Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles

Journal Article · Mon Dec 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532203· OSTI ID:552978

Bohm, A; Loewe, M; Maxson, S; Patuleanu, P; Puentmann, C ^[1]; Gadella, M ^[2]

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1. The University of Texas at Austin, Austin, Texas 78712 (United States)
2. Faculdad de Ciencias, Universidad de Valladolid, E-47011 Valladolid (Spain)

In analogy to Gamow vectors that are obtained from first-order resonance poles of the S-matrix, one can also define higher-order Gamow vectors which are derived from higher-order poles of the S-matrix. An S-matrix pole of r-th order at z{sub R}=E{sub R}{minus}i{Gamma}/2 leads to r generalized eigenvectors of order k=0,1,{hor_ellipsis},r{minus}1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E{sub R}{minus}i{Gamma}/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher-order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher-order poles, the microphysical state obeys a purely exponential decay law. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 552978
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DENSITY MATRIX
EIGENVALUES
EIGENVECTORS
EXPANSION
HILBERT SPACE
MATHEMATICAL OPERATORS
S MATRIX
TIME DEPENDENCE