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Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles (1997)

Bohm, A. ; Loewe, Mark ; Maxson, S. ; [weitere]

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 38 (1997), S. 6072-6100

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: 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 zR=ER−iΓ/2 leads to r generalized eigenvectors of order k=0,1,...,r−1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (ER−iΓ/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. © 1997 American Institute of Physics.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.532203

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Digitale Medien

The Berry connection and Born–Oppenheimer method (1992)

Bohm, A. ; Kendrick, B. ; Loewe, Mark E. ; [weitere]

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 33 (1992), S. 977-989

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ISSN: 1089-7658

Quelle: AIP Digital Archive

Thema: Mathematik , Physik

Notizen: By performing the most general Born–Oppenheimer procedure, the (non-Abelian) Berry connection for quantum systems in a quantum environment is derived. This method is then applied to the rapid rotation of a particle about a slowly changing axis, as exemplified by the electronic motion of a diatomic molecule. The angular part of the resulting dynamics for the quantum environment is equivalent to that of a monopole.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.529751

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The Berry phase in molecular physics (1992)

Bohm, A. ; Kendrick, B. ; Loewe, Mark E.

New York, NY : Wiley-Blackwell

International Journal of Quantum Chemistry 41 (1992), S. 53-75

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ISSN: 0020-7608

Schlagwort(e): Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Chemie und Pharmazie

Notizen: The geometric phase of quantum mechanics is introduced, and its physical effects are then studied in the context of molecular physics. By performing the most general Born-Oppenheimer procedure, we show how gauge groups appear in the study of molecules. This method is then applied to the doubly degenerate Λ-levels of a diatomic molecule. The resulting dynamics for the slow angular motion of the dumbbell is equivalent to that of a Dirac monopole.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1002/qua.560410108

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