Wentzel-Kramers-Brillouin approach and quantum corrections to classical dynamics in the Josephson problem

Journal Article · Tue Jun 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.063628· OSTI ID:21437950

Nissen, Felix; Keeling, Jonathan ^[1]

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1. Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom)

We apply a many-body Wentzel-Kramers-Brillouin (WKB) approach to determine the leading quantum corrections to the semiclassical dynamics of the Josephson model, describing interacting bosons able to tunnel between two localized states. The semiclassical dynamics is known to divide between regular oscillations and self-trapped oscillations where the sign of the imbalance remains fixed. In both cases, the WKB wave functions are matched to Airy functions, yielding a modified Bohr-Sommerfeld quantization condition. At the critical energy dividing normal and self-trapped oscillations, the WKB wave functions should instead be matched to parabolic cylinder functions, leading to a quantization formula that is not just the Bohr-Sommerfeld formula, and recovering the known logarithmic quantum break times at this energy. This work thus provides another illustration of the usefulness of the WKB approach in certain many-body problems.

• OSTI ID: 21437950
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
AIRY FUNCTIONS
APPROXIMATIONS
CALCULATION METHODS
CORRECTIONS
ENERGY LEVELS
FUNCTIONS
JOSEPHSON EFFECT
MANY-BODY PROBLEM
OSCILLATIONS
QUANTIZATION
SEMICLASSICAL APPROXIMATION
TRAPPING
WAVE FUNCTIONS
WKB APPROXIMATION