Comment on "Exact results for survival probability in the multistate Landau-Zener model"

We correct the proof of Brundobler-Elser formula (BEF) provided in [2004 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{37} 4069] and continued in Appendix of [2005 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{38} 907]. After showing that some changes of variables employed in these articles are used erroneously, we propose an alternative change of variables which solves the problem. In our proof, we reveal the connection between the BEF for a general $N$-level Landau-Zener system and the exactly solvable bow-tie model. The special importance of the diabatic levels with maximum/minimum slope is emphasized throughout.Comment: 10 page

Ballistic charge transport in chiral-symmetric few-layer graphene

A transfer matrix approach to study ballistic charge transport in few-layer graphene with chiral-symmetric stacking configurations is developed. We demonstrate that the chiral symmetry justifies a non-Abelian gauge transformation at the spectral degeneracy point (zero energy). This transformation proves the equivalence of zero-energy transport properties of the multilayer to those of the system of uncoupled monolayers. Similar transformation can be applied in order to gauge away an arbitrary magnetic field, weak strain, and hopping disorder in the bulk of the sample. Finally, we calculate the full-counting statistics at arbitrary energy for different stacking configurations. The predicted gate-voltage dependence of conductance and noise can be measured in clean multilayer samples with generic metallic leads.Comment: 6 pages, 5 figures; EPL published versio

Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings

We generalize the Brundobler-Elser hypothesis in the multistate Landau-Zener problem to the case when instead of a state with the highest slope of the diabatic energy level there is a band of states with an arbitrary number of parallel levels having the same slope. We argue that the probabilities of counterintuitive transitions among such states are exactly zero.Comment: 9 pages, 5 figure

Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Quantum Theory of High Harmonic Generation via Above Threshold Ionization and Stimulated Recombination

Fully quantum treatment explicitly presents the high harmonic generation as a three-stage process: above threshold ionization (ATI) is followed by the continuum electron propagation in a laser field and subsequent stimulated recombination back into the initial state. The contributions of all ATI channels add up coherently. All three stages of the process are described by simple, mostly analytical expressions. A very good quantitative agreement with the previous calculations on the harmonic generation by H$^-$ ion is demonstrated, thus supplementing the conceptual significance of the theory with its practical efficiency.Comment: Latex IOP stile, plus 1 figure in a PostScript fil

Ballistic transport in disordered graphene

An analytic theory of electron transport in disordered graphene in a ballistic geometry is developed. We consider a sample of a large width W and analyze the evolution of the conductance, the shot noise, and the full statistics of the charge transfer with increasing length L, both at the Dirac point and at a finite gate voltage. The transfer matrix approach combined with the disorder perturbation theory and the renormalization group is used. We also discuss the crossover to the diffusive regime and construct a ``phase diagram'' of various transport regimes in graphene.Comment: 23 pages, 10 figure