Interaction matrix element fluctuations in quantum dots

Journal Article · Fri Apr 04 04:00:00 EDT 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2915599· OSTI ID:21136989

Kaplan, L ^[1]; Alhassid, Y ^[2]

---

1. Department of Physics, Tulane University, New Orleans, LA 70118 (United States)
2. Center for Theoretical Physics, Sloane Physics Laboratory Yale University, New Haven, CT 06520 (United States)

In the Coulomb blockade regime of a ballistic quantum dot, the distribution of conductance peak spacings is well known to be incorrectly predicted by a single-particle picture; instead, matrix element fluctuations of the residual electronic interaction need to be taken into account. In the normalized random-wave model, valid in the semiclassical limit where the number of electrons in the dot becomes large, we obtain analytic expressions for the fluctuations of two-body and one-body matrix elements. However, these fluctuations may be too small to explain low-temperature experimental data. We have examined matrix element fluctuations in realistic chaotic geometries, and shown that at energies of experimental interest these fluctuations generically exceed by a factor of about 3-4 the predictions of the random wave model. Even larger fluctuations occur in geometries with a mixed chaotic-regular phase space. These results may allow for much better agreement between the Hartree-Fock picture and experiment. Among other findings, we show that the distribution of interaction matrix elements is strongly non-Gaussian in the parameter range of experimental interest, even in the random wave model. We also find that the enhanced fluctuations in realistic geometries cannot be computed using a leading-order semiclassical approach, but may be understood in terms of short-time dynamics.

• OSTI ID: 21136989
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 995; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CHAOS THEORY
DISTRIBUTION
ELECTRONS
FLUCTUATIONS
HARTREE-FOCK METHOD
MATRIX ELEMENTS
PHASE SPACE
QUANTUM DOTS
RANDOMNESS
S MATRIX
SEMICLASSICAL APPROXIMATION
TWO-BODY PROBLEM