Form Of Effective Potential Research Articles

Non-BPS black branes in M-theory over Calabi-Yau threefolds. (Non-)uniqueness and recombination of non-BPS black strings in single modulus CICY and THCY models

We study extremal solutions arising in M-theory compactifications on Calabi-Yau threefolds, focussing on non-BPS attractors for their importance in relation to the Weak Gravity Conjecture (WGC); M2 branes wrapped on two-cycles give rise to black holes, whereas M5 branes wrapped on four-cycles result in black strings. In the low-energy/field theory limit one obtains minimal N = 2, D = 5 supergravity coupled to Abelian vector multiplets. By making use of the effective black hole potential formalism with Lagrange multipliers and of the Attractor Mechanism, we obtain the explicit expressions of the attractor moduli for BPS and non-BPS solutions, and we compute the Bekenstein-Hawking black hole entropy and the black string tension. Furthermore, by focussing on one modulus complete intersection (CICY) or toric hypersurface (THCY) Calabi-Yau threefolds, we investigate the possible non-uniqueness of the attractor solutions, as well as the stability of non-BPS black holes and black strings (restricting to doubly-extremal solutions, for simplicity’s sake). In all models taken into consideration, we find that both BPS and non-BPS extremal black hole attractors are always unique for a given, supporting electric charge configuration; moreover, non-BPS black holes are always unstable, and thus they decay into constituent BPS/anti-BPS pairs: this confirms the WGC, for which macroscopic non-supersymmetric solutions are bound to decay. For what concerns extremal black strings, it is well known they are unique in the BPS case; we confirm uniqueness also for non-BPS strings in one-modulus CICY models. On the other hand, we discover multiple non-BPS extremal black string attractors (with different tensions) in most of the one-modulus THCY models, and we determine the corresponding magnetic configurations supporting them; this indicates the existence of volume-minimizing representatives in the same homology class having different values of their local minimal volume. Moreover, we find that non-BPS (doubly-) extremal black strings, both for single and multiple solutions, are kinematically stable against decay into their constituent BPS/anti-BPS pairs; in Calabi-Yau geometry, this means that the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and thus leading to stable, non-BPS string solutions, which for the WGC are microscopic with small charges.

Dissipation and spontaneous emission in quantum electrodynamical density functional theory based on optimized effective potential: A proof of concept study

We generalize the optimized effective potential (OEP) formalism in the quantum electrodynamical density functional theory (QEDFT) to the case of continuous distribution of photon modes, and study its applicability to dissipative dynamics of electron systems interacting with photons of lossy cavities. Specifically, we test whether this technique is capable of capturing the quantum features of electron-photon interaction related to spontaneous emission and the corresponding energy transfer from the electrons to cavity photons. For this purpose, we analyze a discrete three-site system with one electron coupled to photons of the cavity, which, in fact, is a minimal model allowing to eliminate classical radiation and the corresponding energy loss, but still have nontrivial density dynamics. By considering two typical spectral densities of photon modes, modeling (i) lossy cavity with Lorentzian broadening of photon peaks, and (ii) the Ohmic bath, and several representative dynamical regimes, we find that OEP-QEDFT demonstrates a good qualitative and quantitative performance, especially in the case when the disspation is dominated by one-photon processes.

New cylindrically symmetric solution of Einstein field equations their conservation laws and the particles dynamics

The study explores the particle dynamics, asymptotic behavior, and flatness in Riemann curvature corresponding to the solutions obtained from the Ricci tensor of cylindrical spacetimes. Since these solutions are non-Minkowskian and are proposed to have curvature in almost all the cases, that is why some cylindrically symmetric static vacuum solutions of Einstein Field Equations have been worked out. We explore the Noether symmetries along with their conservation laws of the corresponding static-spacetime and calculate the equation of motions by taking into account Noether symmetries. We study the dynamics of particle in the form of effective potential, effective force.

Effective Potential Formalism at Finite Temperature in Dual QCD and Deconfilnement Phase Transition

We study the pure-gauge QCD phase transition at filnite temperatures in the dual QCD theory, an effective theory of QCD based on the magnetic symmetry. We formulate the effective thermodynamical potential for filnite temperatures using the path-integral formalism in order to investigate the properties of the pure-gauge QCD vacuum. Thermal effects bring a first-order deconfinement phase transition.

Density-functional theory for systems with noncollinear spin: Orbital-dependent exchange-correlation functionals and their application to the Hubbard dimer

A new class of orbital-dependent exchange-correlation (xc) potentials for applications in noncollinear spin-density-functional theory is developed. Starting from the optimized effective potential (OEP) formalism for the exact exchange potential - generalized to the noncollinear case - correlation effects are added via a self-consistent procedure inspired by the Singwi-Tosi-Land-Sjolander (STLS) method. The orbital-dependent xc potentials are applied to the Hubbard dimer in uniform and noncollinear magnetic fields and compared to exact diagonalization and to the Bethe-ansatz local spin-density approximation. The STLS gives the overall best performance for total energies, densities and magnetizations, particularly in the weakly to moderately correlated regime.

Non-singular model universe from a perfect fluid scalar-metric cosmology

To seek for a singularity free model universe from a perfect fluid scalar-metric cosmology, we work in the "\emph{Emergent Cosmology}" (EC) paradigm which is a non-singular alternative for cosmological inflation. By using two methods including Linear Stability Theory and Effective Potential Formalism, we perform a classical analysis on the possible static solutions (that are called usually as Einstein Static Universes (ESU)in literature) in order to study EC paradigm in a FRW background. Our model contains a kinetic term of the scalar field minimally coupled to the background geometry without a potential term. The matter content of the model consists of a perfect fluid plus a cosmological constant $\Lambda$ as a separate source. In the framework of a local dynamical system analysis, we show that in the absence or presence of $\Lambda$, depending on some adopted values for the free parameters of the underlying cosmological model with flat and non-flat spatial geometries, one gets some static solutions which are viable under classical linear perturbations. By extending our study to a global dynamical system analysis, we show that in the presence of $\Lambda$ with non-flat spatial geometries there is a future global de Sitter attractor in this model. Following the second method, we derive a new static solution that represents a stable ESU but this time without dependence on the free parameters of the cosmological model at hand. As a whole, our analysis suggests the possibility of graceful realization of a non-singular EC paradigm (i.e. leaving the initial static phase and entering the inflation period as the universe is evolving) through either preserving or violation of the strong energy condition.

One-loop contributions to neutral minima in the inert doublet model

The vacuum structure of the inert doublet model is analysed at the one-loop level using the effective potential formalism, to verify the validity of tree-level predictions for the properties of the global minimum. An inert minimum (with massive fermions) and an inert-like minimum (with massless fermions) can coexist at tree level. But the one-loop analysis reveals that the allowed parameter space for the coexistence of more than one minimum is larger than the tree-level expected one. It is also shown that for some choices of parameters, the global minimum found at the one-loop level may be inert (or inert-like), contrary to what the tree-level analysis indicates.

Spin-dependent optimized effective potential formalism for open and closed systems

Orbital-based exchange $(x)$ correlation $(c)$ energy functionals, leading to the optimized effective potential (OEP) formalism of density-functional theory (DFT), are gaining increasing importance in ground-state DFT, as applied to the calculation of the electronic structure of closed systems with a fixed number of particles, such as atoms and molecules. These types of functionals prove also to be extremely valuable for dealing with solid-state systems with reduced dimensionality, such as is the case of electrons trapped at the interface between two different semiconductors, or narrow metallic slabs. In both cases, electrons build a quasi-two-dimensional electron gas, or Q2DEG. We provide here a general DFT-OEP formal scheme valid both for Q2DEGs either isolated (closed) or in contact with a particle bath (open), and show that both possible representations are equivalent, being the choice of one or the other essentially a question of convenience. Based on this equivalence, a calculation scheme is proposed which avoids the noninvertibility problem of the density response function for closed systems. We also consider the case of spontaneously spin-polarized Q2DEGs, and find that far from the region where the Q2DEG is localized, the exact $x\text{-only}$ exchange potential approaches two different, spin-dependent asymptotic limits. As an example, aside from these formal results, we also provide numerical results for a spin-polarized jellium slab, using the new OEP formalism for closed systems. The accuracy of the Krieger-Li-Iafrate approximation has been also tested for the same system, and found to be as good as it is for atoms and molecules.

Emergent cosmology revisited

We explore the possibility of emergent cosmology using the effective potential formalism. We discover new models of emergent cosmology which satisfy the constraints posed by the cosmic microwave background (CMB). We demonstrate that, within the framework of modified gravity, the emergent scenario can arise in a universe which is spatially open/closed. By contrast, in general relativity (GR) emergent cosmology arises from a spatially closed past-eternal Einstein Static Universe (ESU). In GR the ESU is unstable, which creates fine tuning problems for emergent cosmology. However, modified gravity models including Braneworld models, Loop Quantum Cosmology (LQC) and Asymptotically Free Gravity result in a stable ESU. Consequently, in these models emergent cosmology arises from a larger class of initial conditions including those in which the universe eternally oscillates about the ESU fixed point. We demonstrate that such an oscillating universe is necessarily accompanied by graviton production. For a large region in parameter space graviton production is enhanced through a parametric resonance, casting serious doubts as to whether this emergent scenario can be past-eternal.

Higgs Mass in the Standard Model, Minimal Supersymmetric Standard Model and LHC

The purpose of the paper is to look into the mass of the Higgs-like particle discovered in CMS and ATLAS experiments recently at CERN,in the context of our theoretical studies on Higgs mass bounds in the standard model within the effective potential formalism published before the LHC announcement in july 2012 and give some critical remarks. Similarly, we also comment on the uncertainty due to dependence on a few parameters of the lightest supersymmetric Higgs mass in minimal supersymmetric standard model given in our paper published before the LHC announcement on Higgs mass.Interesting conclusions about identification of the observed Higgs-like particle are arrived at from these analyses.

Dual Higgs Mechanism for Quarks in Hadrons

We study nonperturbative features of QCD using the dual Ginzburg-Landau (DGL) theory, where the color confinement is realized through the dual Higgs mechanism brought by QCD-monopole condensation. The linear confinement potential appears in the QCD-monopole condensed vacuum. We study the infrared screening effect to the confinement potential by the light-quark pair creation, and derive a compact formula for the screened quark potential. We study the dynamical chiral-symmetry breaking (DχSB) in the DGL theory by solving the Schwinger-Dyson equation. QCD-monopole condensation plays an essential role to DχSB. The QCD phase transition at finite temperature is studied using the effective potential formalism in the DGL theory. We find the reduction of QCD-monopole condensation and the string tension at high temperatures. The surface tension is calculated using the effective potential at the critical temperature Tc. The DGL theory predicts a large mass reduction of glueballs near Tc. We apply the DGL theory to the quark-gluon-plasma (QGP) physics in the ultrarelativistic heavy-ion collisions. We propose a new scenario of the QGP formation via the annihilation of color-electric flux tubes based on the attractive force between them.

N-Midpoint Rule for Calculating the Effective Mesonic Potential at Finite Temperature

The temperature dependence of meson properties is studied by using the effective potential formalism. The effective mesonic potential is numerically calculated using the n-midpoint rule at finite temperature. The meson masses, the phase transition, and the energy density are investigated as functions of temperature. The obtained results are compared with those from other works. The present technique is compared with the Hartree approximation and the imaginary time formalism. We conclude that the calculated effective potential successfully predicts the meson properties, the phase transition, and the critical temperature in comparison with other models and avoid the difficulty that found in the Hartree approximation which depends on cutoff technique.

Adaptation of the projector-augmented-wave formalism to the treatment of orbital-dependent exchange-correlation functionals

ochl [Phys. Rev. B 50 17953 (1994)] for electronic structure calculations. The methodology is illustrated with binding energy curves for C in the diamond structure and LiF in the rock salt structure, comparing results from the Hartree-Fock (HF) formalism and the Optimized Effective Potential (OEP) formalism in the so-called KLI approximation [Krieger, Li, and Iafrate, Phys. Rev. A 45, 101 (1992)] with those of the local density approximation (LDA). While the work here uses pure Fock exchange only, the formalism can be extended to treat orbital-dependent functionals more generally.

Simplification of the time-dependent generalized self-interaction correction method using two sets of orbitals: Application of the optimized effective potential formalism

We propose a simplification of the time-dependent self-interaction correction (TD-SIC) method using two sets of orbitals, applying the optimized effective potential (OEP) method. The resulting scheme is called time-dependent ``generalized SIC-OEP.'' A straightforward approximation, using the spatial localization of one set of orbitals, leads to the ``generalized SIC-Slater'' formalism. We show that it represents a great improvement compared to the traditional SIC-Slater and Krieger-Li-Iafrate formalisms.

Second-Order Perturbation Theory with Fractional Charges and Fractional Spins.

In this work the behavior of MP2 for fractional occupations is investigated. The consideration of fractional charge behavior gives a simple derivation of an expression for the chemical potential (or the derivative of energy with respect to the number of electrons) of MP2. A generalized optimized effective potential formalism (OEP) has been developed in which the OEP is a nonlocal potential, which can be applied to explicit functionals of the orbitals and eigenvalues and also facilitates the evaluation of the chemical potential. The MP2 derivative improves upon the corresponding Koopmans' theorem in Hartree-Fock theory for the ionization energy and also gives a good estimate of the electron affinity. In strongly correlated systems with degeneracies and fractional spins, MP2 diverges, and another corrected second-order perturbative method ameliorates this failure for the energy but still does not recapture the correct behavior for the energy derivatives that yield the gap. Overall we present a view of wave function based methods and their behavior for fractional charges and spins that offers insight into the application of these methods to challenging chemical problems.

Salerno's Model of DNA Re-Analysed: Could Breather Solitons have Biological Significance?

We investigate the sequence-dependent behaviour of localised excitations in a toy, nonlinear model of DNA base-pair opening originally proposed by Salerno. Specifically we ask whether "breather" solitons could play a role in the facilitated location of promoters by RNA polymerase (RNAP). In an effective potential formalism, we find excellent correlation between potential minima and Escherichia coli promoter recognition sites in the T7 bacteriophage genome. Evidence for a similar relationship between phage promoters and downstream coding regions is found and alternative reasons for links between AT richness and transcriptionally-significant sites are discussed. Consideration of the soliton energy of translocation provides a novel dynamical picture of sliding: steep potential gradients correspond to deterministic motion, while "flat" regions, corresponding to homogeneous AT or GC content, are governed by random, thermal motion. Finally we demonstrate an interesting equivalence between planar, breather solitons and the helical motion of a sliding protein "particle" about a bent DNA axis.

Accounting for the Breit interaction in relativistic effective core potential calculations of actinides

The accuracy of accounting for the Breit effects in calculations of atoms and molecules in the framework of the two-component relativistic effective core potential (RECP) formalism is analysed theoretically and illustrated in calculations. Contributions of the Breit interaction between different core and valence shells are studied in the framework of the four-component SCF approximation for uranium and plutonium. It is shown that two-electron Breit effects between valence electrons can be neglected for the calculation of valence energies in systems containing actinides with ‘chemical accuracy’ (1 kcal mol−1 or 350 cm−1), whereas large core–core and core–valence Breit contributions can be efficiently described by one-electron RECP operators. Different versions of generalized RECPs with the Breit interaction taken into account are constructed for uranium and plutonium and compared for accuracy with the corresponding all-electron four-component calculations.

Neutral Higgs boson masses of the MSSM at the one-loop level in an explicitCPviolation scenario

The neutral Higgs sector of the minimal supersymmetric standard model (MSSM) in explicit CP violation scenario is investigated at the one-loop level. Within the context of the effective potential formalism, the masses of the neutral Higgs bosons are calculated at the one-loop level by taking into account the contributions of the following loops of ordinary particles and superpartners: top quark, the scalar top quarks, bottom quark, the scalar bottom quarks, tau lepton, the scalar tau leptons, $W$ boson, the charged Higgs boson, the charginos, $Z$ boson, the scalar and pseudoscalar Higgs bosons, and the neutralinos. Our calculation is an improvement in the sense that both the terms which are quartic in the electroweak coupling constants into account, and the pseudoscalar Higgs loop contribution are explicitly included.

Application of effective potential formalism to mechanical alloying in Ag–Cu and Cu–Fe systems

We have used the competing dynamics model and the effective potential formalism for studying phase stability during mechanical milling of Ag–Cu and Cu–Fe systems. We first present a method for extracting an effective potential for systems in which the atomic mobility may depend on alloy composition. Using an estimate for the typical ballistic diffusivity, we apply this formalism to calculate the dynamical phase diagram for the Ag–Cu and Cu–Fe binary systems under mechanical milling. For the Ag–Cu system, the dynamical phase diagram exhibits a miscibility gap that closes in on itself at low temperatures, due to the exponentially decreasing thermal diffusivity (and hence, increasing influence of ballistic diffusivity) with decreasing temperature. In the Cu–Fe system, in which the effective potential for both the bcc and fcc phases need to be taken into account, the fcc phase is shown to be stabilized at low temperatures for all the alloys, except the almost pure iron (which is stabilized in its bcc form). These results are critically compared with available experimental results.

Top quark seesaw theory of electroweak symmetry breaking

We study electroweak symmetry breaking involving the seesaw mechanism of quark condensation. These models produce a composite Higgs boson involving the left-handed top quark, yet the top mass arises naturally at the observed scale. We describe a schematic model which illustrates the general dynamical ideas. We also consider a generic low-energy effective theory which includes several composite scalars, and we use the effective potential formalism to compute their spectrum. We develop a more detailed model in which certain features of the schematic model are replaced by additional dynamics.