Gyula Dávid

Unified description of Zitterbewegung for spintronic, graphene, and superconducting systems

We present a unified treatment of Zitterbewegung phenomena for a wide class of systems including spintronic, graphene, and superconducting systems. We derive an explicit expression for the time dependence of the position operator of the quasiparticles which can be decomposed into a mean part and an oscillatory term. The latter corresponds to the Zitterbewegung. To apply our result for different systems, one needs to use only vector algebra instead of the more complicated operator algebra.

Relativistic computers and the Turing barrier

We examine the current status of the physical version of the Church-Turing Thesis (PhCT for short) in view of latest developments in spacetime theory. This also amounts to investigating the status of hypercomputation in view of latest results on spacetime. We agree with [D. Deutsch, A. Ekert, R. Lupacchini, Machines, logic and quantum physics, Bulletin of Symbolic Logic 6 (3) (2000) 265–283] that PhCT is not only a conjecture of mathematics but rather a conjecture of a combination of theoretical physics, mathematics and, in some sense, cosmology. Since the idea of computability is intimately connected with the nature of time, relevance of spacetime theory seems to be unquestionable. We will see that recent developments in spacetime theory show that temporal developments may exhibit features that traditionally seemed impossible or absurd. We will see that recent results point in the direction that the possibility of artificial systems computing nonTuring computable functions may be consistent with spacetime theory. All these trigger new open questions and new research directions for spacetime theory, cosmology, and computability. � 2005 Elsevier Inc. All rights reserved.

Perturbation of infinite networks of resistors

The resistance between arbitrary nodes of an infinite network of resistors is calculated when the network is perturbed by removing one bond from the perfect lattice. A relation is given between the resistance and the lattice Green’s function of the perturbed resistor network. By solving the Dyson equation, the Green’s function and the resistance of the perturbed lattice are expressed in terms of those of the perfect lattice. Numerical results are presented for a square lattice.

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.

Uniform tiling with electrical resistors

The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Greens function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagome, diced and decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.

General theory of Zitterbewegung

We derive a general and simple expression for the time dependence of the position operator of a multiband Hamiltonian with arbitrary matrix elements depending only on the momentum of the quasiparticle. Our result shows that in such systems the Zitterbewegung-type term related to a trembling motion of the quasiparticle, always appears in the position operator. Moreover, the Zitterbewegung is, in general, a multifrequency oscillatory motion of the quasiparticle. We derive a few alternative expressions for the amplitude of the oscillatory motion including that related to the Berry connection matrix. We present several examples to demonstrate how general and versatile our result is.

Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a two by two Hamiltonian. As an application we derive an analytical expression for the minimal conductivity tensor of bilayer graphene as a function of a complex parameter

Relation between Zitterbewegung and the charge conductivity, Berry curvature, and the Chern number of multiband systems

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Diverging dc conductivity due to a flat band in a disordered system of pseudospin-1 Dirac-Weyl fermions

related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, this directly affect the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on Landauer approach and we find remarkably good agreement between the two methods. We demonstrate that the minimal conductivity is very sensitive to the change of the parameter

Frequency-dependent magneto-optical conductivity in the generalized .ALPHA.-T3 model

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