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Progress of Theoretical Physics

Decoherence on Quantum Tunneling in the Multi-Dimensional Wave Function Approach

Takahiro Tanaka

Published Jan 1, 1995• 1 citation
Publisher

Abstract

We consider fundamental problems on the understanding of the tunneling phenomena in the context of the multi-dimensional wave function. In this paper, we reconsider the quantum state after tunneling and extend our previous formalism to the case when the quantum state before tunneling is in a squeezed state. Through considering this problem, we reveal that the quantum decoherence plays a crucial role to allow us of the concise description of the quantum state after tunneling.

DOI
10.1143/ptp/93.1.67

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We consider fundamental problems on the understanding of the tunneling phenomena in the context of the multi-dimensional wave function. In this paper, we reconsider the quantum state after tunneling and extend our previous formalism to the case when the quantum state before tunneling is in a squeezed state. Through considering this problem, we reveal that the quantum decoherence plays a crucial role to allow us of the concise description of the quantum state after tunneling.
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We extend a useful formalism to construct a wave function in a multi-dimensional tunneling system and to investigate the quantum excitations of an intrinsic degree of freedom, which is a harmonic oscillator linearly coupled to a tunneling degree of freedom. To demonstrate the usefulness of the formalism, we construct a wave function in an analytic form for a simple tunneling system with a cubic potential. Based on the wave function, we discuss interesting features of the multi-dimensional tunneling system in which the quantum excitations play an important role. It is shown that the quantum excitations of the linearly coupled harmonic oscillators increase the decay width in comparison with the case of no excitations.
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