MONTE CARLO STUDY OF THE TRIANGLE LATTICE GEUCHI-KAWAI MODEL

The triangle lattice Eguchi-Kawai model is studied by using the Monte Carlo technique. The results indicate that in the two-dimensional case U(1) symmetry is not broken but in the three-dimensional case a clear evidence of spontaneous breaking of the U(1) symmetry is observed in the weak coupling region.     

Geometric Analysis of Bifurcation and Symmetry Breaking in a Gross—Pitaevskii Equation

Gross–Pitaevskii and nonlinear Hartree equations are equations of nonlinear Schrödinger type that play an important role in the theory of Bose–Einstein condensation. Recent results of Aschbacher et al.(3) demonstrate, for a class of 3-dimensional models, that for large boson number (squared L ²norm), $N$ , the ground state does not have the symmetry properties of the ground state at small $N$ . We present a detailed global study of the symmetry breaking bifurcation for a 1-dimensional model Gross–Pitaevskii equation, in which the external potential (boson trap) is an attractive double-well, consisting of two attractive Dirac delta functions concentrated at distinct points. Using dynamical systems methods, we present a geometric analysis of the symmetry breaking bifurcation of an asymmetric ground state and the exchange of dynamical stability from the symmetric branch to the asymmetric branch at the bifurcation point.     

Spontaneous breaking of four-fold rotational symmetry in two-dimensional electronic systems explained as a continuous topological transition

The Fermi liquid approach is applied to the problem of spontaneous violation of the C ₄ symmetry in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is traced to the existence of a topological phase transition. This continuous transition is triggered when the Fermi line, driven by the quasiparticle interactions, reaches the van Hove saddle points, where the group velocity vanishes and the density of states becomes singular. An unconventional Fermi liquid emerges beyond the implicated quantum critical point.     

Interacting twisted and untwisted scalar fields in a nonsimply connected space-time

Interacting twisted and untwisted scalar fields are studied in a non-Minkowskian space-time with the topology S¹ × R³. Renormalization of the theory is discussed, and the oneloop effective potential is calculated and used to discuss symmetry breaking and mass generation as a consequence of the non-trivial topology. It is found that an interaction between the twisted and untwisted fields can lead to symmetry breaking.     

Scaling behaviour of charged spin-one partons in a gauge model

In a hadron model in which the fermion constituents are bound by vector-isovector gauge fields, electromagnetism is introduced; by spontaneously breaking the strong (SU(2)) gauge symmetry, the gauge fields become massive. We identify the spinors and vectors with partons, and, assuming the naive parton model hypothesis, we calculate the cross section e⁺e^?→ hadrons and the structure functions of the nucleon; scaling is obtained desoite induces presence of an anomalous magnetic moment term in the coupling of the photon with the charged vector fields; the reason is that the spontaneous breaking of the symmetry indices a vector-meson dominance type of coupling between the photon and the neutral vector, which is just what is necessary to restore scaling.     

Compositional inversion symmetry breaking in ferroelectric perovskites

Cubic perovskite compounds of the form (A(1/3)A(')(1/3)A(")(1/3))BO3 and A(B(1/3)B(')(1/3)B(")(1/3))O3, in which the differentiated cations form an alternating series of monolayers, are studied using first-principles methods. Such compounds are representative of a possible new class of materials in which ferroelectricity is perturbed by compositional breaking of inversion symmetry. For isovalent substitution the ferroelectric double-well potential becomes asymmetric, so that minority domains may no longer survive. The symmetry breaking is enormously stronger for heterovalent substitution; here the double-well behavior is destroyed. Tuning between these behaviors may allow for the optimization of desired materials properties.     

On dynamical symmetry breakdown

We investigate the possibility of dynamical symmetry breaking, that is the appearance of 〈?〉 ≠ 0 due to radiative corrections in scalar theory with the interaction λ?⁴, scalar electrodynamics and non-Abelian gauge theories. We show that in the one-loop approximation at small coupling constant the dynamical symmetry breaking is absent and the only mechanism of spontaneous symmetry breaking remains the Goldstone-Higgs-Kibble effect.     

The effect of an external electric field on the optical properties of a quantum molecule with a resonance D(-)-state

The average binding energy and the level width for the resonant D^(-)-state in a quantum molecule have been calculated in the presence of an external electric field. The calculations were performed in the zeroradius potential model with allowance for the tunneling decay of the resonant state. The external electric field is shown to stimulate the decay of resonant D^(-)-states under conditions of dissipative tunneling. It was found that the curve of the probability of photoionization of the D^(-)-center as a function of the external electric field strength has two peaks that are connected with a change in the symmetry of the double-well oscillator potential of the quantum molecule and with the transformation (caused by the electric field) of envelope wave functions, respectively.     

Landau-Zener tunneling of Bose-Fermi mixture in double-well

The nonlinear Landau-Zener tunneling of a Bose-Fermi mixture in a double-well potential is studied in the present paper. The effect of interaction parameters on bosonic and fermionic tunneling probability is studied for the mixture of ⁴⁰K-⁸⁷Rb. The tunneling phenomena of the system can be controled by adjusting sweeping rate, intraspecies interaction, interspecies interaction and the numbers of bosons and fermions. It is noted that there are three different regions in phase diagram: self-trapping (ST), complete tunneling (CT) and incomplete tunneling (ICT).     

Higgs as a pseudo-Goldstone boson, the mu problem and gauge-mediated supersymmetry breaking

We study the interplay between the spontaneous breaking of a global symmetry of the Higgs sector and gauge-mediated supersymmetry breaking, in the framework of a supersymmetric model with global SU(3) symmetry. In addition to solving the supersymmetric flavor problem and alleviating the little hierarchy problem, this scenario automatically triggers the breaking of the global symmetry and provides an elegant solution to the μ/Bμ problem of gauge mediation. We study in detail the processes of global symmetry and electroweak symmetry breaking, including the contributions of the top/stop and gauge-Higgs sectors to the one-loop effective potential of the pseudo-Goldstone Higgs boson. While the joint effect of supersymmetry and of the global symmetry allows in principle the electroweak symmetry to be broken with little fine-tuning, the simplest version of the model fails to bring the Higgs mass above the LEP bound due to a suppressed tree-level quartic coupling. To cure this problem, we consider the possibility of additional SU(3)-breaking contributions to the Higgs potential, which results in a moderate fine-tuning. The model predicts a rather low messenger scale, a small tanβ value, a light Higgs boson with Standard Model-like properties, and heavy higgsinos.     

Gauge hierarchies of SU(N) grand unification

The structure of spontaneous breaking of SU(N) gauge symmetry for grand unification is investigated. The results obtained are applied to the analysis of SU(8) symmetry for which possible ways of breaking and intermediate symmetries are considered. It is assumed that the SU(8) group unifies the subgroups of colour, standard electroweak and horizontal symmetries. We find conditions which it is necessary to impose on the vacuum expectation values of Higgs multiplets to provide an arbitrary breaking pattern of SU(N) symmetry and conserve any intermediate symmetry. If in the SU(8) models considered fermions and mirror fermions do not violate the (V-A) and (V+A) structure of weak interactions, then their masses should not be greater than ～10² GeV. It is also shown that the contributions of fermion and Higgs multiplets to the renormalization group equation for the coupling constant of any subgroup of SU(N) are identical. Renormalization group identities for the case of arbitrary SU(N) breaking are given where the contribution of Higgs multiplets have been taken into account (but they cancel each other). Using these identities one can calculate the mass values for the breaking of the intermediate symmetries in the SU(8) models, and also exclude part of the possible breaking patterns.     

The spontaneous coherent state transition in the ϕ4-field model with an image mass

It is shown, that in the ?⁴-field model with an image mass (μ²<0) the phase transition is a spontaneous coherent state (SCS) phase transition. The connection between the spontaneous symmetry breaking, the coherent state and the phenomenological Ginzburg-Landau theory is shown.     

Low-lying excited states of quantum antiferromagnets on a triangular lattice

We study low-lying states of theXY and Heisenberg antiferromagnets on a triangular lattice to clarify whether spontaneous symmetry breaking occurs atT=0 in the thermodynamic limit. Approximate forms of low-lying states are proposed, in which degrees of freedom of the sublattice magnetization and of the chirality are separated. These approximate states have a long-range order and twofold structures. It is shown that low-lying states can be accurately described with the present approximation. It has been argued that low-lying states play an important role in symmetry breaking. With the help of this approximation, we discuss the contribution of low-lying states to symmetry breaking of two types, namely creation of the spontaneous sublattice magnetization and the spontaneous chirality. Furthermore, to show evidence for the occurrence of symmetry breaking, we numerically study the low-lying states of finite systems of theXY and Heisenberg antiferromagnets. It is found that the necessary conditions for the symmetry breaking to occur are satisfied in these models.     

A custodial symmetry for the cosmological constant in the effective theories of four-dimensional superstrings

We discuss supersymmetry breaking in the effective supergravity theories of four-dimensional N = 1 superstrings. Improving a recent suggestion, we introduce a superpotential modification that describes spontaneous supersymmetry breaking with vanishing cosmological constant and Str M² = 0 at any minimum of the tree level potential. We prove that in a class of models there are classical minima at which also Str f(M² = 0 for any function f. In particular, the whole one-loop cosmological constant vanishes. We propose a new boson-fermion symmetry of the spectrum, relating the graviton and the “dilatino”, which explains these remarkable properties.     

Phase transitions in De Sitter space

This paper uses zeta-function regularisation to calculate the one-loop functional determinants for fields of any spin in De Sitter space. As an example, we investigate the Coleman-Weinberg spontaneous symmetry breaking mechanism in massless scalar electrodynamics. The effective potential is calculated in Landau gauge. It depends upon the curvature, and upon the renormalised value of ζ (inζRφ²). The phase transition will be first or second order, and the critical curvature and mass are found. The methods can be applied to any gauge theory.     

q-deformed phase space and its lattice structure

A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that lives on such a lattice are derived as wavefunctions in ordinaryx-space.     

q-deformed phase space and its lattice structure

A q-deformed two-dimensional phase space is studied as a model for a noncommutative phase space. A lattice structure arises that can be interpreted as a spontaneous breaking of a continuous symmetry. The eigenfunctions of a Hamiltonian that lives on such a lattice are derived as wavefunctions in ordinaryx-space.     

Gravitational waves as a probe of the gravitino mass

If gaugino condensations occur in the early universe, domain walls are produced as a result of the spontaneous breaking of a discrete R symmetry. Those domain walls eventually annihilate with one another, producing the gravitational waves. We show that the gravitational waves can be a probe for measuring the gravitino mass, if the constant term in the superpotential is the relevant source of the discrete R symmetry breaking.     

Spontaneous symmetry breaking of population in a nonadiabatically driven atomic trap: an Ising-class phase transition

We have observed spontaneous symmetry breaking of the population of Brownian particles between two moving potentials in the spatiotemporally symmetric system. Cold atoms preferentially occupy one of the dynamic double-well potentials, produced in the parametrically driven dissipative magneto-optical trap far from equilibrium, above a critical number of atoms. We find that the population asymmetry, which may be interpreted as the biased Brownian motion, can be qualitatively described by the mean-field Ising-class phase transition. This in situ study may be useful for investigation of dynamic phase transition or temporal behavior of critical phenomena.     

Spontaneous symmetry breaking vacuum energy in cosmology

The gravitational effect of spontaneous symmetry breaking vacuum energy density is investigated by subtracting the flat space-time contribution from the energy in the curved space-time. We find that the remaining effective energy-momentum tensor is too small to cause the acceleration of the universe, although it satisfies the characteristics of dark energy. However, it could provide a promising explanation to the puzzle of why the gravitational effect produced by the huge symmetry breaking vacuum energy in the electroweak theory has not been observed, as it has a sufficiently small value (smaller than the observed cosmic energy density by a factor of 1032).