Mesoscopic Fluctuations in Quantum Dots, Nanoparticles and Nuclei

TL;DR

This paper explores mesoscopic fluctuations in quantum dots, nanoparticles, and nuclei, emphasizing the role of random matrix theory, interactions, and pairing correlations in understanding their statistical and physical properties.

Contribution

It applies random matrix theory to quantum dots and investigates pairing effects in nanoparticles and nuclei, highlighting the importance of interactions beyond simple models.

Findings

Random matrix theory describes conductance fluctuations in chaotic quantum dots.

Pairing correlations influence heat capacity signatures in nuclei.

Mesoscopic effects are significant in nanoparticles smaller than 3 nm.

Abstract

We discuss mesoscopic effects in quantum dots, nanoparticles and nuclei. In quantum dots, we focus on the statistical regime of dots whose single-electron dynamics are chaotic. Random matrix theory methods, developed to explain the statistics of neutron resonances in compound nuclei, are useful in describing the mesoscopic fluctuations of the conductance in such dots. However, correlation effects beyond the charging energy are important in almost-isolated dots. In particular, exchange and residual interactions are necessary to obtain a quantitative description of the mesoscopic fluctuations. Pairing correlations are important in metallic nanoparticles and nuclei. Nanoparticles smaller than \~ 3 nm and nuclei are close to the fluctuation-dominated regime in which the Bardeen-Cooper-Schrieffer theory is not valid. Despite the large fluctuations, we find signatures of pairing correlations in the heat capacity of nuclei. These signatures depend on the particle-number parity of protons and neutrons