Number Of Negative Modes Research Articles

Negative modes of Coleman–De Luccia and black hole bubbles

We study the negative modes of gravitational instantons representing vacuum decay in asymptotically flat space-time. We consider two different vacuum decay scenarios: the Coleman-de Luccia $\mathrm{O}(4)$-symmetric bubble, and $\mathrm{O}(3) \times \mathbb{R}$ instantons with a static black hole. In spite of the similarities between the models, we find qualitatively different behaviours. In the $\mathrm{O}(4)$-symmetric case, the number of negative modes is known to be either one or infinite, depending on the sign of the kinetic term in the quadratic action. In contrast, solving the mode equation numerically for the static black hole instanton, we find only one negative mode with the kinetic term always positive outside the event horizon. The absence of additional negative modes supports the interpretation of these solutions as giving the tunnelling rate for false vacuum decay seeded by microscopic black holes.

Sphalerons and large order behaviour of perturbation theory in lower dimension

Sphalerons - unstable static solutions of classical field equations in ( d + 1)-dimensional spacetime - may be viewed as euclidean solutions in d dimensions. We discuss their role in the large order asymptotics of perturbation theory. Specifically, we calculate their contribution to the large order behaviour of the ground state energy in a quantum mechanical model. When the number of negative modes is odd, the single sphaleron contribution dominates, while this contribution vanishes when the number of negative modes is even. These results are confirmed by numerical calculations.

Eigenmodes in a circular waveguide containing an isotropic chiral material

In this paper, Maxwell's equations and modified constitutive equations are used to investigate the eigenmodes in a circular waveguide containing an isotropic chiral medium for monochromatic radiation of unspecified wavelength. The dispersion equation for this case is derived analytically, solved numerically, and compared to the nonchiral case and to waveguides containing longitudinally magnetized ferrites. The field components are computed and plotted as a function of the radial coordinate as well as the transverse E‐field lines in the circular cross section. Cutoff frequencies, evanescent modes, polarization characteristics of the fields, and the nondegeneracy of positive and negative mode numbers are discussed and contrasted with those of nonchiral, dielectric filled circular waveguides.