Scalar Field Research Articles

Digital quantum simulation of cosmological particle creation with IBM quantum computers

We use digital quantum computing to simulate the creation of particles in a dynamic spacetime. We consider a system consisting of a minimally coupled massive quantum scalar field in a spacetime undergoing homogeneous and isotropic expansion, transitioning from one stationary state to another through a brief inflationary period. We simulate two vibration modes, positive and negative for a given field momentum, by devising a quantum circuit that implements the time evolution. With this circuit, we study the number of particles created after the universe expands at a given rate, both by simulating the circuit and by actual experimental implementation on IBM quantum computers, consisting of hundreds of quantum gates. We find that state-of-the-art error mitigation techniques are useful to improve the estimation of the number of particles and the fidelity of the state.

Gravitational collapse to extremal black holes and the third law of black hole thermodynamics

We construct examples of black hole formation from regular, one-ended asymptotically flat Cauchy data for the Einstein–Maxwell-charged scalar field system in spherical symmetry which are exactly isometric to extremal Reissner–Nordström after a finite advanced time along the event horizon. Moreover, in each of these examples the apparent horizon of the black hole coincides with that of a Schwarzschild solution at earlier advanced times. In particular, our result can be viewed as a definitive disproof of the “third law of black hole thermodynamics.” The main step in the construction is a novel C^{k} characteristic gluing procedure, which interpolates between a light cone in Minkowski space and a Reissner–Nordström event horizon with specified charge to mass ratio \frac{e}{M} . Our setup is inspired by the recent work of Aretakis–Czimek–Rodnianski on perturbative characteristic gluing for the Einstein vacuum equations. However, our construction is fundamentally nonperturbative and is based on a finite collection of scalar field pulses which are modulated by the Borsuk–Ulam theorem.

Signum-gordon shock waves with spherical symmetry in (2+1) and (3+1) dimensions

Abstract This study introduces novel, exact solutions to the scalar field Signum-Gordon equation that feature a discontinuity near the light cone. These solutions, applicable in higher spatial dimensions (n > 1), extend previous limitations to one dimension. Our chosen ansatz leads to an ordinary equation with exact solutions obtained for n = 2 and 3 spatial dimensions. The shock wave’s energy trapped within the light cone is proportional to the wave’s n-dimensional volume and the field discontinuity at the wavefront. The investigation delves further into the behavior of shock waves when their driving force, represented by a delta function at the light cone, is disabled. Disabling this delta function disrupts energy transfer, preventing the wave’s propagation as predicted by analytical calculations. We identify the region within the light cones where the field remains unaffected. Two-dimensional (n = 2) simulations reveal the formation of intriguing structures upon source removal. These structures include a central, stable feature resembling an oscillon and a surrounding ring that breaks down into smaller oscillations.

Effective potential in leading logarithmic approximation in nonrenormalizable SO(N) scalar field theories

The study of the effective potential for nonrenormalizable scalar [Formula: see text] symmetric theories leads to recurrence relations for the coefficients of the leading logarithms due to the Bogoliubov–Parasiuk theorem. These relations can be transformed into generalized renormalization-group (RG) equation which can be solved exactly in the large-N limit.

Long lived quasinormal modes of regular and extreme black holes

Abstract Recently, black hole models in a nonlinear modification of the Maxwell electrodynamics were suggested, possessing simultaneously properties of an extreme charge and regularity \cite{Bronnikov:2024izh}. We study quasinormal modes of a massive scalar field around such black holes and show that they are characterized by a comparatively small damping rate, indicating the possible existence of arbitrarily long-lived quasinormal modes, called {\it quasi-resonances}.

Single and merger soliton dynamics in scalar field dark matter with and without self-interactions

Single and merger soliton dynamics in scalar field dark matter with and without self-interactions

Thermodynamics of stealth black holes

Using Euclidean methods we investigate the thermodynamics of stealth black hole solutions, which are solutions that geometrically are indistinguishable from those of general relativity; however, they are accompanied by a nontrivial additional field that does not backreact to the metric. We find that in general, one can observe shifts in the mass and/or the entropy of such black holes; hence, at least at the thermodynamic level, the stealth solutions may be distinguished by those of general relativity. We also point out an example, the , where a nontrivial scalar field can accompany an (A)dS-Schwarzschild black hole without altering the thermodynamic quantities. We point out that thermodynamic discrepancies arise due to the additional boundary terms emanating from the stealth fields, where care should be given in order for the theory at hand to possess a well-defined variational procedure. Published by the American Physical Society 2025

Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the ΛCDM model

The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing for the construction of modified theories of gravity, since one can take lessons from GR for an “educated guess” of the metric field equations; the field equations for the other fields are then fixed by the obtained Lagrangian (up to terms that are completely independent from the metric tensor). In the present paper, we apply variational bootstrapping to determine metric-affine models which are, in a variational sense, closest to the ΛCDM model of cosmology. Starting from an “educated guess” that formally resembles the Einstein field equations with a cosmological “constant” (actually, a scalar function built from the metric and the connection) and a dark matter term, the method then allows to find “corrected” metric equations and to “bootstrap” the connection field equations. Lagrangians obtained via this method, though imposing some restricting criteria, still encompass a wide variety of metric-affine models. In particular, they allow for a subclass of quadratic metric-affine theories restricted to linear terms in the curvature tensor.

Multi-Objective Optimization in Disaster Backup with Reinforcement Learning

Disaster backup, which occurs over long distances and involves large data volumes, often leads to huge energy consumption and the long-term occupation of network resources. However, existing work in this area lacks adequate optimization of the trade-off between energy consumption and latency. We consider the one-to-many characteristic in disaster backup and propose a novel algorithm based on multicast and reinforcement learning to optimize the data transmission process. We aim to jointly reduce network energy consumption and latency while meeting the requirements of network performance and Quality of Service. We leverage hybrid-step Q-Learning, which can more accurately estimate the long-term reward of each path. We enhance the utilization of shared nodes and links by introducing the node sharing degree in the reward value. We perform path selection through three different levels to improve algorithm efficiency and robustness. To simplify weight selection among multiple objectives, we leverage the Chebyshev scalarization function based on roulette to evaluate the action reward. We implement comprehensive performance evaluation with different network settings and demand sets and provide an implementation prototype to verify algorithm applicability in a real-world network structure. The simulation results show that compared with existing representative algorithms, our algorithm can effectively reduce network energy consumption and latency during the data transmission of disaster backup while obtaining good convergence and robustness.

Dynamical system analysis for extended f(P) gravity coupled with scalar field

In the present article, we have explored the physical characteristics of extended f(P) gravity through the dynamical system analysis. We choose the function f(P) in the form of a polynomial of second order, i.e. f(P)=αP+βP2, where α and β are constant parameters. As an additional dark energy component, we take a canonical scalar field ϕ, and several types of interaction between the dark components are considered. After presenting the field equation for the corresponding cosmological setup, we introduce some dimensionless variables and formulate a nonlinear autonomous system. For the different interaction scenarios, we have investigated the phase space and their physical characteristics and the dynamics of the cosmological solution associated with each critical point. For the first interaction model, the results we obtained by the analysis of phase space reveals that the cosmological solution associated with critical points exhibits two different cosmological epochs, namely the de-sitter epoch and quintessence epoch. For the second interaction model, the solutions represent the quintessence era. We have also studied the dynamical stability properties of each critical point by linear stability theory and determined possible physical constraints to the parameters. The cosmological solutions support cosmic acceleration. Moreover, an analysis of statefinder parameter {r,s} in terms of the dynamical system variable is presented. Based on the mathematical prospects, the modified theory of gravitation based on the extension of f(P) cubic gravity has the potential to manifest an accelerated expansion during late-time evolution.

Fermionic entanglement in the presence of background electric and magnetic fields

In this study, we investigate the fermionic Schwinger effect in the presence of a constant magnetic field within (1+3)-dimensional Minkowski spacetime, considering both constant and pulsed electric fields. We analyze the correlations between Schwinger pairs for the vacuum and maximally entangled states of two fermionic fields. The correlations are quantified using entanglement entropy and Bell’s inequality violation for the vacuum state, while Bell’s inequality violation and mutual information are used for the maximally entangled state. One can observe the variation of the entanglement produced for fermionic modes with respect to different parameters. Additionally, we discuss the key differences from the behaviour of scalar fields in this context. This study offers deeper insights into quantum field theory and the dynamics of entanglement in the fermionic Schwinger effect.

Phantom hairy black holes and wormholes in Einstein-bumblebee gravity

In this paper we study Einstein-bumblebee gravity theory minimally coupled with external matter – a phantom/non-phantom (conventional) scalar field, and derive a series of hairy solutions – bumblebee-phantom (BP) and BP-dS/AdS black hole solutions, regular Ellis-bumblebee-phantom (EBP) and BP-AdS wormholes, etc. We first find that the Lorentz violation (LV) effect can change the so-called black hole no-hair theorem and these scalar fields can give a hair to a black hole. If LV coupling constant ℓ>-1-1$$\\end{document}]]>, the phantom field is admissible and the conventional scalar field is forbidden; if ℓ<-1, the phantom field is forbidden and the conventional scalar field is admissible. By defining the Killing potential ωab, we study the Smarr formula and the first law for the BP black hole, find that the appearance of LV can improve the structure of these phantom hairy black holes – the conventional Smarr formula and the first law of black hole thermodynamics still hold; but for no LV case, i.e., the regular phantom black hole reported in (Phys Rev Lett 96:251101), the first law cannot be constructed at all. We also show there still exists a stable circular orbit around the BP black hole. When the bumblebee potential is linear, we find that the phantom potential and the Lagrange-multiplier λ behave as a cosmological constant Λ.

Exploring null geodesic of Finslerian hairy black hole

Abstract The study of hairy black holes within Finsler space-time is performed based on a fundamental set of criteria. These requirements include the presence of a clearly defined event horizon and compliance with the strong energy condition for the characteristics outside the horizon. This examination is conducted through the gravitational decoupling method to describe the deformation of a Finslerian Schwarzschild (FSch) black hole due to the inclusion of additional arbitrary sources (scalar field, tensor field, fluidlike dark matter, etc). So, it is characterized by the primary hair ( L 0 = α l ) where the parameter l is linked to gauge transformations of the seed FSch metric and α is the deformation factor apart from flag curvature (λ) and mass (M). This study focuses on determining the black hole’s temperature and heat capacity, which are crucial for understanding its thermodynamic properties. Additionally, we examine how the hairy parameters influence these thermodynamic characteristics, providing a deeper understanding of the interplay between the black hole’s structure and its thermal behavior. Moreover, this paper investigates the null geodesics around the Finslerian hairy Schwarzschild black hole, where we obtain the physical parameters associated with these geodesics, including the effective potential, the photon sphere radius, and the impact parameter and investigate the effects of Finslerian parameter ε and hairy parameters ( α , l ) on these values. This study aims to enhance our understanding of the structure of space-time and the behavior of light in proximity to black holes.

Quantum Brownian motion induced by a scalar field in Einstein’s universe under Dirichlet and Neumann boundary conditions

In this paper, the quantum Brownian motion of a point particle induced by the quantum vacuum fluctuations of a real massless scalar field in Einstein’s universe under Dirichlet and Neumann boundary conditions is studied. Using the Wightman functions, general expressions for the renormalized dispersion of the physical momentum are derived. Distinct expressions are found for the dispersion associated with each component of the particle’s physical momentum, indicating that the global properties of homogeneity and isotropy of space are lost, as a consequence of the introduced boundary conditions. Divergences also arise and are related to the compact nature of Einstein’s universe and the introduced boundary conditions.

Nonrenormalizable theories and finite formulation of QFT

In this paper, we show how the finite formulation of quantum field theory based on Callan-Symanzik equations can be generalized to the case of nonrenormalizable theories. We derive an equation for effective action for an arbitrary single scalar field theory, allowing us to perform computations without running in intermediate divergencies. We illustrate the method with the use of λϕ4+ϕ6/M2 theory by the explicit (and fully finite) calculations of the effective potential as well as two-, four- and six-point correlation functions at one-loop level and demonstrate that no quantum corrections to scalar mass m2, depending on M2 scale, are generated. Published by the American Physical Society 2025

Dynamical Systems on Generalised Klein Bottles

We propose a high-dimensional generalisation of the standard Klein bottle extending beyond those considered previously. We address the problem of generating continuous scalar fields (distributions) and dynamical systems (flows) on such state spaces, which can provide a rich source of examples for future investigations. We consider a class of high-dimensional dynamical systems that model distributed information processing within the human cortex, which may be capable of exhibiting some Klein bottle symmetries. We deploy topological data analytic methods in order to analyse their resulting dynamical behaviour and suggesting future challenges.

Black holes in alternative gravity theories

In our quest toward a theory of gravity beyond General Relativity, black holes with their strong gravitational fields represent an important testing ground. Among the numerous alternative theories of gravity, much work in recent years has focused on a set of scalar–tensor theories, where the scalar field couples to higher curvature terms. The properties of the resulting black holes in such theories may differ distinctly from those of the Schwarzschild and Kerr black holes as, for instance, revealed by their shadows or their gravitational wave spectra.

Scalar Field Source Teleparallel Robertson–Walker F(T) Gravity Solutions

This paper investigates the teleparallel Robertson–Walker (TRW) F(T) gravity solutions for a scalar field source. We use the TRW F(T) gravity field equations (FEs) for each k-parameter value case added by a scalar field to find new teleparallel F(T) solutions. For k=0, we find an easy-to-compute F(T) solution formula applicable for any scalar field source. Then, we obtain, for k=−1 and +1 situations, some new analytical F(T) solutions, only for specific n-parameter values and well-determined scalar field cases. We can find by those computations a large number of analytical teleparallel F(T) solutions independent of any scalar potential V(ϕ) expression. The V(ϕ) independence makes the FE solving and computations easier. The new solutions will be relevant for future cosmological applications in dark matter, dark energy (DE) quintessence, phantom energy and quintom models of physical processes.

Derivation of Meson Masses in SU(3) and SU(4) Extended Linear Sigma Model at Finite Temperature

The present study focused on the mesonic potential contributions to the Lagrangian of the extended linear sigma model (eLSM) for scalar and pseudoscalar meson fields across various quark flavors. The present study focused on the low-energy phenomenology associated with quantum chromodynamics (QCD), where mesons and their interactions serve as the pertinent degrees of freedom, rather than the fundamental constituents of quarks and gluons. Given that SU(4) configurations are completely based on SU(3) configurations, the possible relationships between meson states in SU(3) and those in SU(4) were explored at finite temperature. Meson states, which are defined by distinct chiral properties, were grouped according to their orbital angular momentum J, parity P, and charge conjugation C. Consequently, this organization yielded scalar mesons with quantum numbers JPC=0++, pseudoscalar mesons with JPC=0−+, vector mesons with JPC=1−−, and axial vector mesons with JPC=1++. We accomplished the derivation of analytical expressions for a total of seventeen noncharmed meson states and twenty-nine charmed meson states so that an analytical comparison of the noncharmed and charmed meson states at different temperatures became feasible and the SU(3) and SU(4) configurations could be analytically estimated.

Decay of CP-even Higgs H → hγγ in Two Higgs Doublet Model: One-loop analytic results, Ward identity checks

Abstract The first analytic expressions for one-loop induced contributions for the decay of CP-even Higgs H → hγγ with h being Standard-Model-like Higgs boson within the framework of Two Higgs Doublet Model are presented in this paper. The one-loop form factors for the decay processes are written in terms of scalar one-loop Passarino-Veltman functions following the input notations of both packages LoopTools and Collier. Subsequently, physical results for the decay processes can be generated numerically by using one of the above-mentioned packages. The analytic expressions shown in this paper are verified by several numerical checks, for examples, the ultraviolet and infrared finiteness of one-loop amplitude. Furthermore, the amplitude satisfies the Ward identity due to on-shell photons in final states. The identity is also checked numerically in this work. In phenomenological studies, the differential decay rates for H → hγγ as functions of the invariant mass of two photons in final states are first examined in parameter space of the Two Higgs Doublet Models.