Zai-Qiao Bai and Wei-Mou Zheng 2003 J. Phys. A: Math. Gen. 36 2737 doi:10.1088/0305-4470/36/11/306
Quantum evolution near unstable equilibrium point: an algebraic approach
Zai-Qiao Bai1 and Wei-Mou Zheng2
Show affiliationsWe study the quantum evolution of an unstable system in su(1,1) algebra. The evolution of any initial state |k, ν
is recursively obtained. When t → ∞, |
k', ν| exp (−i/
Ht)|k, ν|2 decays as e−4νt or t−4ν in the hyperbolic (H = 2K1) or parabolic (H = 2K1 + 2K3) unstable cases, respectively. The quantum–classic correspondence independent of the Bargmann index ν is established based on the long-time and large-scale behaviour of wavefunctions.
- PACS
- MSC
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81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
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Issue 11 (21 March 2003)
Received 1 August 2002
Published 6 March 2003
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Quantum evolution near unstable equilibrium point: an algebraic approach
Zai-Qiao Bai and Wei-Mou Zheng 2003 J. Phys. A: Math. Gen. 36 2737
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