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This paper investigates the metrics of existing regular black hole space–times and calculates their effective potentials, plotting the corresponding curves. By analyzing these curves, it identifies all types of geodesic structures for test particles in various regular black hole space–times. Using dynamical equations near black holes, it determines two distinct bound orbits for fixed energy levels in different space–times and identifies stable and unstable circular orbits as the energy approaches critical values. Additionally, it provides escape orbits for fixed energy levels across different space–times. Comparative analysis reveals the fastest and slowest periapsis precession rates, identifies space–times with counterclockwise periapsis precession, and highlights those with the most intricate escape orbits for fixed energy levels. [ABSTRACT FROM AUTHOR]

This paper explores the metric of Piero Nicolini's noncommutative black hole spacetime, calculates its effective potential, and presents the corresponding potential curve. By analyzing this curve, we identify various orbit types for test particles and photons in this spacetime. Using the dynamical equations for particles and photons near the black hole, we plot the specific time-like and null geodesic structures. We analyze the impact of different values of the total mass of the source M and angular momentum L on time-like geodesics. Our results indicate that in the Piero black hole spacetime, increases in total mass and angular momentum reduce the perihelion precession rate of the orbit. Notably, the effect of total mass is nonlinear, while the effect of angular momentum is linear. [ABSTRACT FROM AUTHOR]

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. [ABSTRACT FROM AUTHOR]

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits. [ABSTRACT FROM AUTHOR]

We perform a systematic analysis of the one‐loop effective potential of pure d=5$d=5$ supergravities, with supersymmetry fully broken by a Scherk–Schwarz compactification on the circle, as a function of the radial modulus. We discuss the precise correspondence between the effective potential V1$V_1$ in the full compactified theory and its counterpart V1,red$V_{1,red}$ in the reduced theory. We confirm that V1$V_1$ is finite for any N>0$N>0$, in contrast to V1,red$V_{1,red}$. We find that for broken N=8$N=8$ supergravity V1$V_1$ is negative definite even after accounting for the Kaluza–Klein states. We outline a program for future work where the study of a different kind of Scherk‐Schwarz compactifications, still at the field theory level but with at least three extra dimensions, could lead to qualitatively new results. We perform a systematic analysis of the one‐loop effective potential of pure d=5$d=5$ supergravities, with supersymmetry fully broken by a Scherk–Schwarz compactification on the circle, as a function of the radial modulus. We discuss the precise correspondence between the effective potential V1$V_1$ in the full compactified theory and its counterpart V1,red$V_{1,red}$ in the reduced theory. We confirm that V1$V_1$ is finite for any N>0$N>0$, in contrast to V1,red$V_{1,red}$. We find that for broken N = 8 supergravity V1$V_1$ is negative definite even after accounting for the Kaluza–Klein states. We outline a program for future work where the study of a different kind of Scherk‐Schwarz compactifications, still at the field theory level but with at least three extra dimensions, could lead to qualitatively new results. [ABSTRACT FROM AUTHOR]

Achieving the potential for plasma particle interactions by modifying the Deutsch potential has been considered in many studies. One very convenient way to do this is to utilize the method as a dielectric function. In this method, by applying different potentials, it tries to provide corrective terms in the initial potential. As a result of using this method, an effective potential function is obtained from which the plasma characteristics including state equation and thermodynamic features can be derived. Because the screening effects between plasma particles are not taken into account by the Deutsch potential and therefore show different results from the real values, in this paper, we have tried to add corrective terms with the help of Hulthen potential and dielectric response function to it. Thus, an effective potential was obtained and then its equation of state was derived consequently. Finally, the results of this modified potential and the equation of state were compared with the results of other works. [ABSTRACT FROM AUTHOR]

We use some exact results in scalar field theory to revise the analysis by Coleman and Callan about false vacuum decay and propose a simple non-perturbative formalism. We introduce an exact Green's function which incorporates non-perturbative corrections in the strong coupling regimes of the theory. The solution of the scalar field theory involves the Jacobi elliptical function and has been used to calculate the effective potential for any arbitrary coupling values. We demonstrate the use of this formalism in a simple λ ϕ 4 theory, and show that the effective potential exhibits a false minimum at the origin. We then calculate the false vacuum decay rate in the thin wall approximation, and suggest simple analytic formulae that may be useful for the analysis for the first-order phase transition beyond the perturbative regime. In our methodology, we show that the standard results obtained in perturbation theory are reproduced by making the coupling values very small. [ABSTRACT FROM AUTHOR]

The chromomagnetic vacuum of SU(2) gluodynamics is considered in the background of a finite radius flux tube (center vortex) with a homogeneous field inside and a zero field outside. In this background, there are tachyonic modes. These modes cause an instability. It is assumed that the self-interaction of these modes stops the creation of gluons, and it is assumed that a condensate will be formed. For constant condensates, the minimum of the effective potential is found at the tree level. In the background of these condensates, all tachyonic modes acquire non-zero real masses, which will result in a real effective potential of this system. Considering only the tachyonic modes and adding the energy of the background field, the total energy is found to have a minimum at some value of the background field, which depends on the coupling of the initial SU(2) model. For small coupling, this dependence is polynomial in distinction from the Savvidy vacuum where it is exponentially suppressed. The minimum of this energy will deepen with a shrinking radius of the flux tube. It can be expected that this process can be stopped by adding quantum effects. Using the high-temperature expansion of the effective potential, it can be expected that the symmetry, which is broken by the condensate, will be restored at sufficiently high temperatures. [ABSTRACT FROM AUTHOR]

The enhancement of a cryogenic radio frequency 22 pole trap instrument by the addition of ring electrodes is presented in detail. The ring electrodes tightly surround the poles and only a fraction of the applied electric potential penetrates to the trap axis, facilitating the fine control of slow cold ions. A precise computational model, describing the effective mechanical potential created by the applied static and rf fields, governing the ion behaviour, is employed to demonstrate and understand the operation of our setup. The use of ring electrodes for improved extraction of cold stored ions is shown. Variable trapping potentials, placed on one ring electrode, can be used to control the evaporation of only those $ \mbox {H}^{+} $ H + ions from the trap, whose kinetic energy exceeds the barrier. This ring electrode trapping opens new possibilities to study processes of minimal kinetic energy release, e. g. spin exchange. We propose a robust modified method for the determination of temperature dependent ion molecule reaction rates, resistant to effects caused by neutral gas freezing and demonstrate it on the reaction of $ \mbox {CO}^{+}/{\mbox {CO}_{2}}^{+} $ CO + / CO 2 + with $ \mbox {H}_{2}/ $ H 2 / $ \mbox {D}_{2} $ D 2 . Finally, the use of a supercontinuum laser for quick localisation of spectroscopic bands is examined on the $ {\mbox {N}_{2}}^{+} $ N 2 + Meinel system. [ABSTRACT FROM AUTHOR]

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.

For the effective potential in the leading logarithmic approximation, we construct a renormalization group equation that holds for arbitrary scalar field theories, including nonrenormalizable ones, in four dimensions. This equation reduces to the usual renormalization group equation with a one-loop beta-function in the renormalizable case. The solution of this equation sums up the leading logarithmic contributions in the field in all orders of the perturbation theory. This is a nonlinear second-order partial differential equation in general, but it can be reduced to an ordinary one in some cases. In specific examples, we propose a numerical solution of this equation and construct the effective potential in the leading logarithmic approximation. We consider two examples as an illustration: a power-law potential and a cosmological potential of the type. The obtained equation in physically interesting cases opens up the possibility of studying the properties of the effective potential, the presence of additional minima, spontaneous symmetry breaking, stability of the ground state, etc. [ABSTRACT FROM AUTHOR]

Ten years ago the 125 GeV Higgs resonance was discovered at the LHC [1,2], if this boson is a fundamental particle or a particle composed of new strongly interacting particles is still an open question. If this is a composite boson there are still no signals of other possible composite states of this scheme, a possible solution to this problem was recently discussed in Refs. [30,31], where it is argued that the Higgs boson can be a composite dilaton [30]. In this work, considering an effective potential for composite operators we verify that the potential responsible for a light composite scalar boson of O(120) GeV, behaves like ∝Φ4 suggesting that if the Higgs boson is a composite scalar it may be a composite dilaton.

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In this paper, we study the phase transition of the two Higgs-doublets model (2HDM) and consider a scenario of a electroweak phase transition at alignment limit. Using the Cornwall–Jackiw–Tomboulis formalism at finite temperature, we consider the phase transition of the aligned 2HDM in the two-loop double-bubble contribution. By requirement of Goldstone theorem, the effective potential is corrected and the results show that the system obeys a second-order phase transition. A possible thermal history of the early universe has been treated out: the universe undergoes a smooth crossover in the SM, a second-order phase transition in this model before going to a strong first-order transition in the new physics as in recent 2HDMs and supersymmetry (from the EW symmetric to the broken phase). [ABSTRACT FROM AUTHOR]

Introducing the effective potential between plasma particles is one of the common methods to study the behavior of particles in plasma. In this paper, it has been tried to define the effective potential for fully ionized hot dense plasma by using the dielectric response function method. In the dielectric response function method, it is first necessary to introduce an initial potential function, and an effective potential function is obtained with the help of its effect on plasma. The initial potential function used in this paper is the Hulthen potential function, which is used for the first time in these calculations. In the following, the effective potential on the interaction of plasma particles such as electron-ion, electron-electron and ion-ion interaction are compared with other results obtained from other theoretical studies for the same conditions of plasma parameters. The results show that this effective potential includes both the effects of hot dense plasma, i.e. collective effects at long distances and quantum effects at short distances, and represents a very good description of the behavior of particles in hot dense plasma media.

This work is dedicated to the investigation of the superradiant stability of a rotating black hole derived from the nonlinear Maxwell theory of gravity, f (R) . The evaluation of stability and instability in this study will be based on the absence and presence of the magnetic field, respectively, when the magnetic field constant is c 4 = 0 and c 4 ≠ 0 . For the black hole under discussion, analyses of the greybody factors (GFs) and quasi-normal modes (QNMs) are also carried out. To this end, we first consider the Klein–Gordon equation for the scalar waves propagating in the black hole's geometry. The resulting radial equation is then reduced to a one-dimensional Schrödinger-like wave equation with effective potential energy. The effects of the nonlinear Maxwell f (R) gravity theory parameters (q, c, and c 4 ) on the effective potential, GFs, and QNMs are examined. The results demonstrate that, although the parameters q, c, and c 4 all influence the effective potential, they do not affect the GFs and QNMs. All results are presented and summarized using appropriate graphics and tables. [ABSTRACT FROM AUTHOR]

The chromomagnetic vacuum of SU(2) gluodynamics is considered in the background of a finite radius flux tube (center vortex) with a homogeneous field inside and a zero field outside. In this background, there are tachyonic modes. These modes cause an instability. It is assumed that the self-interaction of these modes stops the creation of gluons, and it is assumed that a condensate will be formed. For constant condensates, the minimum of the effective potential is found at the tree level. In the background of these condensates, all tachyonic modes acquire non-zero real masses, which will result in a real effective potential of this system. Considering only the tachyonic modes and adding the energy of the background field, the total energy is found to have a minimum at some value of the background field, which depends on the coupling of the initial SU(2) model. For small coupling, this dependence is polynomial in distinction from the Savvidy vacuum where it is exponentially suppressed. The minimum of this energy will deepen with a shrinking radius of the flux tube. It can be expected that this process can be stopped by adding quantum effects. Using the high-temperature expansion of the effective potential, it can be expected that the symmetry, which is broken by the condensate, will be restored at sufficiently high temperatures.

In the curved space-time, the neutral test particle is not affected by any other force except for the influence of the curved space-time. Similar to the free sub in the flat space, the Lagrangian of the test particle only contains the kinetic energy term—the kinetic energy term of the four-dimensional curved space-time. In the case of small space-time curvature, linear approximation can be made. That is, under the weak field approximation, the Lagrangian quantity degenerates into the Lagrangian quantity in the axisymmetric gravitational field in Newtonian mechanics. In this paper, the curved space-time composed of axisymmetric equidistant black holes is taken as a model. We study the geodesic motion of the test particles around three black holes with equal mass and static axisymmetric distribution, including time-like particles and photons. The three extreme Reissner–Nordstrom black holes are balanced by electrostatic and gravitational forces. We first give the geodesic motion equation of particles in Three black holes space-time, give the relativistic effective potential, discuss the possible motion state of particles, and classify their motion trajectories. Then, the particle motion of the special plane (equatorial plane) is studied. The circular orbits of the two types of particles in the symmetric plane are studied, respectively. The circular orbits outside the symmetric plane are also studied, and their stability is also discussed. We will show the influence of the separation distance of the three black holes on the geodesic motion and explore the change of the relativistic effective potential. Then, the relationship between the inherent quantity and the coordinate quantity in space-time is analyzed. Finally, the chaos of the test particle orbit is explored. [ABSTRACT FROM AUTHOR]

Exciton states are essential to comprehend the basal photoelectric properties in metal halide perovskites (MHPs) and provide reference for their future research, in which the exciton binding energy (EBE), determining the balance of the populations between excitons and free carriers, plays an important role in defining the optoelectronic utilization of MHPs. Thereby, we theoretically study the effects of bound potentials, due to the exciton coupling with the longitudinal optical (LO) phonon, between the electron and hole of the exciton on the EBE applying the variational method by using different effective potentials and two trail wavefunctions. We find that the EBE of this kind of materials is not only related to the chemical composition, but also remains inseparable from the space size, dielectric constant and LO-phonon energy, moreover, these correlations are better described by Barentzen potential. In addition, the results also show that the effects of carriers-LO-phonon coupling can explain the relationships between the EBE and exciton active range and effective Bohr radius to a certain extent, and can analyze their intrinsic correlation among these factors. These findings enable us to explain some experimental results and provide some help to understand optical electric dynamics in MHPs. [ABSTRACT FROM AUTHOR]

We studied the space-time properties of the triangular symmetric black hole in the case of extreme RN black hole. Because the neutral test particle is only affected by space-time in the curved space-time, we chose the triangular symmetric black hole as the model with which to study the motion of the test particle in this case. The curvature tensor and curvature scalar were calculated by giving the metric and the Christoffel Symbol, and then the kinematics equation of the test particle was obtained and analyzed by using these quantities. Then we analyzed the relationship between the coordinate distance and the inherent distance, the relationship between the coordinate time and the inherent time, the inherent velocity and the coordinate velocity of light, and then verified the correctness of general relativity. Next, the one-dimensional effective potential and two-dimensional effective potential of the system under different separation distances were analyzed. Finally, we analyzed and explored the innermost stable circular orbit, calculated all the Lagrange points under this model, and expounded some applications of circular orbit in astrophysics. [ABSTRACT FROM AUTHOR]

In this paper, the effects of strong gravitational lensing are explored in the context of traversable wormholes by determining the existence of photon spheres. The redshift function is defined as Φ (r) = ξ r + η r 2 , where ξ and η are constants. Using this redshift function, the points of maximum potentials are determined which consequently gives the radius of photon spheres. It is obtained that either the throat itself can act as an effective photon sphere or the photon sphere exists outside the throat of the wormhole. Further, the nature of matter supporting the wormhole solutions is examined by analyzing the energy conditions, and the stability of solutions is tested with the help of the TOV (Tolman–Oppenheimer–Volkoff) equation. [ABSTRACT FROM AUTHOR]

In this study, we investigate the greybody factor of a (3+1)-dimensional black hole solution in the context of alternative f (Q) gravity with minimum scalar field coupling. We obtain the radial equation by applying the Klein–Gordon equation and transforming it into a Schrodinger wave equation using the tortoise coordinate. This transformation enables us to determine the effective potential and its graphical behavior for different values of the coupling constant and relevant physical parameters. We obtain two solutions for the radial equation corresponding to the event and cosmological horizons. To determine the greybody factor and its behavior, we combine these two solutions in the intermediate regime. The greybody factor increases with an increase in radius and coupling constant. This indicates that in alternative gravity, the larger black hole will die sooner as compared to cosmic gravity. [ABSTRACT FROM AUTHOR]

The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even for the simplest case of 1 + 1 dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong coupling parameters to each other. He used a variational technique (back to kleinert and Feynman) to extract accurate values for the strong coupling parameters from which he was able to extract precise critical exponents. In this work, we suggest a simple method of using the effective potential (low order) to obtain exact values for the strong-coupling parameters for the ϕ 4 scalar field theory in 0 + 1 and 1 + 1 space–time dimensions. For the 0 + 1 case, our results coincide with the well-known exact values already known from literature while for the 1 + 1 case we test the results by obtaining the corresponding exact critical exponent. As the effective potential is a well-established tool in quantum field theory, we expect that the results can be easily extended to the most important three dimensional case and then the dream of getting exact critical exponents is made possible. [ABSTRACT FROM AUTHOR]

In this paper, we review the status of the computations of the perturbative quantum corrections to the Higgs boson mass in the Standard Model and in its supersymmetric extensions. In particular, supersymmetric theories require a very accurate computation of the Higgs boson mass, which includes corrections even up to the three-loop level, since their predictions are limited by theoretical uncertainties. A discussion about these uncertainties in the context of the Minimal and Next To Minimal Supersymmetric Standard Model is included.

As the U(1) extension of the minimal supersymmetric standard model, the U (1) X SSM has new superfields, such as right-handed neutrinos, and three Higgs singlets. In the U (1) X SSM, the lightest CP-even Higgs mass m h 0 is studied by using the Higgs effective potential with one-loop corrections. We also calculate the Higgs decays h 0 → γ γ , h 0 → V V (V = W , Z) , h 0 → l l ¯ Z , and h 0 → ν ν ¯ Z . The obtained results are reasonable, and they are in favor of the study of the Higgs characteristic and the phenomenology of the U (1) X SSM. [ABSTRACT FROM AUTHOR]

The early Universe has been a subject of research for many cosmologists and it is reviewed and analyzed rigorously in cosmology recently. Thermal history and theory of phase transition coordinate us to elucidate the evolution of the Universe at its early stages and is interesting to get a gist of early universe behavior. At phase transition, effective potential plays a significant role for the kinds of transition that occurred during the evolution. The temperature, at which phase transition occurs, can be determined at minimum effective potential. It is also known fact that temperature of the Universe has changed considerably with its evolution. The present work investigates the time-temperature relation in four-dimensional and fivedimensional cosmological models. A comparison of time-temperature relation in FRW model with that of Kaluza-Klein (K-K) model demonstrates that temperature decreases faster in Kaluza-Klein model. The investigation demonstrates the important role played by extra dimension in the study of time-temperature relation at the early Universe scenario. [ABSTRACT FROM AUTHOR]

We consider the classically scale invariant Higgs-dilaton model of dynamical symmetry breaking extended with an extra scalar field that plays the role of dark matter. The Higgs boson is light near a critical boundary between different symmetry breaking phases, where quantum corrections beyond the usual Gildener-Weinberg approximation become relevant. This implies a tighter connection between dark matter and Higgs phenomenology. The model has only three free parameters, yet it allows for the observed relic abundance of dark matter while respecting all constraints. The direct detection cross section mediated by the Higgs boson is determined by the dark matter mass alone and is testable at future experiments.

This work is dedicated to the investigation of the superradiant stability of a rotating black hole derived from the nonlinear Maxwell theory of gravity, f(R). The evaluation of stability and instability in this study will be based on the absence and presence of the magnetic field, respectively, when the magnetic field constant is c4=0 and c4≠0. For the black hole under discussion, analyses of the greybody factors (GFs) and quasi-normal modes (QNMs) are also carried out. To this end, we first consider the Klein–Gordon equation for the scalar waves propagating in the black hole’s geometry. The resulting radial equation is then reduced to a one-dimensional Schrödinger-like wave equation with effective potential energy. The effects of the nonlinear Maxwell f(R) gravity theory parameters (q, c, and c4) on the effective potential, GFs, and QNMs are examined. The results demonstrate that, although the parameters q, c, and c4 all influence the effective potential, they do not affect the GFs and QNMs. All results are presented and summarized using appropriate graphics and tables.

One-loop effective potential of scalar-tensor gravity with a quartic scalar field self-interaction is evaluated up to first post-Minkowskian order. The potential develops an instability in the strong field regime which is expected from an effective theory. Depending on model parameters the instability region can be exponentially far in a strong field region. Possible applications of the model for inflationary scenarios are highlighted. It is shown that the model can enter the slow-roll regime with a certain set of parameters. [ABSTRACT FROM AUTHOR]

In this paper, we review the status of the computations of the perturbative quantum corrections to the Higgs boson mass in the Standard Model and in its supersymmetric extensions. In particular, supersymmetric theories require a very accurate computation of the Higgs boson mass, which includes corrections even up to the three-loop level, since their predictions are limited by theoretical uncertainties. A discussion about these uncertainties in the context of the Minimal and Next To Minimal Supersymmetric Standard Model is included. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the geodesic motion of massive and massless test particles in the vicinity of a black hole space-time surrounded by perfect fluid (quintessence, dust, radiation, cosmological constant and phantom) in Rastall theory. We obtain analytical solutions of the equations of motion for geodesics in vicinity of space-time of this black hole. For all cases of perfect fluid, we consider some different values of Rastall coupling constant k λ , for which the equations of motion have integer powers of r ~ and can be solved analytically. These analytical solutions are presented in the form of elliptic and also hyperelliptic functions. Also, by using analytical solutions, effective potential and L– E 2 diagrams, we plot some examples of possible orbits. Moreover, different orbits are classified using angular momentum, conserved energy, electrical charge and Rastall parameters. Furthermore, we show that when Rastall parameter becomes zero ( N = 0 ), our results are consistent with the analysis of a Reissner–Nordström black hole, however; when both Rastall parameter and electric charge vanish (N = Q = 0) , the results are the same as the analysis of a Schwarzschild black hole. In addition, the application of astrophysics of these results has also been investigated. [ABSTRACT FROM AUTHOR]

In the curved space-time, the neutral test particle is not affected by any other force except for the influence of the curved space-time. Similar to the free sub in the flat space, the Lagrangian of the test particle only contains the kinetic energy term—the kinetic energy term of the four-dimensional curved space-time. In the case of small space-time curvature, linear approximation can be made. That is, under the weak field approximation, the Lagrangian quantity degenerates into the Lagrangian quantity in the axisymmetric gravitational field in Newtonian mechanics. In this paper, the curved space-time composed of axisymmetric equidistant black holes is taken as a model. We study the geodesic motion of the test particles around three black holes with equal mass and static axisymmetric distribution, including time-like particles and photons. The three extreme Reissner–Nordstrom black holes are balanced by electrostatic and gravitational forces. We first give the geodesic motion equation of particles in Three black holes space-time, give the relativistic effective potential, discuss the possible motion state of particles, and classify their motion trajectories. Then, the particle motion of the special plane (equatorial plane) is studied. The circular orbits of the two types of particles in the symmetric plane are studied, respectively. The circular orbits outside the symmetric plane are also studied, and their stability is also discussed. We will show the influence of the separation distance of the three black holes on the geodesic motion and explore the change of the relativistic effective potential. Then, the relationship between the inherent quantity and the coordinate quantity in space-time is analyzed. Finally, the chaos of the test particle orbit is explored.

We studied the space-time properties of the triangular symmetric black hole in the case of extreme RN black hole. Because the neutral test particle is only affected by space-time in the curved space-time, we chose the triangular symmetric black hole as the model with which to study the motion of the test particle in this case. The curvature tensor and curvature scalar were calculated by giving the metric and the Christoffel Symbol, and then the kinematics equation of the test particle was obtained and analyzed by using these quantities. Then we analyzed the relationship between the coordinate distance and the inherent distance, the relationship between the coordinate time and the inherent time, the inherent velocity and the coordinate velocity of light, and then verified the correctness of general relativity. Next, the one-dimensional effective potential and two-dimensional effective potential of the system under different separation distances were analyzed. Finally, we analyzed and explored the innermost stable circular orbit, calculated all the Lagrange points under this model, and expounded some applications of circular orbit in astrophysics.

In high temperature SU(2) gluodynamics, the condensation of the zero component gauge field potential and its gauge-fixing dependence are investigated. The and Polyakov's loop are mutually related. The two-loop effective potential is recalculated in the background relativistic gauge. It depends on the parameter , has a nontrivial minimum and satisfies Nielsen's identity. These signs mean gauge invariance of the condensation phenomenon. We express in terms of and obtain the effective potential of order parameter which is independent of and has a nontrivial minimum position. Hence the condensate value is detected. We show that the equation relating and observable coincides with the special characteristic orbit in the )-plane along which the is -independent. In this way the link between these two gauge invariant descriptions is established. The minimum value of Polyakov loop, the two-loop Debye mass and thermodynamical pressure are calculated. We also show that condensate stabilizes the charged gluon spectrum in the chromomagneric field which is spontaneously generated at high temperature due to Savvidy's mechanism. These two fields form a self-consistent background of plasma. Comparison with results of other authors (and other approaches) is given. [ABSTRACT FROM AUTHOR]

As the U(1) extension of the minimal supersymmetric standard model, the U(1)XSSM has new superfields, such as right-handed neutrinos, and three Higgs singlets. In the U(1)XSSM, the lightest CP-even Higgs mass mh0 is studied by using the Higgs effective potential with one-loop corrections. We also calculate the Higgs decays h0→γγ, h0→VV(V=W,Z), h0→ll¯Z, and h0→νν¯Z. The obtained results are reasonable, and they are in favor of the study of the Higgs characteristic and the phenomenology of the U(1)XSSM.

The Coleman-Weinberg mechanism can realise different phases of dynamical symmetry breaking. In each phase a combination of scalars, corresponding to the pseudo-Goldstone boson of scale invariance, has a loop-suppressed mass. We show that additional scalars, beyond the pseudo-Goldstone bosons, can become light at critical points in the parameter space where two different phases co-exist. We present a minimal implementation of the mechanism in multi-scalar models, detailing how loop-suppressed masses and mixings can be computed. We discuss realisations of the resulting multi-phase criticality principle and its relevance to the case of the Higgs boson.

The potential for generating electricity with photovoltaic systems is high in Colombia given its geographical position in the tropic. Some departments in Colombia have low electricity coverage and high rates. In the department of Putumayo there is a low coverage rate and high energy costs, while the solar radiation potential is high. Due to the geographical differences of the Putumayo subregions, the radiation potential for electricity generation is unknown. In addition, in this department the energy tariffs are above the national average. The objective of this paper is to determine the effective potential for solar photovoltaic power generation in the Putumayo department with a detailed methodology considering the information of different remote database and meteorological stations and some technical conditions. It was found that the highest effective solar potential occurs in the Amazon region, and the lowest in the Andean region in the Putumayo. On the other hand, when evaluating electricity consumption and tariffs in the regions, it is concluded that consumption can be satisfied with photovoltaic systems by producing self-generating electricity and distributed generation. [ABSTRACT FROM AUTHOR]

In this paper, we study the ground state energy of a massless scalar field and generation of topological mass by considering a quasi-periodically identified Minkowski spacetime and the "half-Einstein universe", that is, an Einstein universe where the massless scalar field satisfies the Dirichlet boundary condition. The analysis is performed considering one and two-loop contributions to the effective potential in both cases. We also compare our results with earlier studies. [ABSTRACT FROM AUTHOR]

The effective potential in this work is the sum of zero, first and second order potential obtained by using Poisson bracket. The effective Potential was developed for a system in which electron, muon and tau orbiting around the nucleus of helium and helium like atoms.· Kryukov and Oks (2021) developed effective potential for muon only for low order potential but in this work the effective potential was developed for muon and tau of higher order potential of both helium and helium like atoms with example. In addition, the velocity of tau is greater than velocity of muon and electron in a different path around the nucleus of helium and helium like atoms. Also effective potential is directly proportional to eccentricity and momentum of electron. The effective potential is low at zero radian and increase from O to -1 radian and O to + 1 radian. [ABSTRACT FROM AUTHOR]

The escape dynamics of a damped system of two coupled particles in a truncated potential well under biharmonic excitation are investigated. It is assumed that excitation frequencies are tuned to the modal natural frequency of the relative motion and to the modal frequency of the centre of mass on the bottom of the potential well. Although the escape is essentially a non-stationary process, the critical force strongly depends on the stationary amplitude of the relative vibrations within the pair of masses. The characteristic escape curve for the critical force moves up on the frequency-escape threshold plane with increasing relative vibrations, which can be interpreted as a stabilizing effect due to the high-frequency excitation. To obtain the results, new modelling techniques are suggested, including the reduction in the effect of the high-frequency excitation using a probability density function-based convolution approach and an energy-based approach for the description of the evolution of the slow variables. To validate the method, the coupled pair of particles is investigated with various model potentials. [ABSTRACT FROM AUTHOR]

This article deals with a special case of the Sturm–Liouville boundary value problem (BVP), an eigenvalue problem characterized by the Sturm–Liouville differential operator with unknown spectra and the associated eigenfunctions. By examining the BVP in the Schrödinger form, we are interested in the problem where the corresponding invariant function takes the form of a reciprocal quadratic form. We call this BVP the modified second Paine–de Hoog–Anderssen (PdHA) problem. We estimate the lowest-order eigenvalue without solving the eigenvalue problem but by utilizing the localized landscape and effective potential functions instead. While for particular combinations of parameter values that the spectrum estimates exhibit a poor quality, the outcomes are generally acceptable although they overestimate the numerical computations. Qualitatively, the eigenvalue estimate is strikingly excellent, and the proposal can be adopted to other BVPs.

We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner–Nordström, Kerr, and Kerr–Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider interactions of scalar particles, photons, and fermions with nonextremal rotating charged black holes in a minimal five-dimensional gauge supergravity. We analyze the behavior of effective potentials in second-order relativistic Schrödinger-type equations. In all cases, we establish the existence of the regime of particles "falling" on event horizons. An alternative can be collapsars with fermions in stationary bound states without a regime of particles "falling." [ABSTRACT FROM AUTHOR]

Structure and properties of model colloidal suspensions in bulk solutions have been investigated using classical molecular dynamics simulations. The system consists of spherical particles (macroscopic colloids and microscopic counterions and/or coions) in a continuum solvent and is described using the primitive model. Variations in different properties with system parameters (colloid size, charge, concentration etc.) have been investigated. An effective one-component model [Adelman SA. J. Chem. Phys. 1976;64:724–731] of the multicomponent suspension is used to calculate the effective colloid–colloid potential, which develops an attractive minimum with increase in charge, size and concentration of colloid. [ABSTRACT FROM AUTHOR]

We develop a generalized Newton scheme called IHNC (inverse hypernetted-chain iteration) for the construction of effective pair potentials for systems of interacting point-like particles. The construction is realized in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation of the inverse of the Jacobian of the forward operator. In contrast to the full Newton method realized in the Inverse Monte Carlo (IMC) scheme, the IHNC algorithm requires only a single molecular dynamics computation of the radial distribution function per iteration step and no further expensive cross-correlations. Numerical experiments are shown to demonstrate that the method is as efficient as the IMC scheme, and that it easily allows to incorporate thermodynamical constraints. [ABSTRACT FROM AUTHOR]