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Application of Path Integrals in Complex Time to Coupled-Channels Tunneling Phenomena

A. Rapisarda, C.H. Dasso

Published Jan 1, 1991• 0 citations
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Complex-time path-integral formalism for quantum tunneling

Hideaki Aoyama, Toshiyuki Harano

arXiv:hep-th/9412093•Nuclear Physics B•Jul 1, 1995•7 citations

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Masa‐aki Sakagami

Vistas in Astronomy•Jan 1, 1993•0 citations

Complex-time path-integral formalism for quantum tunneling

Aoyama, H, Harano, T

The complex-time formalism is developed in the framework of the path-integral formalism, to be used for analysis of the quantum tunneling phenomena. We show that subleading complex-time saddle-points do not account for the right WKB result. Instead, we develop a reduction formula, which enables us to construct Green functions from simple components of the potential, for which saddle-point method is applicable. This method leads us to the valid WKB result, which incorporates imaginary-time instantons and bounces, as well as the real-time boundary conditions.

•Dec 12, 1994•6 citations

Recent Developments of the Theory of Tunneling

Hideaki Aoyama, 敏幸 原野, Hisashi Kikuchi +3 more

Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary time, its application to various quantum systems, complex time formalism, asympton theory for the large order analysis of the perturbation theory, are reviewed in a self-contained manner.

arXiv:hep-th/9704025•Progress of Theoretical Physics Supplement•Feb 1, 1997•22 citations

Path Integral for Mixed Tunneling, Polychronic Tunneling and Quantum Gravity

Yutaro Shoji

Quantum tunneling in a many-body system is much more non-trivial than that in a one-body system. The most characteristic phenomenon is the mixed tunneling, which has been studied in many fields for decades. For instance, let us consider a system where there are two coupled particles and only one of them feels a potential barrier. Quantum tunneling of such a system is not described by either Euclidean or Lorentzian time evolution and the exponent of the WKB wave function becomes complex. Recently, a similar phenomenon, polychronic tunneling, has been proposed in quantum gravity, which enhances the decay rate of a meta-stable vacuum by many orders of magnitude. In this paper, we present path integral formalism that is applicable to such systems. The formalism can be directly extended to quantum gravity and has some implications on the problem of time in quantum gravity. We also discuss a possible relation to the conventional path integral.

arXiv:2212.06774•Dec 13, 2022•0 citations

Path Integrals and Coupled-Wave Problems

World Scientific lecture notes in physics•Dec 1, 1990•0 citations
The complex-time formalism is developed in the framework of the path-integral formalism, to be used for analysis of the quantum tunneling phenomena. We show that subleading complex-time saddle-points do not account for the right WKB result. Instead, we develop a reduction formula, which enables us to construct Green functions from simple components of the potential, for which saddle-point method is applicable. This method leads us to the valid WKB result, which incorporates imaginary-time instantons and bounces, as well as the real-time boundary conditions.
Quantum tunneling in a many-body system is much more non-trivial than that in a one-body system. The most characteristic phenomenon is the mixed tunneling, which has been studied in many fields for decades. For instance, let us consider a system where there are two coupled particles and only one of them feels a potential barrier. Quantum tunneling of such a system is not described by either Euclidean or Lorentzian time evolution and the exponent of the WKB wave function becomes complex. Recently, a similar phenomenon, polychronic tunneling, has been proposed in quantum gravity, which enhances the decay rate of a meta-stable vacuum by many orders of magnitude. In this paper, we present path integral formalism that is applicable to such systems. The formalism can be directly extended to quantum gravity and has some implications on the problem of time in quantum gravity. We also discuss a possible relation to the conventional path integral.