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Title 
The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics 

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Published in  Muga, J.G., Sala Mayato, R., and Egusquiza, I.L. Time in Quantum Mechanics. Berlin: Springer. 2002, p. 256278  
Collection 
Lecture Notes in Physics 

Abstract  The local Larmor clock is used to derive a hierarchy of local densities of states. At the bottom of this hierarchy are the partial density of states for which represent the contribution to the local density of states if both the incident and outgoing scattering channel are prescribed. On the next higher level is the injectivity which represents the contribution to the local density of states if only the incident channel is prescribed regardless of the final scattering channel. The injectivity is related by reciprocity to the emissivity of a point into a quantum channel. The sum of all partial density of states or the sum of all injectivities or the sum of all emissivities is equal to the local density of states. The use of the partial density of states is illustrated for a number of different electron transport problems in mesoscopic physics: The transmission from a tunneling tip into a mesoscopic conductor, the discussion of inelastic or phase breaking scattering with a voltage probe, and the acconductance of mesoscopic conductors. The transition from a capacitive response (positive timedelay) to an inductive response (negative timedelay) for a quantum point contact is used to illustrate the difficulty in associating timescales with a linear response analysis. A brief discussion of the offdiagonal elements of a partial density of states matrix is presented. The offdiagonal elements permit to investigate carrier fluctuations away from the average carrier density. The work concludes with a discussion of the relation between the partial density of states matrix and the WignerSmith delay time matrix.  
Keywords  Quantum Physics  
Identifiers  ISBN: 9783540432944 arXiv: quantph/0103164  
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Citation (ISO format)  BUTTIKER, Markus. The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics. In: Muga, J.G., Sala Mayato, R., and Egusquiza, I.L. (Ed.). Time in Quantum Mechanics. Berlin : Springer, 2002. p. 256278. (Lecture Notes in Physics) https://archiveouverte.unige.ch/unige:4481 