P T Leung et al 1997 J. Phys. A: Math. Gen. 30 2153 doi:10.1088/0305-4470/30/6/035
Two-component eigenfunction expansion for open systems described by the wave equation II: linear space structure
P T Leung, S S Tong and K Young
Show affiliationsFor a broad class of open systems described by the wave equation, the eigenfunctions (which are quasinormal modes) provide a complete basis for simultaneously expanding outgoing wavefunctions 
. In this paper, the linear space structure associated with this expansion is developed. Under a modified inner product, the time-evolution operator is self-adjoint, even though energy is not conserved for the system alone. Thus, the eigenfunctions are mutually orthogonal. Consequently, the usual tools of eigenfunction expansions can be transcribed to these open systems. As an example, the time-independent perturbation theory is developed in straightforward analogy with quantum mechanics, giving the shift in both the real part and the imaginary part of the eigenvalues 
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- PACS
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03.65.Yz Decoherence; open systems; quantum statistical methods
- MSC
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81Q15 Perturbation theories for operators and differential equations
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
- Subjects
- Dates
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Issue 6 (21 March 1997)
Received 28 March 1996, in final form 10 September 1996
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Two-component eigenfunction expansion for open systems described by the wave equation II: linear space structure
P T Leung et al 1997 J. Phys. A: Math. Gen. 30 2153
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Two-component eigenfunction expansion for open systems described by the wave equation I: completeness of expansion
P T Leung et al 1997 J. Phys. A: Math. Gen. 30 2139
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