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- W2086060907 abstract "We consider an invariant quantum Hamiltonian H=−ΔLB+V in the L2 space based on a Riemannian manifold M̃ with a countable discrete symmetry group Γ. Typically, M̃ is the universal covering space of a multiply connected Riemannian manifold M and Γ is the fundamental group of M. On the one hand, following the basic step of the Bloch analysis, one decomposes the L2 space over M̃ into a direct integral of Hilbert spaces formed by equivariant functions on M̃. The Hamiltonian H decomposes correspondingly, with each component HΛ being defined by a quasiperiodic boundary condition. The quasiperiodic boundary conditions are in turn determined by irreducible unitary representations Λ of Γ. On the other hand, fixing a quasiperiodic boundary condition (i.e., a unitary representation Λ of Γ) one can express the corresponding propagator in terms of the propagator associated with the Hamiltonian H. We discuss these procedures in detail and show that in a sense they are mutually inverse." @default.
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- W2086060907 date "2008-03-01" @default.
- W2086060907 modified "2023-09-27" @default.
- W2086060907 title "Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry" @default.
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- W2086060907 doi "https://doi.org/10.1063/1.2898484" @default.
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