Oscillon lifetime in the presence of quantum fluctuations

Paul M. Saffin,Paul Tognarelli,Anders Tranberg

doi:10.1007/jhep08(2014)125

Paul M. Saffin, Paul Tognarelli + Show 1 more

Open Access

https://doi.org/10.1007/jhep08(2014)125

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Abstract

We consider the stability of oscillons in 2+1 space-time dimensions, in the presence of quantum fluctuations. Taking the oscillon to be the inhomogeneous mean field of a self-interacting quantum scalar field, we compare its classical evolution to the evolution in the presence of quantum fluctuations. The evolution of these and their back reaction onto the mean field is implemented through the inhomogeneous Hartree approximation, in turn computed as a statistical ensemble of field realizations. We find that although the lifetime of the oscillon is dramatically reduced compared to the classical limit, the regions of longevity are similar in the space of Gaussian initial configurations.

Highlights

Setup and modelIn the absence of back-reaction from the perturbations in the equation (2.3), this initial configuration would obey the classical dynamics and for certain values of A0, r0 evolve into an oscillon
Taking the oscillon to be the inhomogeneous mean field of a self-interacting quantum scalar field, we compare its classical evolution to the evolution in the presence of quantum fluctuations
The evolution of these and their back reaction onto the mean field is implemented through the inhomogeneous Hartree approximation, in turn computed as a statistical ensemble of field realizations

Summary

Setup and model

In the absence of back-reaction from the perturbations in the equation (2.3), this initial configuration would obey the classical dynamics and for certain values of A0, r0 evolve into an oscillon. When the two-point correlator of the perturbations is small, the initial configuration remains perturbatively close to the expected, oscillon solutions of the quantum mean-field dynamics. The quantum fields can be rescaled, as the classical fields, according to Φ → |m2|/λΦ and δφ → |m2|/λδφ, along with the rescaling of the co-ordinates x → x/m This sets the mass and coupling effectively equal to unity, in exact parallel to the classical rescaling, for both the mean and perturbation dynamics. This implementation scales as N 2 × M , which is potentially smaller than N 4 ( we will see here that the gain for inhomogeneous systems of the present type is only a factor of a few)

Classical and quantum oscillons

Classical and quantum basins of attraction

Conclusion