Self-interaction Term Research Articles

Dynamic transition to spontaneous scalarization in boson stars

We show that the phenomenon of spontaneous scalarization predicted in neutron stars within the framework of scalar-tensor tensor theories of gravity, also takes place in boson stars without including a self-interaction term for the boson field (other than the mass term), contrary to what was claimed before. The analysis is performed in the physical (Jordan) frame and is based on a 3+1 decomposition of spacetime assuming spherical symmetry.

Cascading cosmology

We develop a fully covariant, well-posed 5D effective action for the 6D cascading gravity brane-world model, and use this to study cosmological solutions. We obtain this effective action through the 6D decoupling limit, in which an additional scalar degree mode, \pi, called the brane-bending mode, determines the bulk-brane gravitational interaction. The 5D action obtained this way inherits from the sixth dimension an extra \pi self-interaction kinetic term. We compute appropriate boundary terms, to supplement the 5D action, and hence derive fully covariant junction conditions and the 5D Einstein field equations. Using these, we derive the cosmological evolution induced on a 3-brane moving in a static bulk. We study the strong- and weak-coupling regimes analytically in this static ansatz, and perform a complete numerical analysis of our solution. Although the cascading model can generate an accelerating solution in which the \pi field comes to dominate at late times, the presence of a critical singularity prevents the \pi field from dominating entirely. Our results open up the interesting possibility that a more general treatment of degravitation in a time-dependent bulk, or taking into account finite brane-thickness effects, may lead to an accelerating universe without a cosmological constant.

Discontinuities of the Chemical Potential in Reduced Density Matrix Functional Theory

Abstract Using the discontinuity of the chemical potential as a function of excess charge, the fundamental gaps for finite systems and the band gaps of extended solids are determined within reduced density matrix functional theory. We also present the necessary and sufficient conditions for the one-body reduced density matrix of a system with fractional charge to be ensemble N-representable. The performance of most modern day reduced density matrix functionals is assessed for the gaps and the correlation energy of finite systems. Our results show that for finite systems the PNOF, BBC3, and power functionals yield very accurate correlation energies while for a correct description of the fundamental gap the removal of self-interaction terms is essential. For extended solids we find that the power functional captures the correct band gap behavior for conventional semiconductors as well as strongly correlated Mott insulators, where a gap is obtained in absence of any magnetic ordering.

Super Yang–Mills theory from nonlinear supersymmetry

The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang–Mills (SYM) theory is studied for N=3 SUSY in two-dimensional space–time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu–Goldstone fermion self-interaction terms.

Localized Hartree product treatment of multiple protons in the nuclear-electronic orbital framework

An approximation for treating multiple quantum nuclei within the nuclear-electronic orbital (NEO) framework for molecular systems is presented. In the approximation to NEO-Hartree-Fock, the nuclear wave function is represented by a Hartree product rather than a Slater determinant, corresponding to the neglect of the nuclear exchange interactions. In the approximation to NEO-density functional theory, the nuclear exchange-correlation functional is chosen to be the diagonal nuclear exchange interaction terms, thereby eliminating the nuclear self-interaction terms. To further enhance the simplicity and computational efficiency, the nuclear molecular orbitals or Kohn-Sham orbitals are expanded in terms of localized nuclear basis sets. These approximations are valid because of the inherent localization of the nuclear orbitals and the numerical insignificance of the nuclear exchange interactions in molecular systems. Moreover, these approximations lead to substantial computational savings due to the reduction in both the number of integrals that must be calculated and the size of the matrices that must be diagonalized. These nuclear Hartree product approximation (HPA) methods scale linearly with the number of quantum protons and are highly parallelizable. Applications to a water hexamer, glycine dimer, and 32-water cluster, where all hydrogen nuclei are treated quantum mechanically, illustrate the accuracy and computational efficiency of the nuclear HPA methods. These strategies will facilitate the implementation of explicitly correlated NEO methods for molecular systems with multiple quantum protons.

Wave-Corpuscle Mechanics for Electric Charges

It is well known that the concept of a point charge interacting with the electromagnetic (EM) field has a problem. To address that problem we introduce the concept of wave-corpuscle to describe spinless elementary charges interacting with the classical EM field. Every charge interacts only with the EM field and is described by a complex valued wave function over the 4-dimensional space time continuum. A system of many charges interacting with the EM field is defined by a local, gauge and Lorentz invariant Lagrangian with a key ingredient—a nonlinear self-interaction term providing for a cohesive force assigned to every charge. An ideal wave-corpuscle is an exact solution to the Euler-Lagrange equations describing both free and accelerated motions. It carries explicitly features of a point charge and the de Broglie wave. Our analysis shows that a system of well separated charges moving with nonrelativistic velocities are represented accurately as wave-corpuscles governed by the Newton equations of motion for point charges interacting with the Lorentz forces. In this regime the nonlinearities are “stealthy” and don’t show explicitly anywhere, but they provide for the binding forces that keep localized every individual charge. The theory can also be applied to closely interacting charges as in hydrogen atom where it produces discrete energy spectrum.

Effects of the cosmological constant on chaos in an FRW scalar field universe

The dependence of chaos on two parameters of the cosmological constant and the self-interacting coefficient in the imaginary phase space for a closed Friedman–Robertson–Walker (FRW) universe with a conformally coupled scalar field, as the full understanding of the dependence in real phase space, is investigated numerically. It is found that Poincaré plots for the two parameters less than 1 are almost the same as those in the absence of the cosmological constant and self-interacting terms. For energies below the energy threshold of 0.5 for the imaginary problem in which there are no cosmological constant and self-interacting terms, an abrupt transition to chaos occurs when at least one of the two parameters is 1. However, the strength of the chaos does not increase for energies larger than the threshold. For other situations of the two parameters larger than 1, chaos is weaker, and even disappears as the two parameters increase.

Galileon cosmology

We study the cosmology of a galileon scalar-tensor theory, obtained by covariantizing the decoupling Lagrangian of the Dvali-Gabadadze-Poratti (DGP) model. Despite being local in $3+1$ dimensions, the resulting cosmological evolution is remarkably similar to that of the full $4+1$-dimensional DGP framework, both for the expansion history and the evolution of density perturbations. As in the DGP model, the covariant galileon theory yields two branches of solutions, depending on the sign of the galileon velocity. Perturbations are stable on one branch and ghostlike on the other. An interesting effect uncovered in our analysis is a cosmological version of the Vainshtein screening mechanism: at early times, the galileon dynamics are dominated by self-interaction terms, resulting in its energy density being suppressed compared to matter or radiation; once the matter density has redshifted sufficiently, the galileon becomes an important component of the energy density and contributes to dark energy. We estimate conservatively that the resulting expansion history is consistent with the observed late-time cosmology, provided that the scale of modification satisfies ${r}_{c}\ensuremath{\gtrsim}15\text{ }\text{ }\mathrm{Gpc}$.

Parallel Dynamics of Continuous Hopfield Model Revisited

We have applied the generating functional analysis (GFA) to the continuous Hopfield model. We have also confirmed that the GFA predictions in some typical cases exhibit good consistency with computer simulation results. When a retarded self-interaction term is omitted, the GFA result becomes identical to that obtained using the statistical neurodynamics as well as the case of the sequential binary Hopfield model.

Exploring the Limit of Accuracy of the Global Hybrid Meta Density Functional for Main-Group Thermochemistry, Kinetics, and Noncovalent Interactions

The hybrid meta density functionals M05-2X and M06-2X have been shown to provide broad accuracy for main group chemistry. In the present article we make the functional form more flexible and improve the self-interaction term in the correlation functional to improve its self-consistent-field convergence. We also explore the constraint of enforcing the exact forms of the exchange and correlation functionals through second order (SO) in the reduced density gradient. This yields two new functionals called M08-HX and M08-SO, with different exact constraints. The new functionals are optimized against 267 diverse main-group energetic data consisting of atomization energies, ionization potentials, electron affinities, proton affinities, dissociation energies, isomerization energies, barrier heights, noncovalent complexation energies, and atomic energies. Then the M08-HX, M08-SO, M05-2X, and M06-2X functionals and the popular B3LYP functional are tested against 250 data that were not part of the original training data for any of the functionals, in particular 164 main-group energetic data in 7 databases, 39 bond lengths, 38 vibrational frequencies, and 9 multiplicity-changing electronic transition energies. These tests include a variety of new challenges for complex systems, including large-molecule atomization energies, organic isomerization energies, interaction energies in uracil trimers, and bond distances in crowded molecules (in particular, cyclophanes). The M08-HX functional performs slightly better than M08-SO and M06-2X on average, significantly better than M05-2X, and much better than B3LYP for a combination of main-group thermochemistry, kinetics, noncovalent interactions, and electronic spectroscopy. More important than the slight improvement in accuracy afforded by M08-HX is the conformation that the optimization procedure works well for data outside the training set. Problems for which the accuracy is especially improved by the new M08-HX functional include large-molecule atomization energies, noncovalent interaction energies, conformational energies in aromatic peptides, barrier heights, multiplicity-changing excitation energies, and bond lengths in crowded molecules.

Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector

We carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector, comprising a SQUID with mechanically compliant loop segment, which is embedded in a microwave transmission line resonator. The SQUID is approximated as a nonlinear current-dependent inductance, inducing an external flux tunable nonlinear Duffing self-interaction term in the microwave resonator mode equation. Motion of the compliant SQUID loop segment is transduced inductively through changes in the external flux threading SQUID loop, giving a ponderomotive radiation pressure-type coupling between the microwave and mechanical resonator modes. Expressions are derived for the detector signal response and noise, and it is found that a soft-spring Duffing self-interaction enables a closer approach to the displacement detection standard quantum limit, as well as cooling closer to the ground state.

Supersymmetric codimension-two branes and U(1)Rmediation in 6D gauged supergravity

We construct a consistent supersymmetric action for brane chiral and vector multiplets in a six-dimensional chiral gauged supergravity. A nonzero brane tension can be accommodated by allowing for a brane-localized Fayet-Iliopoulos term proportional to the brane tension. When the brane chiral multiplet is charged under the bulk U(1)_R, we obtain a nontrivial coupling to the extra component of the U(1)_R gauge field strength as well as a singular scalar self-interaction term. Dimensionally reducing to 4D on a football supersymmetric solution, we discuss the implication of such interactions for obtaining the U(1)_R D-term in the 4D effective supergravity. By assuming the bulk gaugino condensates and nonzero brane F- and/or D-term for the uplifting potential, we have all the moduli stabilized with a vanishing cosmological constant. The brane scalar with nonzero R charge then gets a soft mass of order the gravitino mass. The overall sign of the soft mass squared depends on the sign of the R charge as well as whether the brane F- or D-term dominates.

Complete Gluonic Phase in Two-Flavour Colour Superconductivity

We study a typical complete gluonic phase (LGP) in two-flavour colour superconductivity (2SC) by calculating the essential cubic and quartic interfering term between the gluonic condensates «Az(8)» and «Az(6)» with a gauged NJL model. It is proven that the coefficients of the cubic interfering term and the vacuum contributions of the cubic and quartic interfering term are all equal to zeroes. The coefficients of the quartic interfering term and the «Az(6)»'s quartic self-interaction term at stationary points of Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase are calculated. Comparisons among the effective potentials of LGP, g2SC and LOFF phase indicate that LGP could be the genuine ground state of 2SC for some reasonable parameters.

Empirical functionals for reduced-density-matrix-functional theory

We present fully empirical exchange-correlation functionals to be used within reduced-density-matrix-functional theory (RDMFT). These are of the popular $J\text{\ensuremath{-}}K$ form [involving only Coulomb- $(J)$ and exchange- $(K)$ type integrals over the natural orbitals], where the function of the occupation numbers that multiplies the Fock orbital term is written as a Pad\'e approximant. The coefficients of the Pad\'e approximant are optimized for a test set of eight molecules, and then refined for a larger set of $35\phantom{\rule{0.3em}{0ex}}\text{molecules}$. Two different approaches were tried, either keeping the self-interaction terms, or by removing them explicitly from the functional. The functionals thus obtained involve very few parameters, but are able to outperform other RDMFT functionals, yielding correlation energies that are, on average, even slightly better than second-order M\o{}ller-Plesset theory.

Effect of the boundary shape in the effective theory of fractional quantum Hall edges

Starting from a microscopic description of a system of strongly interacting electrons in a strong magnetic field in a finite geometry, we construct the boundary low energy effective theory for a fractional quantum Hall droplet taking into account the effects of a smooth edge. The effective theory obtained is the standard chiral boson theory (chiral Luttinger theory) with an additional self-interacting term which is induced by the boundary. As an example of the consequences of this model, we show that such modification leads to a nonuniversal reduction in the tunneling exponent which is independent of the filling fraction. This is in qualitative agreement with experiments, which systematically found exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory.

Local-field effects in magnetodielectric media: Negative refraction and absorption reduction

We give a microscopic derivation of the Clausius-Mossotti relations for a homogeneous and isotropic magnetodielectric medium consisting of radiatively broadened atomic oscillators. To this end the diagram series of electromagnetic propagators is calculated exactly for an infinite bicubic lattice of dielectric and magnetic dipoles for a small lattice constant compared to the resonance wavelength $\ensuremath{\lambda}$. Modifications of transition frequencies and linewidth of the elementary oscillators are taken into account in a self-consistent way by a proper incorporation of the singular self-interaction terms. We show that in radiatively broadened media sufficiently close to the free-space resonance the real part of the index of refraction approaches the value $\ensuremath{-}2$ in the limit of $\ensuremath{\rho}{\ensuremath{\lambda}}^{3}⪢1$, where $\ensuremath{\rho}$ is the number density of scatterers. Since at the same time the imaginary part vanishes as $1∕\ensuremath{\rho}$, local field effects can have important consequences for realizing low-loss negative index materials.

Avoiding singularity problems associated with meta-GGA (generalized gradient approximation) exchange and correlation functionals containing the kinetic energy density

Convergence problems of meta-GGA (generalized gradient approximation) XC (exchange and correlation) functionals containing a self-interaction correction term are traced back to a singularity of the latter that occurs at critical points of the electron density. This is demonstrated for the bond critical point of equilibrium and stretched H2. A simple remedy is suggested that cures meta-XC functionals such as VSXC, TPSS, M05, M06, and their derivatives without extra cost.

Restrictions over two-dimensional gauge models with Thirring-like interaction

Some years ago, it was shown how fermion self-interacting terms of the Thirring-type impact the usual structure of massless two-dimensional gauge theories [1]. In that work only the cases of pure vector and pure chiral gauge couplings have been considered and the corresponding Thirring term was also pure vector and pure chiral respectively, such that the vector (or chiral) Schwinger model should not lose its chirality structure due to the addition of the quartic interaction term. Here we extend this analysis to a generalized vector and axial coupling both for the gauge interaction and the quartic fermionic interactions. The idea is to perform quantization without losing the original structure of the gauge coupling. In order to do that we make use of an arbitrariness in the definition of the Thirring-like interaction.

Cylindrically symmetric solitons in Einstein-Yang-Mills theory

Recently new Einstein-Yang-Mills (EYM) soliton solutions were presented which describe superconducting strings with Kasner asymptotics [D. V. Gal'tsov, E. A. Davydov, and M. S. Volkov, hep-th/0610183.]. Here we study the static cylindrically symmetric SU(2) EYM system in more detail. The ansatz for the gauge field corresponds to superposition of the azimuthal ${B}_{\ensuremath{\varphi}}$ and the longitudinal ${B}_{z}$ components of the color magnetic field. We derive sum rules relating data on the symmetry axis to asymptotic data and show that generic asymptotic structure of regular solutions is Kasner. Solutions starting with vacuum data on the axis generically are divergent. Regular solutions correspond to some bifurcation manifold in the space of parameters which has the low-energy limiting point corresponding to string solutions in flat space (with the divergent total energy) and the high-curvature point where gravity is crucial. Some analytical results are presented for the low-energy limit, and numerical bifurcation curves are constructed in the gravitating case. Depending on the parameters, the solution looks like a straight string or a pair of straight and circular strings. The existence of such nonlinear superposition of two strings becomes possible due to self-interaction terms in the Yang-Mills action which suppress contribution of the circular string near the polar axis.

Comments on proposed gravitational modifications of Schrödinger dynamics and their experimental implications

We discuss aspects of gravitational modifications of Schrödinger dynamics proposed by Diósi and Penrose. We consider first the Diósi–Penrose criterion for gravitationally induced state vector reduction, and compute the reduction time expected for a superposition of a uniform density cubical solid in two positions displaced by a small fraction of the cube side. We show that the predicted effect is much smaller than would be observable in the proposed Marshall et al mirror experiment. We then consider the ‘Schrödinger–Newton’ equation for an N-particle system. We show that in the independent particle approximation, it differs from the usual Hartree approximation applied to the Newtonian potential by self-interaction terms, which do not have a consistent Born rule interpretation. This raises doubts about the use of the Schrödinger–Newton equation to calculate gravitational effects on molecular interference experiments. When the effects of Newtonian gravitation on molecular diffraction are calculated using the standard many-body Schrödinger equation, no washing out of the interference pattern is predicted.