dorsal/arxiv
View SchemaRigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems
| Authors | C. Pacher, W. Boxleitner, E. Gornik |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407134 |
| URL | https://arxiv.org/abs/quant-ph/0407134 |
| DOI | 10.1103/PhysRevB.71.125317 |
| Journal | Phys. Rev. B 71, 125317 (2005) |
Abstract
The velocity $v_{res}$ of resonant tunneling electrons in finite periodic structures is analytically calculated in two ways. The first method is based on the fact that a transmission of unity leads to a coincidence of all still competing tunneling time definitions. Thus, having an indisputable resonant tunneling time $\tau_{res},$ we apply the natural definition $v_{res}=L/\tau_{res}$ to calculate the velocity. For the second method we combine Bloch's theorem with the transfer matrix approach to decompose the wave function into two Bloch waves. Then the expectation value of the velocity is calculated. Both different approaches lead to the same result, showing their physical equivalence. The obtained resonant tunneling velocity $v_{res}$ is smaller or equal to the group velocity times the magnitude of the complex transmission amplitude of the unit cell. Only at energies where the unit cell of the periodic structure has a transmission of unity $v_{res}$ equals the group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are performed. For typical parameters the resonant velocity is below one third of the group velocity.
{
"annotation_id": "aea700a8-7aaa-4dc0-853b-dd15e049b087",
"date_created": "2026-03-02T18:02:10.295000Z",
"date_modified": "2026-03-02T18:02:10.295000Z",
"file_hash": "a887b701c673871b52f6c1b7c61818c5417560ff8913eb8672a5c1855c5f65cd",
"private": false,
"record": {
"abstract": "The velocity $v_{res}$ of resonant tunneling electrons in finite periodic\nstructures is analytically calculated in two ways. The first method is based on\nthe fact that a transmission of unity leads to a coincidence of all still\ncompeting tunneling time definitions. Thus, having an indisputable resonant\ntunneling time $\\tau_{res},$ we apply the natural definition\n$v_{res}=L/\\tau_{res}$ to calculate the velocity. For the second method we\ncombine Bloch\u0027s theorem with the transfer matrix approach to decompose the wave\nfunction into two Bloch waves. Then the expectation value of the velocity is\ncalculated. Both different approaches lead to the same result, showing their\nphysical equivalence. The obtained resonant tunneling velocity $v_{res}$ is\nsmaller or equal to the group velocity times the magnitude of the complex\ntransmission amplitude of the unit cell. Only at energies where the unit cell\nof the periodic structure has a transmission of unity $v_{res}$ equals the\ngroup velocity. Numerical calculations for a GaAs/AlGaAs superlattice are\nperformed. For typical parameters the resonant velocity is below one third of\nthe group velocity.",
"arxiv_id": "quant-ph/0407134",
"authors": [
"C. Pacher",
"W. Boxleitner",
"E. Gornik"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevB.71.125317",
"journal_ref": "Phys. Rev. B 71, 125317 (2005)",
"title": "Rigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems",
"url": "https://arxiv.org/abs/quant-ph/0407134"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "29df27ad-46c8-41be-83fe-bc2acc7fe2fb",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}