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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 977-989 
    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.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 365-374 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A proof of the existence of an essentially self-adjoint extension of a symmetric ∼(SO0(4,1)) Nelson operator, which is constructed out of the generators of a positive mass, arbitrary spin unitary irreducible representation of the Poincaré group, is presented. Our analysis of ∼(SO0(4,1)) and its Lie algebra provides us with an example of an observation of Harish-Chandra: There exist subspaces of the space of differentiable vectors of a representation of a noncompact group which are invariant under the Lie algebra, but the closures of the subspaces are not invariant under the group. The chief results of this paper should hold true for ∼(SO0(n,1)). In particular, we should have a realization of an arbitrary principal series irreducible unitary representation of SO0(n,1) on the direct sum of two identical unitary irreducible representation spaces of the motion group in an n-dimensional Minkowski space, which has one timelike dimension.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6072-6100 
    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.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 2593-2604 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The exponential decay (or growth) of resonances provides an arrow of time which is described as the semigroup time evolution of Gamow vector in a new formulation of quantum mechanics. Another direction of time follows from the fact that a state must first be prepared before observables can be measured in it. Applied to scattering experiments, this produces another quantum mechanical arrow of time. The mathematical statements of these two arrows of time are shown to be equivalent. If the semigroup arrow is interpreted as microphysical irreversibility and if the arrow of time from the prepared in-state to its effect on the detector of a scattering experiment is interpreted as causality, then the equivalence of their mathematical statements implies that causality and irreversibility are interrelated. © 1995 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1163-1170 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The analogy between the representations of SU(1,1/1) and SU(2,2/1) is explained and used to suggest the latter as a spectrum supergroup of superconformal relativistic quantum mechanics for systems with rotational degrees of freedom.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1463-1470 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The geometric phase has been defined as the holonomy of two bundles with different base spaces and different connections. In this article we establish the relation between the Berry–Simon and the Anandan–Aharonov definitions for a large class of cyclic Hamiltonians (with N-fold degeneracy) using the classifying theorem for principal fiber bundles.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2528-2532 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Arguments are presented that make the choice of the connection, which gives rise to the Berry phase not only natural, but unique, both in the Abelian and the non-Abelian cases. Invariance is invoked under unitary transformations of the probability amplitudes in quantum systems to force the connection to be invariant under the unitary group. Because the action is not free, the horizontal subspace chosen by the connection has to be invariant under the little group, and that makes it orthogonal to the fiber's direction, yielding the conventional Berry connection. The argument works just as well for the non-Abelian case, where the fibers are orthonormal frames (Stiefel manifolds), and the state space a Grassmanian, with a transitive but not free unitary action.
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  • 8
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Advanced Materials 4 (1992), S. 234-238 
    ISSN: 0935-9648
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 40 (1991), S. 491-500 
    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: Two possible reaction paths for the pyrolysis of the ethylester of glyoxylic acid have been studied by ab initio molecular orbital calculations. The basis sets 3-21G and 6-31G* have been used, and electron correlation has been included by Møller-Plesset calculations up to fourth order. Our calculations indicate that the reaction leading to acid and ethylene through a 6-membered ring transition state is favored relative to a process involving a formyl hydrogen transfer via a 5-membered ring to the alkyl unit leading to ethane, CO, and CO2. The predicted activation energies for these two reactions obtained at the highest level of calculation, MP4(SDTQ)/6-31G*, are 50.4 and 71.7 kcal/mol, respectively. The transition states have RHF wave functions that are stable relative to UHF solutions using the 3-21G basis. The geometry of the transition states and IRC following indicate that both reactions are strongly asynchronous: The C—O bond rupture is virtually completed before hydrogen transfer occurs. For comparative purposes, analogous calculations have been performed for the ethylester of formic acid, where it is confirmed that a 6-membered ring transition state is preferred relative to a 4-membered one by around 42 kcal/mol at the highest level of calculation.
    Additional Material: 3 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 41 (1992), S. 53-75 
    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.
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