Role of the trigonal warping on the minimal conductivity of bilayer graphene.

Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is 3 times as large as that without trigonal warping and 6 times larger than that in single layer graphene. Although the trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low-energy excitations, our result shows that its role cannot be neglected in the zero-energy minimal conductivity.

Clustering of Fermi particles with arbitrary spin.

A single l-shell model is investigated for a system of fermions of spin s and an attractive s-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different l,s values and particle numbers N. As a generalization of Cooper pairing it is shown that when N=mu(2s+1), mu=1,2,..., 2l+1, the ground state consists of clusters of (2s+1) particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.

Quantum irregular scattering induced by tunneling.

Irregular behavior in a simple two-dimensional scattering model is investigated in the quantum domain. The scattering potential is composed from Dirac deltas on a stadium shaped curve. The unusual feature of the model is that the irregular patterns disappear in the classical limit because the main mechanism leading to resonances in the cross section data is the quantum tunneling. Calculations for the standard characteristics such as nearest-neighbor distribution of eigenphases of the S-matrix, the distribution of the S-matrix elements and the correlation function of the total cross section are performed. Deviations from the usual predictions for irregular scattering have been found in certain regions, which can be traced back to the fact that the model does not have such a characteristic time like the classical escape rate, which survives the classical limit.

Statistical properties of chaos demonstrated in a class of one-dimensional maps.

One-dimensional maps with complete grammar are investigated in both permanent and transient chaotic cases. The discussion focuses on statistical characteristics such as Lyapunov exponent, generalized entropies and dimensions, free energies, and their finite size corrections. Our approach is based on the eigenvalue problem of generalized Frobenius-Perron operators, which are treated numerically as well as by perturbative and other analytical methods. The examples include the universal chaos function relevant near the period doubling threshold. Special emphasis is put on the entropies and their decay rates because of their invariance under the most general class of coordinate changes. Phase-transition-like phenomena at the border state of chaos due to intermittency and super instability are presented.