Spin accumulation encoded in electronic noise for mesoscopic billiards with finite tunneling rates

We study the effects of spin accumulation (inside reservoirs) on electronic transport with tunneling and reflections at the gates of a quantum dot. Within the stub model, the calculations focus on the current-current correlation function for the flux of electrons injected into the quantum dot. The linear response theory used allows us to obtain the noise power in the regime of thermal crossover as a function of parameters that reveal the spin polarization at the reservoirs. The calculation is performed employing diagrammatic integration within the universal groups (ensembles of Dyson) for a nonideal, nonequilibrium chaotic quantum dot. We show that changes in the spin distribution determine significant alterations in noise behavior at values of the tunneling rates close to zero, in the regime of strong reflection at the gates.

Stickiness in a bouncer model: A slowing mechanism for Fermi acceleration

Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables' velocity and time. The system is characterized by a control parameter epsilon and experiences a transition from integrable (epsilon = 0) to nonintegrable (epsilon not equal 0). For small values of epsilon, the phase space shows a mixed structure where periodic islands, chaotic seas, and invariant tori coexist. As the parameter epsilon increases and reaches a critical value epsilon(c), all invariant tori are destroyed and the chaotic sea spreads over the phase space, leading the particle to diffuse in velocity and experience Fermi acceleration (unlimited energy growth). During the dynamics the particle can be temporarily trapped near periodic and stable regions. We use the finite time Lyapunov exponent to visualize this effect. The survival probability was used to obtain some of the transport properties in the phase space. For large epsilon, the survival probability decays exponentially when it turns into a slower decay as the control parameter epsilon is reduced. The slower decay is related to trapping dynamics, slowing the Fermi Acceleration, i.e., unbounded growth of the velocity.

Scaling invariance for the escape of particles from a periodically corrugated waveguide

The escape dynamics of a classical light ray inside a corrugated waveguide is characterised by the use of scaling arguments. The model is described via a two-dimensional nonlinear and area preserving mapping. The phase space of the mapping contains a set of periodic islands surrounded by a large chaotic sea that is confined by a set of invariant tori. When a hole is introduced in the chaotic sea, letting the ray escape, the histogram of frequency of the number of escaping particles exhibits rapid growth, reaching a maximum value at n(p) and later decaying asymptotically to zero. The behaviour of the histogram of escape frequency is characterised using scaling arguments. The scaling formalism is widely applicable to critical phenomena and useful in characterisation of phase transitions, including transitions from limited to unlimited energy growth in two-dimensional time varying billiard problems. (C) 2011 Elsevier B.V. All rights reserved.

Energy-level statistics of interacting trapped bosons

It is a well-established fact that statistical properties of energy-level spectra are the most efficient tool to characterize nonintegrable quantum systems. The statistical behavior of different systems such as complex atoms, atomic nuclei, two-dimensional Hamiltonians, quantum billiards, and noninteracting many bosons has been studied. The study of statistical properties and spectral fluctuations in interacting many-boson systems has developed interest in this direction. We are especially interested in weakly interacting trapped bosons in the context of Bose-Einstein condensation (BEC) as the energy spectrum shows a transition from a collective nature to a single-particle nature with an increase in the number of levels. However this has received less attention as it is believed that the system may exhibit Poisson-like fluctuations due to the existence of an external harmonic trap. Here we compute numerically the energy levels of the zero-temperature many-boson systems which are weakly interacting through the van der Waals potential and are confined in the three-dimensional harmonic potential. We study the nearest-neighbor spacing distribution and the spectral rigidity by unfolding the spectrum. It is found that an increase in the number of energy levels for repulsive BEC induces a transition from a Wigner-like form displaying level repulsion to the Poisson distribution for P(s). It does not follow the Gaussian orthogonal ensemble prediction. For repulsive interaction, the lower levels are correlated and manifest level-repulsion. For intermediate levels P(s) shows mixed statistics, which clearly signifies the existence of two energy scales: external trap and interatomic interaction, whereas for very high levels the trapping potential dominates, generating a Poisson distribution. Comparison with mean-field results for lower levels are also presented. For attractive BEC near the critical point we observe the Shnirelman-like peak near s = 0, which signifies the presence of a large number of quasidegenerate states.