Symmetry Breaking Potential Research Articles

Spontaneous symmetry breaking and linear effective potentials

The convexity of a scalar effective potential is a well-known property, and, in the situation of spontaneous symmetry breaking, leads to the so-called Maxwell construction, characterized by a flat effective potential between the minima of the bare potential. Simple derivations are given here, which show how linear effective potentials arise from nontrivial saddles points which dominate the partition function, for a self-interacting scalar field and for a Yukawa model.

Dynamical dark energy and spontaneously generated gravity

We study the cosmological evolution of an induced gravity model with a scale symmetry breaking potential for the scalar field and the presence of barotropic fluids. The radiation to matter transition, following inflation and reheating, influences the dynamics of such a field through its non-minimal coupling. Indeed one finds, as a consequence of such a transition, that the scalar field is shifted from the potential minimum (which is associated with a zero cosmological constant). We illustrate how, under certain conditions on the potential, such a dynamics can lead to a suitable amount of dark energy explaining the present accelerated expansion. In such an approach, however, for long enough times, the dark energy will disappear.

Massive hopfions

The Skyrme-Faddeev model is a (3+1)-dimensional model which has knotted, string-like, soliton solutions. In this paper we investigate a Skyrme-Faddeev model with an SO(3) symmetry breaking potential. We then rescale this model and take the mass to infinity. This infinite mass model is found to have compact knotted solutions. In all of the investigated massive models we find similar charged solutions as in the usual, m=0, model. We also find that their energies follow a similar power growth as the m=0 model.

Spontaneous breaking of SU(3) to finite family symmetries — a pedestrian’s approach

Non-Abelian discrete family symmetries play a pivotal role in the formulation of models with tri-bimaximal lepton mixing. We discuss how to obtain symmetries such as A4, semidirect product of Z7 and Z3, and Delta(27) from an underlying SU(3) gauge symmetry. Higher irreducible representations are required to achieve the spontaneous breaking of the continuous group. We present methods of identifying the required vacuum alignments and discuss in detail the symmetry breaking potentials.

Anisotropic inflation from charged scalar fields

We consider models of inflation with U(1) gauge fields and charged scalar fields including symmetry breaking potential, chaotic inflation and hybrid inflation. We show that there exist attractor solutions where the anisotropies produced during inflation becomes comparable to the slow-roll parameters. In the models where the inflaton field is a charged scalar field the gauge field becomes highly oscillatory at the end of inflation ending inflation quickly. Furthermore, in charged hybrid inflation the onset of waterfall phase transition at the end of inflation is affected significantly by the evolution of the background gauge field. Rapid oscillations of the gauge field and its coupling to inflaton can have interesting effects on preheating and non-Gaussianities.

Slow-roll inflation with the Gauss-Bonnet and Chern-Simons corrections

We study slow-roll inflation with the Gauss-Bonnet and Chern-Simons corrections. We obtain general formulas for the observables: spectral indices, tensor-to-scalar ratio and circular polarization of gravitational waves. The Gauss-Bonnet term violates the consistency relation r = −8nT. Particularly, blue spectrum nT > 0 and scale invariant spectrum |8nT|/r << 1 of tensor modes are possible. These cases require the Gauss-Bonnet coupling function of ξ,ϕ ∼ 108/MPl. We use examples to show new-inflation-type potential with 10MPl symmetry breaking scale and potential with flat region in ϕ≳10MPl lead to observationally consistent blue and scale invariant spectra, respectively. Hence, these interesting cases can actually be realized. The Chern-Simons term produce circularly polarized tensor modes. We show an observation of these signals supports existence of the Chern-Simons coupling function of ω,ϕ ∼ 108/MPl. Thus, with future observations, we can fix or constrain the value of these coupling functions, at the CMB scale.

Inflation and reheating in spontaneously generated gravity

Inflation is studied in the context of induced gravity (IG) $\gamma \sigma^2 R$, where $R$ is the Ricci scalar, $\sigma$ a scalar field and $\gamma$ a dimensionless constant, and diverse symmetry-breaking potentials $V(\sigma)$ are considered. In particular we compared the predictions for Landau-Ginzburg (LG) and Coleman-Weinberg (CW) type potentials and their possible generalizations with the most recent data. We find that large field inflation generally leads to fewer constraints on the parameters and the shape of the potential whereas small field inflation is more problematic and, if viable, implies more constraints, in particular on the parameter $\gamma$. We also examined the reheating phase and obtained an accurate analytical solution for the dynamics of inflaton and the Hubble parameter by using a multiple scale analysis (MSA). The solutions were then used to study the average expansion of the Universe, the average equation of state for the scalar field and both the perturbative and resonant decays of the inflaton field.

Localized gravity on topological Abelian Higgs strings

In this work there are proposed several new 6D brane worlds based on exact topological solutions to the vortex equations for the Abelian Higgs model, with suitable boundary conditions and symmetry breaking potentials similar to the mexican hat. Just as happens for RS domain wall brane worlds, it is shown that the massless mode of linearized gravity is localized in the neighborhood of the string–vortex solution while there are not massive bounded states. The correction to the newtonian limit of the effective 4D gravity is calculated.

Gauge invariant nonlinear electrodynamics motivated by a spontaneous breaking of the Lorentz symmetry

We introduce a new version of non-linear electrodynamics which is produced by a spontaneous symmetry breaking of Lorentz invariance induced by the non-zero expectation value of the electromagnetic field strength. The symmetry breaking potential is argued to effectively arise from the integration of massive gauge bosons and fermions in an underlying fundamental theory. All possible choices of the vacuum lead only to the remaining invariant subgroups T(2) and HOM(2). We explore the plane wave solutions of the linearized sector of the model for an arbitrary vacuum. They present two types of dispersion relations. One corresponds to the case of the usual Maxwell electrodynamics with the standard polarization properties of the fields. The other dispersion relation involves anisotropies determined by the structure of the vacuum. The model is stable in the small Lorentz invariance violation approximation. We have embedded our model in the photon sector of the Standard Model Extension in order to set bounds for our parameters. The one-way anisotropic speed of light is calculated for a general vacuum and its isotropic component is strongly bounded by ${\tilde \delta c}/c < 2 \times 10^{-32}$. The anisotropic violation contribution is estimated by introducing an alternative definition for the difference of the two-way speed of light in perpendicular directions $\Delta c$, which is also strongly bounded by ${\Delta c}/c < 10^{-32}$. Finally, we speculate on the relation of the vacuum energy of the model with the cosmological constant and propose a connection between the vacuum fields and the intergalactic magnetic fields.

Gaps and tails in graphene and graphane

We study the density of states (DOS) in monolayer and bilayer graphene in the presence of a random potential that breaks sublattice symmetries. While a uniform symmetry-breaking potential (SBP) opens a uniform gap, a random SBP also creates tails in the DOS. The latter can close the gap again, preventing the system from becoming an insulator. However, for a sufficiently large gap the tails contain localized states with nonzero DOS. These localized states allow the system to conduct at nonzero temperature via variable-range hopping. This result is in agreement with recent experimental observations in graphane by Elias et al (2009 Science 323 610).

Diffusion in the random gap model of monolayer and bilayer graphene

In this paper we study the effect of a fluctuating gap in mono- and bilayer graphene, created by a symmetry-breaking random potential. We identify a continuous symmetry for the two-particle Green's function which is spontaneously broken in the average two-particle Green's function and leads to a massless fermion mode. Within a loop expansion it is shown that the massless mode is dominated on large scales by small loops. This result indicates diffusion of electrons. Although the diffusion mechanism is the same in mono- and in bilayer graphene, the amount of scattering is much stronger in the latter. Physical quantities at the neutrality point, such as the density of states, the diffusion coefficient, and the conductivity, are determined by the one-particle scattering rate. All these quantities vanish at a critical value of the average symmetry-breaking potential, signaling a continuous transition to an insulating behavior.

Density functional study of collective electron localization: detection by persistentcurrent

We apply the optimized effective potential (OEP) implementation of density functionaltheory (DFT) to the model system of interacting spinless electrons on a quantum ring.The ring encircles a magnetic flux that induces a persistent current. In a perfectrotationally invariant system the current does not depend on the electron–electroninteraction (the latter is characterized by a standard dimensionless parameterrS) and hence is not sensitive to the microscopic structure of the electron correlated state.This changes, however, if a symmetry-breaking external potential is introduced or, in arealistic system, due to the crystal lattice potential (Hamer et al 1987 J. Phys. A: Math.Gen. 20 5677–93). In our model, we calculate the persistent current as a function ofrS in thepresence of a weak Gaussian-shaped ‘impurity’ potential. We find that while below a threshold valuerS<rSc≈2.05 the current isindependent of rS, itdecays exponentially for rS>rSc. This signals the formation of an electron Wigner crystal pinnedby the impurity potential. The electron density, homogeneous belowrSc, indeed shows a periodic modulation atrS>rSc. The modulationamplitude follows a (rS−rSc)1/2 behaviour which is characteristic for a second-order phase transition, as expected in themean-field-type DFT-OEP approach. Our calculation shows that the macroscopic current,which is a quantity directly accessible in DFT, can serve as an indicator of the formation ofa correlated electron state.

Autonomous rigid body attitude synchronization

Control laws to synchronize attitudes in a swarm of fully actuated rigid bodies, in the absence of a common reference attitude or hierarchy in the swarm, are proposed in [Smith, T. R., Hanssmann, H., & Leonard, N.E. (2001). Orientation control of multiple underwater vehicles with symmetry-breaking potentials. In Proc. 40th IEEE conf. decision and control (pp. 4598–4603); Nair, S., Leonard, N. E. (2007). Stable synchronization of rigid body networks. Networks and Heterogeneous Media, 2(4), 595–624]. The present paper studies two separate extensions with the same energy shaping approach: (i) locally synchronizing the rigid bodies’ attitudes, but without restricting their final motion and (ii) relaxing the communication topology from undirected, fixed and connected to directed, varying and uniformly connected. The specific strategies that must be developed for these extensions illustrate the limitations of attitude control with reduced information.

Energy functional for the three-level Lipkin model

We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three nondegenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials.

Sphaleron–bisphaleron bifurcations in a custodial-symmetric two-doublets model

The standard electroweak model is extended by means of a second Brout–Englert–Higgs doublet. The symmetry breaking potential is chosen in such a way that (i) the Lagrangian possesses a custodial symmetry, (ii) a static, spherically symmetric ansatz of the bosonic fields consistently reduces the Euler–Lagrange equations to a set of differential equations. The potential involves, in particular, products of fields of the two doublets, with a coupling constant λ3. Static, finite energy solutions of the classical equations are constructed. The regular, non-trivial solutions with the lowest classical energy can be of two types: sphalerons or bisphalerons, according to the coupling constants. Special emphasis is put on the bifurcation between these two types of solutions which is analyzed in the function of the different constants of the model, namely of λ3.

Metastable anisotropy orientation of nematic quantum Hall fluids

We analyze the experimental observation of metastable anisotropy resistance orientation at half-filled quantum Hall fluids by means of a model of a quantum nematic liquid in an explicit symmetry-breaking potential. We interpret the observed ``rotation'' of the anisotropy axis as a process of nucleation of nematic domains and compute the nucleation rate within this model. By comparing with experiment, we are able to predict the critical radius of nematic bubbles---${R}_{c}\ensuremath{\sim}2.6\text{ }\ensuremath{\mu}\text{m}$. Each domain contains about ${10}^{4}$ electrons.

Pseudospin, supersymmetry and the shell structure of atomic nuclei

The evolution of single-particle energies with varying isospin asymmetry in the shell model is an important issue when predicting changes in the shell structure for exotic nuclei. In many cases pseudospin partner levels, that are almost degenerate in energy for stable nuclei, are relevant in extracting the size of the shell gaps. A breaking of the pseudospin symmetry can affect the size of these gaps and change the magic numbers accordingly. The strength of the pseudospin splitting is expected to depend in particular on isovector-dependent and tensor contributions to the effective nuclear interaction. A description employing supersymmetric quantum mechanics allows to derive a pseudospin symmetry breaking potential that is regular in contrast to the pseudospin–orbit potential in the conventional relativistic treatment. The derived perturbation potential provides a measure to quantify the symmetry breaking and it can be employed to improve mean-field calculations in order to better reproduce the experimentally observed shell evolution. General potentials with exact pseudospin symmetry are obtained that can be used in relativistic mean-field Hamiltonians.

Isospin-breaking two-nucleon force with explicit Δ excitations

We study the leading isospin-breaking contributions to the two-nucleon two-pion exchange potential due to explicit \ensuremath{\Delta} degrees of freedom in chiral effective field theory. In particular, we find important contributions due to the delta mass splittings to the charge symmetry breaking potential that act opposite to the effects induced by the nucleon mass splitting.

Spontaneous Lorentz and diffeomorphism violation, massive modes, and gravity

Theories with spontaneous local Lorentz and diffeomorphism violation contain massless NambuGoldstone modes, which arise as field excitations in the minimum of the symmetry-breaking potential. If the shape of the potential also allows excitations above the minimum, then an alternative gravitational Higgs mechanism can occur in which massive modes involving the metric appear. The origin and basic properties of the massive modes are addressed in the general context involving an arbitrary tensor vacuum value. Special attention is given to the case of bumblebee models, which are gravitationally coupled vector theories with spontaneous local Lorentz and diffeomorphism violation. Mode expansions are presented in both local and spacetime frames, revealing the Nambu-Goldstone and massive modes via decomposition of the metric and bumblebee fields, and the associated symmetry properties and gauge fixing are discussed. The class of bumblebee models with kinetic terms of the Maxwell form is used as a focus for more detailed study. The nature of the associated conservation laws and the interpretation as a candidate alternative to Einstein-Maxwell theory are investigated. Explicit examples involving smooth and Lagrange-multiplier potentials are studied to illustrate features of the massive modes, including their origin, nature, dispersion laws, and effects on gravitational interactions. In the weak static limit, the massive mode and Lagrange-multiplier fields are found to modify the Newton and Coulomb potentials. The nature and implications of these modifications are examined.

TWISTED SEMILOCAL STRINGS WITH TWO HIGGS-DOUBLETS

The standard electroweak model is extended by means of a second Brout–Englert–Higgs–doublet. The symmetry breaking potential is chosen in such a way that (i) the Lagrangian possesses a custodial symmetry, (ii) a stationary, axially symmetric ansatz of the bosonic fields consistently reduces the Euler–Lagrange equations to a set of differential equations. The potential involves, in particular, a direct interaction between the two doublets. Magnetic, stationary, axially-symmetric solutions of the classical equations are constructed. Some of them can be assimilated to embedded Nielsen–Olesen strings. From these solutions there are bifurcations and new solutions appear which exhibit the characteristics of the recently constructed twisted semilocal strings. A special emphasis is set on "doubly-twisted" solutions for which the two doublets present different time-dependent phase factors. They are regular and have a finite energy which can be lower than the energy of the embedded twisted solution. Electric-type solutions, such that the fields oscillate asymptotically far from the symmetry-axis, are also reported.