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Coupled Anharmonic Oscillators. I. Equal-Mass Case
Abstract
This is the first in a series of papers on the large-order behavior of perturbation theory for coupled anharmonic oscillators. We exploit previously published dispersion techniques to convert the calculation of perturbation theory in large order into a barrier-penetration problem. We then introduce new semiclassical methods for describing tunneling through nonspherically symmetric, $N$-dimensional potentials. To illustrate our new methods, we calculate the large-order behavior of perturbation theory for a simple system of two equal-mass oscillators with quartic coupling. Our predictions are in complete agreement with computer calculations. We then extend our results to oscillators with ${x}^{2N}$ coupling, $N$-oscillator systems, and some infinite-oscillator systems.
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Research works printed but not linked: 17
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Cited by
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Fate of the false vacuum. II. First quantum corrections
Callan, C. G., & Coleman, S. (1977) · Physical Review D · doi:10.1103/physrevd.16.1762 · Cited by 1,789
Decay theory of unstable quantum systems
Fonda, L., Ghirardi, G. C., & Rimini, A. (1978) · Reports on Progress in Physics · doi:10.1088/0034-4885/41/4/003 · Cited by 627
Boundary conditions in quantum cosmology
Vilenkin, A. (1986) · Physical Review D · doi:10.1103/physrevd.33.3560 · Cited by 428
Quantum cosmology and the initial state of the Universe
Vilenkin, A. (1988) · Physical Review D · doi:10.1103/physrevd.37.888 · Cited by 391
Metadata
- Authors
- Banks, T., Bender, C. M., & Wu, T. T.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1973-11-15
- Volume
- 8
- Issue
- 10
- Pages
- 3346-3366
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2107349523
- Cited by
- 249
- References
- 0
- FWCI
- 1.23
- Type
- journal article
- Language
- en
- Open access
- closed
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