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 three times as large as that without trigonal warping, and six 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.Comment: 4 pages, 1 figur

Exact quantum state for N=1 supergravity

For N=1 supergravity in 3+1 dimensions we determine the graded algebra of the quantized Lorentz generators, supersymmetry generators, and diffeo-morphism and Hamiltonian generators and find that, at least formally, it closes in the chosen operator ordering. Following our recent conjecture and generalizing an ansatz for Bianchi-type models we proposed earlier we find an explicit exact quantum solution of all constraints in the metric representation

Transition from Poissonian to GOE level statistics in a modified Artin's billiard

One wall of Artin's billiard on the Poincar\'e half plane is replaced by a one-parameter ($c_p$) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuousand gradual transition from the Poisson like to GOE level statistics due to the small perturbations breaking the symmetry responsible for the 'arithmetic chaos' at $c_p=1$ is studied. Another GOE \rightrrow Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in boh cases. The study supports the existence of a scaling region around $c_p=1$. A finite size scaling relation for the Brody-parameter as a function of $1-c_p$ and the number of levels considered can be established

Emergence of bound states in ballistic magnetotransport of graphene antidots

An experimental method for detection of bound states around an antidot formed from a hole in a graphene sheet is proposed by measuring the ballistic two terminal conductances. In particularly, we consider the effect of bound states formed by magnetic field on the two terminal conductance and show that one can observe Breit-Wigner like resonances in the conductance as a function of the Fermi level close to the energies of the bound states. In addition, we develop a new numerical method in which the computational effort is proportional to the linear dimensions, instead of the area of the scattering region beeing typical for the existing numerical recursive Green's function method.Comment: 7 pages, 6 figure

Semiclassical Solution of the Quantum Hydrodynamic Equation for Trapped Bose-condensed Gas in the l=0 Case

In this paper the quantum hydrodynamic equation describing the collective, low energy excitations of a dilute atomic Bose gas in a given trapping potential is investigated with the JWKB semiclassical method. In the case of spherically symmetric harmonic confining potential a good agreement is shown between the semiclassical and the exact energy eigenvalues as well as wave functions. It is also demonstrated that for larger quantum numbers the calculation of the semiclassical wave function is numerically more stable than the exact polynomial with large alternating coefficients.Comment: 12 pages, 7 figure

Semiclassical wave functions and energy levels of Bose-condensed gases in spherically symmetric traps

The WKB-approximation for the Bogoliubov-equations of the quasi-particle excitations in Bose-gases with condensate is worked out in the case of spherically symmetric trap potentials on the basis of the resulting quantization rule. The excitation spectrum is calculated numerically and also analytically in certain limiting cases. It is found that the energy levels of a Bohr-Sommerfeld type quantization may be considerably shifted when the classical turning point gets close to the surface of the condensate.Comment: 4 pages Latex, 1 ps-fil

Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check

We investigate the exact master equation of Hu, Paz, and Zhang for a quantum harmonic oscillator at zero temperature with a Lorentz-Drude type Ohmic spectral density. This master equation plays an important role in the study of quantum Brownian motion and in various applications. In this paper, we give an analytical evaluation of the coefficients of this non-Markovian master equation without Lindblad form, which allows us to investigate consistencies of the solutions, the positivity of the stationary density operator, and the boundaries of the model's parameters.Comment: 17 pages, 8 figure