Spectrum and Quantum Dynamics
Different spectral subspaces of a self-adjoint operator T in general entail different behaviors of the unitary evolution group e−itT (particularly as |t|→∞). In this chapter many such dynamical issues are discussed; the main motivation is when T corresponds to the Schrödinger operator of a quantum system. Some related physical concepts, such as quantum return probability and test operators, are used to probe the large-time behaviors. The cornerstones of such results are the concepts of precompactness, almost periodicity and the Wiener and Riemann-Lebesgue lemmas.
KeywordsSpectral Measure Compact Operator Landau Level Quantum Dynamics Periodic Trajectory
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