Variational approach to tunneling. beyond the semiclassical approximation of Langer and Lipatov- perturbation coefficients to all orders (original) (raw)
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Abstract
We present a variational approach to tunneling amplitudes which considerably improves the semiclassical approximation. The accuracy is good even for low barriers, as illustrated by an application to an anharmonic oscillator 12x2+14gx4 in zero and one dimension, where we calculate the left-hand cut in the complex g plane. For small −g, i.e., near the tip of the cut where the barrier is high, the new approximation reproduces the semiclassical limit and thus the large-order factorial divergence of the perturbation coefficients. Important progress is reached at larger −g where barriers are low and for −g → ∞ where we explain the proper asymptotic behavior with an extremely small error. The agreement of the approximate imaginary parts with the exact one is so good on the entire cut that they can be inserted into a dispersion relation to yield accurate results also for all _g_>0. All perturbation coefficients are very close to the exact ones down to low orders in g so that the method promises to be a good starting-point for the development of new powerful resummation procedures.
References (13)
- H. Kleinert
Phys. Lett. B
(1992)
- J.S. Langer
Ann. Phys.
(1967)
- J. Zinn-Justin
Quantum field theory
(1990)
- H. Kleinert et al.
Phys. Lett. B
(1991)
- H. Kleinert
Systematic corrections to variational calculation of effective classical potential
(September 1992)
- R.P. Feynman et al.
Phys. Rev. A
(1986)
R. Giachetti et al.
Phys. Rev. Lett.
(1985)
Int. J. Magn. Mater.
(1986)
H. Kleinert
Phys. Lett. B
(1986)
Phys. Lett. A
(1986)
Phys. Lett. A
(1986)
W. Janke et al.
Phys. Lett. A
(1986)
Chem. Phys. Lett.
(1987)
W. Janke et al.
Phys. Lett. B
(1988)
R. Giachetti et al.
Phys. Rev. B
(1986)
Phys. Rev. A
(1988)
Phys. Rev. A
(1988)
Phys. Rev. A
(1988)
A. Cuccoli et al.
Phys. Rev. B
(1990)
R. Giachetti _et al._W. JankeS. Srivastava et al.
Phys. Rev. A
(1991)
There are more references available in the full text version of this article.
Cited by (27)
Work supported in part by Deutsche Forschungsgemeinschaft under grant no. Kl. 256.
Copyright © 1993 Published by Elsevier B.V.