of the SPPs field is nearly independent of the 400-nm pulse polarization. These results pave a way for SPPs-based applications and offer a possible solution for drawing a space–time field of SPPs in three dimensions.

Real-space Bell inequalities in de Sitter

Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as cosmological density fluctuations. In this work, we show how Bell operators can be constructed for quantum fields in real space, and for Gaussian states we compute their expectation value in terms of the field power spectra. We then apply our formalism to a scalar field in de-Sitter space-time. We find that, in spite of the tremendous production of entangled particles with opposite wave momenta on large scales, Bell inequalities are not violated in real space. The reason is that, when considering measurements of a field at two distinct locations in real space, one implicitly traces over the configuration of the field at every other location, leading to a mixed bipartite system. This “effective decoherence” effect is responsible for the erasure of quantum features, and casts some doubts on our ability to reveal the quantum origin of cosmological structures. We finally discuss these results in the light of quantum discord.

A Dynamical Systems Perspective to Characterize the El Niño Diversity in Spatiotemporal Patterns

El Niño is the long-lasting anomalous warming of sea surface temperature (SST) and surface air temperature (SAT) over the tropical Pacific. Each El Niño event has its unique impact on the overlaying atmosphere, where the warming exhibits diversity in spatiotemporal patterns. It still remains an open question for discriminating the El Niño diversity, since the single area-averaging SST index often fails to distinguish the impact of the event diversity, which is partially due to the nonlinear and non-uniform variations of the warming patterns. Here, we introduced the Dynamical Systems metrics (DSMs) to measure instantaneous dimensions and persistence of the SAT warming patterns over the tropical Pacific. Our results show that different SAT warming patterns can be discriminated by their corresponding values of dimension and persistence, then the central Pacific and eastern Pacific El Niño events can be discriminated by DSM. Particularly, through the analyses of El Niño events, we can interpret the physical meaning of DSM parameters applied to the space-time SAT field: an instantaneous dimension reflects whether the sub-regions of the SAT field are consistently varying and to what degree the spatial pattern of anomalies is homogeneous, while the instantaneous persistence indicates how long an anomalous SAT pattern can be maintained. This work analyzes the spatiotemporal variability of El Niño from a dynamical system perspective, and DSM may also serve as a useful tool to study extreme events related to SST anomalies.

Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem

The renormalization of the vacuum energy in quantum field theory (QFT) is usually plagued with theoretical conundrums related not only with the renormalization procedure itself, but also with the fact that the final result leads usually to very large (finite) contributions incompatible with the measured value of Lambda in cosmology. As a consequence, one is bound to extreme fine-tuning of the parameters and so to sheer unnaturalness of the result and of the entire approach. We may however get over this adversity using a different perspective. Herein, we compute the zero-point energy (ZPE) for a nonminimally coupled (massive) scalar field in FLRW spacetime using the off-shell adiabatic renormalization technique employed in previous work. The on-shell renormalized result first appears at sixth adiabatic order, so the calculation is rather cumbersome. The general off-shell result yields a smooth function rho _{mathrm{vac}}(H) made out of powers of the Hubble rate and/or of its time derivatives involving different (even) adiabatic orders sim H^N (N=0, 2,4,6,ldots ), i.e. it leads, remarkably enough, to the running vacuum model (RVM) structure. We have verified the same result from the effective action formalism and used it to find the beta -function of the running quantum vacuum. No undesired contributions sim m^4 from particle masses appear and hence no fine-tuning of the parameters is needed in rho _{mathrm{vac}}(H). Furthermore, we find that the higher power sim H^6 could naturally drive RVM-inflation in the early universe. Our calculation also elucidates in detail the equation of state of the quantum vacuum: it proves to be not exactly -1 and is moderately dynamical. The form of rho _{mathrm{vac}}(H) at low energies is also characteristic of the RVM and consists of an additive term (the so-called ‘cosmological constant’) together with a small dynamical component sim nu H^2 (|nu |ll 1). Finally, we predict a slow (sim ln H) running of Newton’s gravitational coupling G(H). The physical outcome of our semiclassical QFT calculation is revealing: today’s cosmic vacuum and the gravitational strength should be both mildly dynamical.

The space-time structure of turbulence for lidar-assisted wind turbine control

Lidar-assisted wind turbine control has been proven to be beneficial for turbine load reduction. It relies on the preview of incoming turbulence provided by a nacelle lidar, which allows the turbine controller to react to the flow disturbances before their impact on the turbine. When assessing its benefits, previous studies mainly use the standard turbulence parameters suggested by the IEC 61400-1 standard and assume Taylor's frozen hypothesis. Based on atmospheric turbulence observations, the parameters of the Mann spectral turbulence model differ significantly from the values recommended in the standard, and they vary, e.g., with atmospheric stability. Also, turbulence evolution from upstream to the rotor position conflicts with the frozen turbulence hypothesis, and its effect on the preview quality by a nacelle lidar still needs quantification. This work presents a simple method to extend the Mann model to account for the temporal evolution of turbulence using a space-time spectral velocity tensor. Under various atmospheric stability conditions, we derive the space-time tensor parameters and evaluate the space-time tensor using data from a five-beam lidar and a meteorological mast, we found good agreement between the space-time tensor and the measurement data. In addition, a numerical method for simulating a four-dimensional (4D) space-time velocity field based on the space-time tensor is presented. In the end, we analyze the importance of including the temporal evolution of turbulence for assessing lidar wind preview quality.

Analytical field equation and wave function solutions of the Bianchi type I universe in vacuum f(R) gravity

It has been proposed that f(R) gravity is a viable proxy for General Relativity and a means for an alternative to dark energy. Within this context, we present the analytical solutions to the Bianchi type I universe. For this spacetime, the Killing and homothetic vector fields categorize the space into fourteen classes. Noether’s theorem is used to determine the first integrals associated with each isometry for every class and we use the geometry of the Noether point symmetries of the space to establish potential functions. We also quantize the Lagrangian of the spacetime to derive the Wheeler–DeWitt equation and successively determine invariant solutions for the wave function of the universe from the Lie point symmetries admitted by the equation. Finally, for all cases, exact classical solutions to the field equations are found.

Relativistic motions of spin-zero quantum oscillator field in a global monopole space-time with external potential and AB-effect

In this paper, we analyze a spin-zero relativistic quantum oscillator in the presence of the Aharonov–Bohm magnetic flux in a space-time background produced by a point-like global monopole (PGM). Afterwards, we introduce a static Coulomb-type scalar potential and subsequently with the same type of vector potential in the quantum system. We solve the generalized Klein–Gordon oscillator analytically for different functions (e.g. Coulomb- and Cornell-type functions) and obtain the bound-states solutions in each case. We discuss the effects of topological defects associated with the scalar curvature of the space-time and the Coulomb-type external potentials on the energy profiles and the wave function of these oscillator fields. Furthermore, we show that the obtained energy eigenvalues depend on the magnetic quantum flux which gives rise to the gravitational analogue of the Aharonov–Bohm (AB) effect.

ROTATED EMPIRICAL ORTHOGONAL FUNCTION ANALYSIS FOR SPATIO-TEMPORAL DATA ANALYSIS

Given any space-time field, Empirical orthogonal function (EOF) analysis finds a set of orthogonal spatial patterns along with a set of associated uncorrelated time series or principal components (PCs). Spatial orthogonality and temporal uncorrelation of EOFs and PCs respectively impose limits on the physical interpretability of EOF patterns. This is because physical processes are not independent, and therefore physical modes are expected in general to be non-orthogonal. Rotated empirical orthogonal functions (REOF) were introduced to generate general localized structures by compromising some of the EOF properties such as orthogonality. EOF and REOF analysis are carried out for the significant wave height (SWH) data for the Bay of Bengal (BOB) region for the period 1958 to 2001. Separate experiments were conducted for all the months together and also for July and December representing the southwest and northeast monsoon periods. The first eigenmodes account for 84%, 68%, and 59% of the total variability for the above three cases respectively. The REOF proved to be more effective than EOF for the above region.