Scalar Field Research Articles

Incorporating interface effects into multi-material topology optimization by improving interface configuration: An energy-based approach

Interfaces between structural multi-materials generally exhibit asymmetric resistance to tension and compression. Given this interface behavior, this work suggests an energy-based approach to improve the interface configuration for multi-material topology optimization. Based on the strain spectral decomposition, we decompose the structural elastic strain energy into tensile and compressive portions. In the density-based topology optimization framework, we use the gradient-based method to track the interface between multiple materials. Then, we construct an interface-associated scalar field to penalize the tensile portion of the strain energy, causing a pseudo-degradation of the strain energy at the interface region. Finally, within limited material usages and by minimizing the linear weighted structural strain energy and its pseudo-degradation, multi-material topology optimization with improved interface configuration is achieved. Several 2D and 3D numerical examples are investigated, by which the effectiveness and robustness of the suggested approach are fairly validated.

Superradiance of rotating black holes surrounded by dark matter

In rotating black hole background surrounded by dark matter, we investigated the super-radiant phenomenon of massive scalar field and its associated instability. Using the method of asymptotic matching, we computed the amplification factor of scalar wave scattering to assess the strength of super-radiance. We discussed the influence of dark matter density on amplification factor in this black hole background. Our result indicates that the presence of dark matter has suppressive influence on black hole super-radiance. We also computed the net extracted energy to further support this result. Finally, we analyzed the super-radiant instability caused by massive scalar field using the black hole bomb mechanism and found that the presence of dark matter has no influence on the super-radiant instability condition.

Symmetry-resolved entanglement entropy for local and non-local QFTs

In this paper, we investigate symmetry-resolved entanglement entropy (SREE) in free bosonic quantum many-body systems. Utilizing a lattice regularization scheme, we compute symmetry-resolved Rényi entropies for free complex scalar fields and a specific class of non-local field theories, where entanglement entropy (EE) exhibits volume-law scaling. We present effective and approximate eigenvalues for the correlation matrix used in computing SREE and demonstrate their consistency with numerical results. Furthermore, we explore the equipartition of EE, verifying its effective behavior in the massless limit. Finally, we comment on EE in non-local quantum field theories and provide an explicit expression for the symmetry-resolved Rényi entropies.

Stability analysis of the cosmological dynamics of O(D, D)-complete stringy gravity

The massless fields in the universal NS-NS sector of string theory form O(D, D) multiplets of Double Field Theory, which is a theory that provides a T-duality covariant formulation of supergravity, leading to a stringy modification of General Relativity. In this framework, it is possible to write down the extensions of the Einstein field equations and the Friedmann equations in such a way that the coupling of gravitational and matter sectors is dictated by the O(D, D) symmetry universally. In this paper, we obtain the autonomous form of the O(D, D)-complete Friedmann equations, find the critical points and perform their stability analysis. We also include the phase portraits of the system. Cosmologically interesting cases of scalar field, radiation, and matter are separately considered and compared with the Chameleon models in a similar setting. Accelerating phases and the conditions for their existence are also given for such cases.

Position dependent mass dissipative scalar field at finite temperature

Position dependent mass dissipative scalar field is a theoretical framework that combines the concepts of position-dependent mass and dissipative systems in the context of scalar field theory. In this framework, the mass of the scalar field is allowed to vary with position, leading to interesting physical phenomena such as non-locality and non-Hermiticity. We consider a generalized classical Lagrangian for the system and by developing a theoretical formulation, quantized system canonically. In follow, two-point correlation functions of the system is obtained at finite temperature and Free energy of the system is calculated in terms of Matsubara frequencies. This research can provide insights into the behavior of particles and fields in non-uniform environments, and has potential applications in various fields of physics.

Quasinormal mode of Schwarzschild black hole with geometric correction

We investigated the quasinormal modes (QNMs) for scalar, Dirac and electromagnetic fields of a Schwarzschild black hole with geometric corrections. In addition to the inherent modes of the Schwarzschild black hole, we discovered the existence of purely imaginary modes induced by the geometric corrections, which dominated the behavior of the perturbation when geometric corrections were pretty small. Notably, we found that these purely imaginary modes are prominent, and their imaginary parts are proportional to the correction parameter ϵ. We also explored the large-l limit using the WKB approximation for scalar field. This opens up the possibility of observed geometric corrections in the future.

Asymptotic decay and quasinormal frequencies of scalar and Dirac fields around dilaton-de Sitter black holes

We study the decay of Dirac and massive scalar fields at asymptotically late times in the background of the charged asymptotically de Sitter dilatonic black holes. It is shown that the asymptotic decay is exponential and oscillatory for large and intermediate mass of the field, while for zero and small mass it is pure exponential without oscillations. This reflects the dominance of quasinormal modes of the empty de Sitter spacetime at asymptotically late times. We also show that the earlier WKB calculation of the massive scalar field spectrum does not allow one to find the fundamental mode with reasonable accuracy.

Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.

Reconstruction of the Dark Energy Scalar Field Potential by Gaussian Process

Dark energy is believed to be responsible for the acceleration of the Universe. In this paper, we reconstruct the dark energy scalar field potential V(ϕ) using the Hubble parameter H(z) through Gaussian process analysis. Our goal is to investigate dark energy using various H(z) data sets and priors. We find that the selection of the prior and the H(z) data set significantly affects the reconstructed V(ϕ). We compare two models, Power Law and Free Field, to the reconstructed V(ϕ) by computing the reduced chi-square. The results suggest that the models are generally in agreement with the reconstructed potential within a 3σ confidence interval, except in the case of Observational H(z) data with the Planck 18 prior. Additionally, we simulate H(z) data to measure the effect of increasing the number of data points on the accuracy of reconstructed V(ϕ). We find that doubling the number of H(z) data points can improve the accuracy rate of reconstructed V(ϕ) by 5%–30%.

Interaction of a black hole with scalar field in cosmology background

Recent data from elliptical galaxies indicate that the growth in the masses of black holes exceeds what is expected from the accretion of surrounding matter, and this growth appears to be dependent on the expansion of the universe. This phenomenon can be explained by considering the accretion of dark energy, which is responsible for cosmological expansion, into these black holes. In this paper, we investigate the perturbative interaction of a black hole with a real scalar field ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} (which can represent dark energy) in a cosmological background using an appropriate metric. We derive solutions for the field ϕ(t,r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi (t, r)$$\\end{document}, the black hole mass M(t), and the expansion rate H(t), and discuss the behaviour of the scalar field ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} in the vicinity of the black hole, with respect to exterior and interior observers.

Entanglement harvesting and quantum discord of alpha vacua in de Sitter space

The CPT invariant vacuum states of a scalar field in de Sitter space, called α-vacua, are not unique. We explore the α-vacua from the quantum information perspective by a pair of static Unruh-DeWitt (UDW) detectors coupled to a scalar field with either monopole or dipole coupling, which are in time-like zero separation or space-like antipodal separation. The analytical form of the reduced final state of the UDW detector is derived. We study the entanglement harvesting and quantum discord of the reduced state, which characterize the quantum entanglement and quantum correlation of the underlying α-vacua, respectively. Our results imply that the quantum entanglement gravitated by de Sitter gravity behaves quite differently for time-like and space-like separations. It experiences “sudden death” for the former and grows for the latter as the measuring time or the value of α increases. This demonstrates the nonlocal nature of quantum entanglement. For the quantum discord, we find no “sudden death” behavior, and it experiences superhorizon suppression, which explains the superhorizon decoherence in the inflationary universe scenario. Overall, the time-like or space-like quantum entanglement and correlation behave differently on their dependence of α, measuring time and spectral gaps, with details discussed in this work.

On the (in)consistency of perturbation theory at finite temperature

A well-known difficulty of perturbative approaches to quantum field theory at finite temperature is the necessity to address theoretical constraints that are not present in the vacuum theory. In this work, we use lattice simulations of scalar correlation functions in massive ϕ4 theory to analyse the extent to which these constraints affect the perturbative predictions. We find that the standard perturbative predictions deteriorate even in the absence of infrared divergences at relatively low temperatures, and that this is directly connected to the analytic structure of the propagators used in the expansion. This suggests that the incorporation of non-perturbative thermal effects in the propagators is essential for a consistent perturbative formulation of scalar quantum field theories at finite temperature. By utilising the spectral constraints imposed on finite-temperature correlation functions, we explore how these effects manifest themselves in the lattice data, and discuss why the presence of distinct thermoparticle excitations provides a potential resolution to these issues.

Coleman-Weinberg dynamics of ultralight scalar dark matter and GeV-scale right-handed neutrinos

We consider an extension of the Standard Model by three singlet fermions and one singlet real scalar field. The scalar is an ultralight dark matter candidate whose abundance is set by dynamically induced misalignment from the Higgs portal. We focus on parameter space where the Coleman-Weinberg potential both fixes the dark matter relic abundance, and predicts the mass scale of right-handed neutrinos. The model prefers scalar masses in the range of 10 μeV ≲ mϕ ≲ 10 meV, and can be tested via direct searches for a light scalar (e.g. fifth force tests), or by searching for right-handed neutrinos in laboratory experiments.

Scalar field perturbation of hairy black holes in EsGB theory

We investigate scalar field perturbations of the hairy black holes involved with spontaneous symmetry breaking of the global U(1) symmetry in Einstein-scalar-Gauss-Bonnet theory for asymptotically flat spacetimes. We consider the mechanism that black holes without hairs become unstable at the critical point of the coupling constant and undergo a phase transition to hairy black holes in the symmetry-broken phase driven by spontaneous symmetry breaking. This transition occurs near the black hole horizon due to the diminishing influence of the Gauss-Bonnet term at infinity. To examine such process, we introduce a scalar field perturbation on the newly formed background spacetime. We solve the linearized perturbation equation using Green’s function method. We begin by solving the Green’s function, incorporating the branch cut contribution. This allows us to analytically investigate the late-time behavior of the perturbation at both spatial and null infinity. We found that the late-time behavior only differs from the Schwarzschild black hole by a mass term. We then proceed to calculate the quasinormal modes (QNMs) numerically, which arise from the presence of poles in the Green’s function. Our primary interest lies in utilizing QNMs to investigate the stability of the black hole solutions both the symmetric and symmetry-broken phases. Consistent with the prior study, our analysis shows that hairy black holes in the symmetric phase become unstable when the quadratic coupling constant exceeds a critical value for a fixed value of the quartic coupling constant. In contrast, hairy black holes in the symmetry-broken phase are always stable at the critical value. These numerical results provide strong evidence for a dynamical process that unstable black holes without hairs transition into stable hairy black holes in the symmetry-broken phase through the spontaneous symmetry breaking.

Thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity

In this study, we examined the thermal fluctuations, deflection angle, and greybody factor of a high-dimensional Schwarzschild black hole in scalar–tensor–vector gravity (STVG). We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities. By analyzing the changes in the corrected specific heat, we found that thermal fluctuations made the small black hole more stable. It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole. Additionally, by utilizing the Gauss–Bonnet theorem, the deflection angle was obtained in the weak field limit, and the effects of the two parameters on the results were visualized. Finally, we calculated the bounds on the greybody factor of a massless scalar field. We observed that as the STVG parameter around the black hole increased, the weak deflection angle became larger, and more scalar particles can reach infinity. However, the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.

Scalar field solutions and energy bounds for modeling spatial oscillations in Schwarzschild black holes based on the Regge–Wheeler equation

This text discusses the behavior of solutions and the energy stability within Schwarzschild spacetimes, with a particular emphasis on the behavior of massless scalar fields under the influence of a non-rotating and spherically symmetric black hole. The stability of solutions in the proximity of the event horizon of black holes in general relativity remains an open question, especially given the difficulties introduced by minor perturbations that may resemble Kerr solutions. To address this, this work explores a simplified model, including massless scalar fields, to better understand perturbation behaviors around black holes under the Schwarzschild approach. We depart from Richard Price’s work in connection with how scalar, electromagnetic, and gravitational fields behave. The tortoise coordinate transformation is considered to set the stage for numerical solutions to the wave equations. Afterward, we explore energy estimates, which are used to gauge stability and wave behavior over time. Our analysis reveals that the time evolution of the energy does not exceed twice its initial value. Further and under the assumption of initial conditions in L2−spaces, we obtain an exponential decreasing behavior in the energy time evolution. A question to continue exploring is how perturbations in L2 in the initial conditions that introduce Kerr solutions as a second-order effect in the linearized equations perturb this obtained exponential decay.

Gravitational radiation in generalized Brans–Dicke theory: compact binary systems

This paper investigates the generation and properties of gravitational radiation within the framework of generalized Brans–Dicke (GBD) theory, with a specific emphasis on its manifestation in compact binary systems. The study begins by examining the weak field equations in GBD theory, laying the foundation for subsequent analyses. Solutions to the linearized field equations for point particles are then presented, providing insights into the behavior of gravitational fields in the context of GBD theory. The equation of motion of point mass is explored, shedding light on the dynamics of compact binary systems within the GBD framework. The primary focus of this study lies in the comprehensive exploration of gravitational radiation generated by compact binaries. The energy momentum tensor and the associated gravitational wave (GW) radiation power in GBD theory are investigated, elucidating the relationship between these fundamental concepts. Furthermore, detailed calculations are provided for the GW radiation power originating from both tensor fields and scalar fields. Based on our calculations, both scalar fields contribute to GW radiation by producing dipole radiation. We also study the period derivative of compact binaries in this theory. By comparing with the observational data of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307, we put bounds on the two parameters of the theory: the Brans–Dicke coupling parameter ω0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{0}$$\\end{document} and the mass of geometrical scalar field mf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_f$$\\end{document}, resulting in a lower bound ω0>6.09723×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{0}>6.09723\ imes 10^6$$\\end{document} for a massless BD scalar field and the geometrical field whose mass is smaller than 10-29GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-29} \ ext { GeV}$$\\end{document}. The obtained bound on ω0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _0$$\\end{document} is two orders of magnitude stricter than those derived from solar system data. Finally, we find the phase shift that GWs experience in the frequency domain during their propagation. These calculations offer a quantitative understanding of the contributions from different components within the GBD theory, facilitating a deeper comprehension of the overall behavior and characteristics of gravitational radiation.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime* *Supported by the National Natural Science Foundation of China (11925503) and the Guangdong Major project of Basic and Applied Basic Research (2019B030302001). The computation is completed on the HPC Platform of Huazhong University of Science and Technology

We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime. Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field. Through our numerical results, we obtain a formula that determines critical amplitude in terms of cosmological constant Λ: , where σ denotes the initial width of the scalar field and is the initial position of the scalar field. Notably, we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.

Capacity of entanglement for scalar fields in squeezed states

We study various aspects of capacity of entanglement in the squeezed states of a scalar field theory. This quantity is a quantum informational counterpart of heat capacity and characterizes the width of the eigenvalue spectrum of the reduced density matrix. In particular, we carefully examine the dependence of capacity of entanglement and its universal terms on the squeezing parameter in the specific regimes of the parameter space. Remarkably, we find that the capacity of entanglement obeys a volume law in the large squeezing limit. We discuss how these results are consistent with the behavior of other entanglement measures including entanglement and Renyi entropies. We also comment on the existence of consistent holographic duals for a family of Gaussian states with generic squeezing parameter based on the ratio of entanglement entropy and the capacity of entanglement. Published by the American Physical Society 2024

A scalar field theory of 1+1-dimensional laser wakefield accelerators

Abstract A relativistic non-linear scalar field theory is developed from a 2+2-dimensional decomposition of the cold plasma field equations, and the theory is used to investigate a 1+1-dimensional description of a laser wakefield accelerator. The relationship between the properties of a compact laser pulse and its wake is explored. Non-linear solutions are sought describing a regular (i.e. unbroken) wake driven by a prescribed rectangular circularly-polarised laser pulse. An upper bound on the dimensionless amplitude a 0 of the laser pulse is determined as a function of the phase speed v of the wake. The asymptotic behaviour of the upper bound on a 0 as v → c is shown to agree with well-established, but approximate, results obtained using the conventional encoding of the plasma degrees of freedom. Our approach leads to a closed-form expression for the upper bound on a 0 which is exact for all values of the phase speed of the wake, unlike conventional results that are applicable only when v is sufficiently close to c.