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Register a new userSpectral boundary conditions and solitonic solutions in a classical Sellmeier dielectric
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Electromagnetic field interactions in a dielectric medium represent a longstanding field of investigation, both at the classical level and at the quantum one. We propose a 1+1 dimensional toy-model which consists of an half-line filling dielectric medium, with the aim to set up a simplified situation where technicalities related to gauge invariance and, as a consequence, physics of constrained systems are avoided, and still interesting features appear. In particular, we simulate the electromagnetic field and the polarization field by means of two coupled scalar fields $phi$,$psi$ respectively, in a Hopfield-like model. We find that, in order to obtain a physically meaningful behaviour for the model, one has to introduce spectral boundary conditions depending on the particle spectrum one is dealing with. This is the first interesting achievement of our analysis. The second relevant achievement is that, by introducing a nonlinear contribution in the polarization field $psi$, with the aim of mimicking a third order nonlinearity in a nonlinear dielectric, we obtain solitonic solutions in the Hopfield model framework, whose classical behaviour is analyzed too.
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We construct rolling tachyon solutions of open and boundary string field theory (OSFT and BSFT, respectively), in the bosonic and supersymmetric (susy) case. The wildly oscillating solution of susy OSFT is recovered, together with a family of time-dependent BSFT solutions for the bosonic and susy string. These are parametrized by an arbitrary constant r involved in solving the Green equation of the target fields. When r=0 we recover previous results in BSFT, whereas for r attaining the value predicted by OSFT it is shown that the bosonic OSFT solution is the derivative of the boundary one; in the supersymmetric case the relation between the two solutions is more complicated. This technical correspondence sheds some light on the nature of wild oscillations, which appear in both theories whenever r>0.
The correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary world sheets can be expressed in terms of Wilson graphs in appropriate three-manifolds. We present a systematic approach to boundary conditions that break bulk symmetries. It is based on the construction, by `alpha-induction, of a fusion ring for the boundary fields. Its structure constants are the annulus coefficients and its 6j-symbols give the OPE of boundary fields. Symmetry breaking boundary conditions correspond to solitonic sectors.
We explore boundary scattering in the sine-Gordon model with a non-integrable family of Robin boundary conditions. The soliton content of the field after collision is analysed using a numerical implementation of the direct scattering problem associated with the inverse scattering method. We find that an antikink may be reflected into various combinations of an antikink, a kink, and one or more breathers, depending on the values of the initial antikink velocity and a parameter associated with the boundary condition. In addition we observe regions with an intricate resonance structure arising from the creation of an intermediate breather whose recollision with the boundary is highly dependent on the breather phase.
The effects induced by the quantum vacuum fluctuations of one massless real scalar field on a configuration of two partially transparent plates are investigated. The physical properties of the infinitely thin plates are simulated by means of Dirac-$delta-delta^prime$ point interactions. It is shown that the distortion caused on the fluctuations by this external background gives rise to a generalization of Robin boundary conditions. The $T$-operator for potentials concentrated on points with non defined parity is computed with total generality. The quantum vacuum interaction energy between the two plates is computed using the $TGTG$ formula to find positive, negative, and zero Casimir energies. The parity properties of the $delta-delta^prime$ potential allow repulsive quantum vacuum force between identical plates.
This paper examines the complex trajectories of a classical particle in the potential V(x)=-cos(x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically that there are two special classes of trajectories x(t) determined only by the energy of the particle and not by the initial position of the particle. The first class consists of periodic trajectories; that is, trajectories that return to their initial position x(0) after some real time T. The second class consists of trajectories for which there exists a real time T such that $x(t+T)=x(t) pm2 pi$. These two classes of classical trajectories are analogous to valence and conduction bands in quantum mechanics, where the quantum particle either remains localized or else tunnels resonantly (conducts) through a crystal lattice. These two special types of trajectories are associated with sets of energies of measure 0. For other energies, it is shown that for long times the average velocity of the particle becomes a fractal-like function of energy.
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