dorsal/arxiv
View SchemaThe Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics
| Authors | M. Buttiker |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103164 |
| URL | https://arxiv.org/abs/quant-ph/0103164 |
| Journal | in "Time in Quantum Mechanics", edited by J. G. Muga, R. Sala Mayato and I. L. Egusquiza, Lecture Notes in Physics (Springer, Berlin, 2002).p. 256. Monographs; m72 ISBN 3-540-43294-9 |
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 ac-conductance of mesoscopic conductors. The transition from a capacitive response (positive time-delay) to an inductive response (negative time-delay) for a quantum point contact is used to illustrate the difficulty in associating time-scales with a linear response analysis. A brief discussion of the off-diagonal elements of a partial density of states matrix is presented. The off-diagonal 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 Wigner-Smith delay time matrix.
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"abstract": "The local Larmor clock is used to derive a hierarchy of local densities of\nstates. At the bottom of this hierarchy are the partial density of states for\nwhich represent the contribution to the local density of states if both the\nincident and outgoing scattering channel are prescribed. On the next higher\nlevel is the injectivity which represents the contribution to the local density\nof states if only the incident channel is prescribed regardless of the final\nscattering channel. The injectivity is related by reciprocity to the emissivity\nof a point into a quantum channel. The sum of all partial density of states or\nthe sum of all injectivities or the sum of all emissivities is equal to the\nlocal density of states. The use of the partial density of states is\nillustrated for a number of different electron transport problems in mesoscopic\nphysics: The transmission from a tunneling tip into a mesoscopic conductor, the\ndiscussion of inelastic or phase breaking scattering with a voltage probe, and\nthe ac-conductance of mesoscopic conductors. The transition from a capacitive\nresponse (positive time-delay) to an inductive response (negative time-delay)\nfor a quantum point contact is used to illustrate the difficulty in associating\ntime-scales with a linear response analysis. A brief discussion of the\noff-diagonal elements of a partial density of states matrix is presented. The\noff-diagonal elements permit to investigate carrier fluctuations away from the\naverage carrier density. The work concludes with a discussion of the relation\nbetween the partial density of states matrix and the Wigner-Smith delay time\nmatrix.",
"arxiv_id": "quant-ph/0103164",
"authors": [
"M. Buttiker"
],
"categories": [
"quant-ph",
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"journal_ref": "in \"Time in Quantum Mechanics\", edited by J. G. Muga, R. Sala\n Mayato and I. L. Egusquiza, Lecture Notes in Physics (Springer, Berlin,\n 2002).p. 256. Monographs; m72 ISBN 3-540-43294-9",
"title": "The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics",
"url": "https://arxiv.org/abs/quant-ph/0103164"
},
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