Quantum-Dot Ground-State Energies and Spin Polarizations: Soft versus Hard Chaos

We consider how the nature of the dynamics affects ground state properties of ballistic quantum dots. We find that “mesoscopic Stoner fluctuations” that arise from the residual screened Coulomb interaction are very sensitive to the degree of chaos. It leads to ground state energies and spin polarizations whose fluctuations strongly increase as a system becomes less chaotic. The crucial features are illustrated with a model that depends on a parameter that tunes the dynamics from nearly integrable to mostly chaotic.

Figure 1

Inverse participation ratio as a function of the orbital index for $(+,+)$. From top down: $(\lambda ,\kappa )=(+0.20,1.00)$ [nearly integrable], $(-0.20,1.00)$ [mixed], and $(-0.80,1.00)$ [mostly chaotic].

Figure 2

Integrated peak spacing distribution with $\zeta =0.8$ for RMT/RPW prediction [7] (dotted line), mostly chaotic (solid line), mixed (dash-dotted line), and nearly integrable (dashed line) regimes.

Figure 3

Successive filling of the $(+,+)$ orbitals $i=63$ to $69$ as the number of particles in the dot goes from $N=129$ to $135$ for $(\lambda ,\kappa )=(+0.20,1.00)$ and $\zeta =0.8$. The spacing between the horizontal lines is proportional to the actual level spacings. The numbers in the right column are the corresponding IPRs.