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  • 1
    Electronic Resource
    Electronic Resource
    The Berry connection and Born–Oppenheimer method (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 977-989 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529751
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6072-6100 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532203
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The Berry phase in molecular physics (1992)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 41 (1992), S. 53-75 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560410108
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    Paper (German National Licenses)
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