Friedel theorem for one dimensional relativistic spin-1/2 systems
The Friedel sum rule is generalized to relativistic systems of spin-1/2 particles in one dimension. The change of the total energy due to the presence of an impurity is studied. The relation of the sum rule with the relativistic Levinson theorem is presented. Density oscillations in such systems are discussed. Since the Friedel theorem has been of major importance in understanding the impurity scattering in materials, the present results may be useful to explain some phenomena in one dimensional atomic chain, quantum wire, and fermionic many body systems.
PACS.34.10.+x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) 11.80.Et Partial-wave analysis 31.10.+z Theory of electronic structure, electronic transitions, and chemical binding 73.21.Hb Quantum wires
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