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complex-time approach for semi-classical quantum tunneling.Image.Marked文档.pdf

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complex-time approach for semi-classical quantum tunneling.Image.Marked文档

KUCP-0072 KUNS-1302 November 1994 Complex-time approach for 4 9 semi-classical quantum tunneling 9 1 v Hideaki Aoyama⋆ o N Department of Fundamental Sciences 2 Faculty of Integrated Human Studies 1 Kyoto University, Kyoto 606-01, Japan 1 v and 6 8 † 0 Toshiyuki Harano 1 1 Department of Physics, Faculty of Science 4 9 Kyoto University, Kyoto 606-01, Japan / h t - p e h ABSTRACT : v i X The complex-time method for quantum tunneling is studied. In one- r a dimensional quantum mechanics, we construct a reduction formula for a Green function in the number of turning points based on the WKB approx- imation. This formula yields a series, which can be interpreted as a sum over the complex-time paths. The weights of the paths are determined. ⋆ E-mail address: aoyama@phys.h.kyoto-u.ac.jp † E-mail address: harano@gauge.scphys.kyoto-u.ac.jp The imaginary-time method is quite useful for study of the tunneling phe- nomena in quantum ﬁeld theories. Existence of the solutions of the equation of motion, instanton and bounce, allows one to apply the semi-classical approxima- tion for path-integral. It is known to lead to valid results, which o