Effect Of Symmetry Breaking Perturbations Research Articles

Effects of symmetry-breaking perturbations on excitonic states bound to systems of reduced symmetry

Using an invariant expansion, we build an Hamiltonian describing the influence of the crystal-field, the electron-hole exchange interaction, and any symmetry-breaking perturbations on the fine structure of excitons bound to systems of reduced symmetry: D2d, C3v, and C2v. Several perturbations are considered, including, but not limited to, an electric field, a magnetic field, a strain field, and their combinations. For each symmetry system considered, symmetrized excitonic wave functions, build from heavy- and light-holes states, are used to expand the Hamiltonian in the form of matrices, whose eigenvalues directly provide the energy of the excitonic states and whose eigenstates can be used to determine oscillator strengths of optical transitions. Using this model, we satisfactorily reproduce the excitonic emission observed from nitrogen dyads in GaAs and tellurium dyads in strained ZnSe. We also present Hamiltonians for independent heavy- and light-hole subsystems. Comparing the two models, we demonstrate that the splitting observed in strained quantum dots of C2v symmetry does not necessarily imply a significant anisotropic exchange interaction. This splitting can be produced by a weak coupling between heavy- and light-hole bands.

Theory of quantum transport in carbon nanotubes: Perfect conductance, dynamical conductivity, and inter-wall interaction

A brief review is given on transport properties of carbon nanotubes mainly from a theoretical point of view. The topics include an effective-mass description of electronic states, the absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, the presence of a perfectly conducting channel, and effects of symmetry breaking perturbations. The dynamical conductivity in the presence of a perfect channel and inter-wall interactions in double-wall nanotubes are also discussed.

Effect of symmetry-breaking perturbations in the one-dimensionalSU(4)spin-orbital model

We study the effect of symmetry breaking perturbations in the one-dimensional SU(4) spin-orbital model. We allow the exchange in spin ($J_1$) and orbital ($J_2$) channel to be different and thus reduce the symmetry to SU(2) $\otimes$ SU(2). A magnetic field $h$ along the $S^z$ direction is also applied. Using the formalism developped by Azaria et al we extend their analysis of the isotropic $J_1=J_2$, h=0 case and obtain the low-energy effective theory near the SU(4) point in the asymmetric case. An accurate analysis of the renormalization group flow is presented with a particular emphasis on the effect of the anisotropy. In zero magnetic field, we retrieve the same qualitative low-energy physics than in the isotropic case. In particular, the massless behavior found on the line $J_1=J_2>K/4$ extends in a large anisotropic region. We discover though that the anisotropy plays its trick in allowing non trivial scaling behaviors of the physical quantities. When a magnetic field is present the effect of the anisotropy is striking. In addition to the usual commensurate-incommensurate phase transition that occurs in the spin sector of the theory, we find that the field may induce a second transition of the KT type in the remaining degrees of freedom to which it does not couple directly. In this sector, we find that the effective theory is that of an SO(4) Gross-Neveu model with an h-dependent coupling that may change its sign as h varies.

Effect of symmetry-breaking perturbations on flow-induced oscillations in tubes

Three-dimensional oscillatory motions of a cantilevered tube conveying a fluid are examined when the rotational and reflection symmetries of the tube are destroyed by small perturbations breaking the rotational symmetry. At flow rates past a critical value, two primary branches of standing waves, or motions restricted to a plane are found. Depending on the mass ratio β, qualitatively distinct phenomena are predicted. The standing wave may either undergo a pitchfork bifurcation into a traveling wave, representing elliptic motions of the tube, or may coexist with traveling waves arising due to a saddle-node bifurcation. In another distinct case, the standing wave solutions for the rotationally symmetric tube system are affected by the symmetry-breaking perturbations, only to the extent that the perturbations define the plane of motion. Secondary bifurcations and codimension-two bifurcations to modulated waves are also considered. The results of the analysis are confirmed qualitatively by means of some experiments.

Effects of symmetry-breaking perturbations on the onset of the “Smale-horseshoe” chaos

We shall consider in detail, by means of Melnikov method, the appearance of transverse homoclinic points in 1-dimensional problems whose potential term is given by an even function perturbed by some parity-breaking term. After having described the two possible and essentially different situations one can find, we shall introduce two methods in order to carefully analyze in each case the effects of the symmetry perturbing term on the appearance of homoclinic points (and therefore on the onset of the typical “Smale horseshoe” chaotic motion). As examples for the various cases, we shall consider a perturbed Duffing equation the equation for the Josephson junction, and finally an equation for which we can provide the explicit solution, and which becomes in this way a good test for the results.

Effects of symmetry-breaking perturbations on the three-state Potts model

The effects of linear and quadratic symmetry-breaking perturbations on the continuous version of the three-state Potts model are analysed, using both Landau's theory of phase transitions and renormalisation-group techniques. Variation of the strength of the perturbations produces many different types of phase diagrams, featuring lambda lines, first-order lines, critical, tricritical and triple points and other complexities. Universal amplitude ratios characterising the multicritical points are calculated to first order in epsilon =4-d.