Quantumdots
| dc.creator | Lieb, E. H. | |
| dc.creator | Solovej, J. P. | |
| dc.creator | Yngvason, J. | |
| dc.date | 1994-04-29 | |
| dc.date.accessioned | 2026-07-25T23:33:09Z | |
| dc.description | Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular magnetic field $B$ may be present. We review some recent rigorous results for these systems. We have shown that a Thomas-Fermi type theory for the ground state is asymptotically correct when $N$ and $B$ tend to infinity. There are several mathematically and physically novel features. 1. The derivation of the appropriate Lieb-Thirring inequality requires some added effort. 2. When $B$ is appropriately large the TF ``kinetic energy'' term disappears and a peculiar ``classical'' continuum electrostatic theory emerges. This is a two dimensional problem, but with a three dimensional Coulomb potential. 3. Corresponding to this continuum theory is a discrete ``classical'' electrostatic theory. The former provides an upper bound and the latter a lower bound to the true quantum energy; the problem of relating the two classical energies offers an amusing exercise in electrostatics. | |
| dc.description | 20 pages, self-extracting uufile containing a plain TeX file and 2 postscript figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9404099 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9404099 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/99411 | |
| dc.subject | Condensed Matter | |
| dc.title | Quantumdots | |
| dc.type | text |