arXiv subjects

Caio H. Lewenkopf

Publications and source records attributed to Caio H. Lewenkopf.

41 records · Page 3Linked to original sources

arXiv1998

Coulomb blockade peak spacing fluctuations in deformable quantum dots: a further test to Random Matrix Theory

We propose a mechanism to explain the fluctuations of the ground state energy in quantum dots in the Coulomb blockade regime. Employing the random matrix theory we show that shape deformations may change the adjacent peak spacing distribution from Wigner-Dyson to nearly Gaussian even in the absence of strong charging energy fluctuations. We find that this distribution is solely determined by the average number of anti-crossings between consecutive conductance peaks and the presence or absence of a magnetic field. Our mechanism is tested in a dynamical model whose underlying classical dynamics is chaotic. Our results are in good agreement with recent experiments and apply to quantum dots with spin resolved or spin degenerate states.

cond-mat.mes-hall↗

arXiv1997

Semiclassical limit of universal parametric density correlations

Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term obtained from Random Matrix Theory. The advantage of the semiclassical approach is to provide a simple recipe for the calculation of the non-universal scaling parameter from elements of the underlying classical dynamics specific to the system. We discuss recent improvements of the theory, which introduce a requantization of the smoothed level density.

chao-dyn↗

arXiv1996

Parametric correlation of Coulomb blockade conductance peaks in chaotic quantum dots

We investigate the autocorrelator of conductance peak heights for quantum dots in the Coulomb blockade regime. Analytical and numerical results based on Random Matrix Theory are presented and compared to exact numerical calculations based on a simple dynamical model. We consider the case of preserved time-reversal symmetry, which is realized experimentally by varying the shape of the quantum dot in the absence of magnetic fields. Upon a proper rescaling, the correlator becomes independent of the details of the system and its form is solely determined by symmetry properties and the number of channels in the leads. The magnitude of the scaling parameter is estimated by a semiclassical approach.

cond-mat↗

arXiv1996

Parametric Conductance Correlation for Irregularly Shaped Quantum Dots

We propose the autocorrelator of conductance peak heights as a signature of the underlying chaotic dynamics in quantum dots in the Coulomb blockade regime. This correlation function is directly accessible to experiments and its decay width contains interesting information about the underlying electron dynamics. Analytical results are derived in the framework of random matrix theory in the regime of broken time-reversal symmetry. The final expression, upon rescaling, becomes independent of the details of the system. For the situation when the external parameter is a variable magnetic field, the system-dependent, nonuniversal field scaling factor is obtained by a semiclassical approach. The validity of our findings is confirmed by a comparison with results of an exact numerical diagonalization of the conformal billiard threaded by a magnetic flux line.

cond-mat↗

arXiv1995

Levy Diffusion and Classes of Universal Parametric Correlations

A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be labeled by a parameter $α\in (0,2]$, in a manner analogous to Lévy diffusion. Universality is obtained after scaling by the (anomalous) diffusion constant $D_α$ (the usual scaling is divergent for $α<2$). For each $α$, correlation functions are universal, and distinct. The previous results in the literature correspond to the limiting case of superdiffusion, $α=2$.

chao-dyn↗