Decohering d-dimensional quantum resistance

The Landauer scattering approach to 4-probe resistance is revisited for the case of a d-dimensional disordered resistor in the presence of decoherence. Our treatment is based on an invariant-embedding equation for the evolution of the coherent reflection amplitude coefficient in the length of a 1-dimensional disordered conductor, where decoherence is introduced at par with the disorder through an outcoupling, or stochastic absorption, of the wave amplitude into side (transverse) channels, and its subsequent incoherent re-injection into the conductor. This is essentially in the spirit of B{\"u}ttiker's reservoir-induced decoherence. The resulting evolution equation for the probability density of the 4-probe resistance in the presence of decoherence is then generalised from the 1-dimensional to the d-dimensional case following an anisotropic Migdal-Kadanoff-type procedure and analysed. The anisotropy, namely that the disorder evolves in one arbitrarily chosen direction only, is the main approximation here that makes the analytical treatment possible. A qualitatively new result is that arbitrarily small decoherence reduces the localisation-delocalisation transition to a crossover making resistance moments of all orders finite.Comment: 14 pages, 1 figure, revised version, to appear in Phys. Rev.

Enhanced Transmission Due to Disorder

The transmissivity of a one-dimensional random system that is periodic on average is studied. It is shown that the transmission coefficient for frequencies corresponding to a gap in the band structure of the average periodic system increases with increasing disorder while the disorder is weak enough. This property is shown to be universal, independent of the type of fluctuations causing the randomness. In the case of strong disorder the transmission coefficient for frequencies in allowed bands is found to be a non monotonic function of the strength of the disorder. An explanation for the latter behavior is provided.Comment: 9 pages, RevTeX 3.0, 4 Postscript figure

Geometry of Empty Space is the Key to Near-Arrest Dynamics

We study several examples of kinetically constrained lattice models using dynamically accessible volume as an order parameter. Thereby we identify two distinct regimes exhibiting dynamical slowing, with a sharp threshold between them. These regimes are identified both by a new response function in dynamically available volume, as well as directly in the dynamics. Results for the selfdiffusion constant in terms of the connected hole density are presented, and some evidence is given for scaling in the limit of dynamical arrest.Comment: 11 page

Transmission, reflection and localization in a random medium with absorption or gain

We study reflection and transmission of waves in a random tight-binding system with absorption or gain for weak disorder, using a scattering matrix formalism. Our aim is to discuss analytically the effects of absorption or gain on the statistics of wave transport. Treating the effects of absorption or gain exactly in the limit of no disorder, allows us to identify short- and long lengths regimes relative to absorption- or gain lengths, where the effects of absorption/gain on statistical properties are essentially different. In the long-lengths regime we find that a weak absorption or a weak gain induce identical statistical corrections in the inverse localization length, but lead to different corrections in the mean reflection coefficient. In contrast, a strong absorption or a strong gain strongly suppress the effect of disorder in identical ways (to leading order), both in the localization length and in the mean reflection coefficient.Comment: Important revisions and expansion caused by a crucial property of $\hat Q

Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks

Topological inhomogeneity gives rise to spectral anomalies that can induce Bose-Einstein Condensation (BEC) in low dimensional systems. These anomalies consist in energy regions composed of an infinite number of states with vanishing weight in the thermodynamic limit (hidden states). Here we present a rigorous result giving the most general conditions for BEC on complex networks. We prove that the presence of hidden states in the lowest region of the spectrum is the necessary and sufficient condition for condensation in low dimension (spectral dimension $\bar{d}\leq 2$), while it is shown that BEC always occurs for $\bar{d}>2$.Comment: 4 pages, 10 figure

Multifractal Behaviour of n-Simplex Lattice

We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an {\em n}-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, $\beta_L$, associated with resistance scaling, for any n. Using current cumulant method we calculate the exact noise exponent for n-simplex lattices.Comment: Latex, 9 pages including one figur

Crossover of conductance and local density of states in a single-channel disordered quantum wire

The probability distribution of the mesoscopic local density of states (LDOS) for a single-channel disordered quantum wire with chiral symmetry is computed in two different geometries. An approximate ansatz is proposed to describe the crossover of the probability distributions for the conductance and LDOS between the chiral and standard symmetry classes of a single-channel disordered quantum wire. The accuracy of this ansatz is discussed by comparison with a large-deviation ansatz introduced by Schomerus and Titov in Phys. Rev. B \textbf{67}, 100201(R) (2003).Comment: 19 pages, 5 eps figure

Non glassy ground-state in a long-range antiferromagnetic frustrated model in the hypercubic cell

We analize the statistical mechanics of a long-range antiferromagnetic model defined on a D-dimensional hypercube, both at zero and finite temperatures. The associated Hamiltonian is derived from a recently proposed complexity measure of Boolean functions, in the context of neural networks learning processes. We show that, depending of the value of D, the system either presents a low temperature antiferromagnetic stable phase or the global antiferromagnetic order disappears at any temperature. In the last case the ground state is an infinitely degenerated non-glassy one, composed by two equal size anti-aligned antiferromagnetic domains. We also present some results for the ferromagnetic version of the model.Comment: 8 pages, 5 figure

Electronic and Magnetic Properties of Nanographite Ribbons

Electronic and magnetic properties of ribbon-shaped nanographite systems with zigzag and armchair edges in a magnetic field are investigated by using a tight binding model. One of the most remarkable features of these systems is the appearance of edge states, strongly localized near zigzag edges. The edge state in magnetic field, generating a rational fraction of the magnetic flux (\phi= p/q) in each hexagonal plaquette of the graphite plane, behaves like a zero-field edge state with q internal degrees of freedom. The orbital diamagnetic susceptibility strongly depends on the edge shapes. The reason is found in the analysis of the ring currents, which are very sensitive to the lattice topology near the edge. Moreover, the orbital diamagnetic susceptibility is scaled as a function of the temperature, Fermi energy and ribbon width. Because the edge states lead to a sharp peak in the density of states at the Fermi level, the graphite ribbons with zigzag edges show Curie-like temperature dependence of the Pauli paramagnetic susceptibility. Hence, it is shown that the crossover from high-temperature diamagnetic to low-temperature paramagnetic behavior of the magnetic susceptibility of nanographite ribbons with zigzag edges.Comment: 13 pages including 19 figures, submitted to Physical Rev