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Quantum tunneling from paths in complex time

Sebastian F. Bramberger1,*, George Lavrelashvili2,†, and Jean-Luc Lehners1,‡

  • 1Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam-Golm, Germany
  • 2Department of Theoretical Physics, A.Razmadze Mathematical Institute I.Javakhishvili Tbilisi State University, GE-0177 Tbilisi, Georgia

  • *sebastian.bramberger@aei.mpg.de
  • †george.lavrelashvili@tsu.ge
  • ‡jlehners@aei.mpg.de
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Phys. Rev. D 94, 064032 – Published 13 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.064032

Abstract

We study quantum mechanical tunneling using complex solutions of the classical field equations. Simple visualization techniques allow us to unify and generalize previous treatments, and straightforwardly show the connection to the standard approach using Euclidean instanton solutions. We demonstrate that the negative modes of solutions along various contours in the complex time plane reveal which paths give the leading contribution to tunneling and which do not, and we provide a criterion for identifying the negative modes. Central to our approach is the solution of the background and perturbation equations not only along a single path, but over an extended region of the complex time plane. Our approach allows for a fully continuous and coherent treatment of classical evolution interspersed by quantum tunneling events and is applicable in situations where singularities are present and also where Euclidean solutions might not exist.

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Phys. Rev. D 94, 064032– Published 13 September, 2016
  • Received 7 June 2016

© 2016 American Physical Society

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