arXiv subjects

A. D. Stone

Publications and source records attributed to A. D. Stone.

25 records · Page 2Linked to original sources

arXiv1998

Changing the Electronic Spectrum of a Quantum Dot by Adding Electrons

The temperature dependence of Coulomb blockade peak height correlation is used to investigate how adding electrons to a quantum dot alters or "scrambles" its electronic spectrum. Deviations from finite-temperature random matrix theory with an unchanging spectrum indicate spectral scrambling after a small number of electrons are added. Enhanced peak-to-peak correlations at low temperature are observed. Peak height statistics show similar behavior in several dot configurations despite significant differences in correlations.

cond-mat.mes-hall↗

arXiv1998

Quantum Chaos in Quantum Wells

We develop a quantitative semiclassical theory for the resosnant tunneling through a quantum well in a tilted magnetic field. It is shown, that in the leading semiclassical approximation the tunneling current depends only on periodic orbits within the quantum well. Further corrections (due to e.g. "ghost" effect) can be expressed in terms of closed, but non-periodic orbits, started at the "injection point". The results of the semiclassical theory are shown to be in good agreement with both the experimental data and numerical calculations.

cond-mat.mes-hall↗

arXiv1998

Conductance Peak Distributions in Quantum Dots at Finite Temperature: Signatures of the Charging Energy

We derive the finite temperature conductance peak distributions and peak-to-peak correlations for quantum dots in the Coulomb blockade regime assuming the validity of random matrix theory. The distributions are universal, depending only on the symmetry class and the temperature measured in units of the mean level spacing, $Δ$. When the temperature is comparable to $Δ$ several resonances contribute to the same conductance peak and we find significant deviations from the previously known $T \ll Δ$ distributions. In contrast to the $T \ll Δ$ case, these distributions show a strong signature of the charging energy and charge quantization on the dot.

cond-mat.mes-hall↗

arXiv1996

Periodic Orbit Theory of the Transition to Chaos in Quantum Wells

An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce periodic orbits. We calculate their period and stability analytically and find an infinite sequence of destabilizations followed by restabilizations as the chaos parameter increases. This phenomenon explains the re-entrant frequency-doubling of the density of states peaks observed in recent magnetotunneling experiments.

cond-mat↗

arXiv1994

Quantum chaos in a deformable billiard: Applications to quantum dots

We perform a detailed numerical study of energy-level and wavefunction statistics of a deformable quantum billiard focusing on properties relevant to semiconductor quantum dots. We consider the family of Robnik billiards generated by simple conformal maps of the unit disk; the shape of this family of billiards may be varied continuously at fixed area by tuning the parameters of the map. The classical dynamics of these billiards is well-understood and this allows us to study the quantum properties of subfamilies which span the transition from integrability to chaos as well as families at approximately constant degree of chaoticity (Kolmogorov entropy). In the regime of hard chaos we find that the statistical properties of interest are well-described by random-matrix theory and completely insensitive to the particular shape of the dot. However in the nearly-integrable regime non-universal behavior is found. Specifically, the level-width distribution is well-described by the predicted $χ^2$ distribution both in the presence and absence of magnetic flux when the system is fully chaotic; however it departs substantially from this behavior in the mixed regime. The chaotic behavior corroborates the previously predicted behavior of the peak-height distribution for deformed quantum dots. We also investigate the energy-level correlation functions which are found to agree well with the behavior calculated for quasi-zero-dimensional disordered systems.

cond-mat↗

arXiv1993

Resonance Lineshapes in Quasi-One-Dimensional Scattering

An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in microstructures or transmission resonances in waveguide junctions. The generic resonance is shown to have the asymmetric Fano lineshape. The asymmetry parameter q is independent of coupling to the quasi-bound level implying a scaling property of the resonances which can be tested in transport experiments.

cond-mat↗

arXiv1992

Weak-Localization and Integrability in Ballistic Cavities

We demonstrate the existence of an interference contribution to the average magnetoconductance, G(B), of ballistic cavities and use it to test the semiclassical theory of quantum billiards. G(B) is qualitatively different for chaotic and regular cavities, an effect explained semiclassically by the differing classical distribution of areas. The magnitude of G(B) is poorly explained by the semiclassical theory of coherent backscattering (elastic enhancement factor)-- correlations beyond time-reversed pairs of trajectories must be included-- but is in agreement with random matrix theory.

cond-mat↗