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Causality And Relativistic Localization In One-Dimensional Hamiltonians, R E. Wagner, B T. Shields, M R. Ware, Qichang Su, Rainer Grobe
Causality And Relativistic Localization In One-Dimensional Hamiltonians, R E. Wagner, B T. Shields, M R. Ware, Qichang Su, Rainer Grobe
Faculty publications – Physics
We compare the relativistic time evolution of an initially localized quantum particle obtained from the relativistic Schrodinger, the Klein-Gordon and the Dirac equations. By computing the amount of the spatial probability density that evolves outside the light cone we quantify the amount of causality violation for the relativistic Schrodinger Hamiltonian. We comment on the relationship between quantum field theoretical transition amplitudes, commutators of the fields and their bilinear combinations outside the light cone as indicators of a possible causality violation. We point out the relevance of the relativistic localization problem to this discussion and comment on ideas about the supposed …
Electron-Positron Pair Creation Induced By Quantum-Mechanical Tunneling, M Jiang, W Su, X Lu, Z M. Sheng, Y T. Li, J Zhang, Rainer Grobe, Qichang Su
Electron-Positron Pair Creation Induced By Quantum-Mechanical Tunneling, M Jiang, W Su, X Lu, Z M. Sheng, Y T. Li, J Zhang, Rainer Grobe, Qichang Su
Faculty publications – Physics
We study the creation of electron-positron pairs from the vacuum induced by two spatially displaced static electric fields. The strength and spatial width of each localized field is less than required for pair creation. If, however, the separation between the fields is less than the quantum-mechanical tunneling length associated with the corresponding quantum scattering system, the system produces a steady flux of electron-positron pairs. We compute the time dependence of the pair-creation probability by solving the Dirac equation numerically for various external field sequences. For the special case of two very narrow fields we provide an analytical expression for the …