1,111 research outputs found
Localization properties of a tight-binding electronic model on the Apollonian network
An investigation on the properties of electronic states of a tight-binding
Hamiltonian on the Apollonian network is presented. This structure, which is
defined based on the Apollonian packing problem, has been explored both as a
complex network, and as a substrate, on the top of which physical models can
defined. The Schrodinger equation of the model, which includes only nearest
neighbor interactions, is written in a matrix formulation. In the uniform case,
the resulting Hamiltonian is proportional to the adjacency matrix of the
Apollonian network. The characterization of the electronic eigenstates is based
on the properties of the spectrum, which is characterized by a very large
degeneracy. The rotation symmetry of the network and large number of
equivalent sites are reflected in all eigenstates, which are classified
according to their parity. Extended and localized states are identified by
evaluating the participation rate. Results for other two non-uniform models on
the Apollonian network are also presented. In one case, interaction is
considered to be dependent of the node degree, while in the other one, random
on-site energies are considered.Comment: 7pages, 7 figure
Traffic by multiple species of molecular motors
We study the traffic of two types of molecular motors using the two-species
symmetric simple exclusion process (ASEP) with periodic boundary conditions and
with attachment and detachment of particles. We determine characteristic
properties such as motor densities and currents by simulations and analytical
calculations. For motors with different unbinding probabilities, mean field
theory gives the correct bound density and total current of the motors, as
shown by numerical simulations. For motors differing in their stepping
probabilities, the particle-hole symmetry of the current-density relationship
is broken and mean field theory fails drastically. The total motor current
exhibits exponential finite-size scaling, which we use to extrapolate the total
current to the thermodynamic limit. Finally, we also study the motion of a
single motor in the background of many non-moving motors.Comment: 23 pages, 6 figures, late
Organization of complex networks without multiple connections
We find a new structural feature of equilibrium complex random networks
without multiple and self-connections. We show that if the number of
connections is sufficiently high, these networks contain a core of highly
interconnected vertices. The number of vertices in this core varies in the
range between and , where is the number of
vertices in a network. At the birth point of the core, we obtain the
size-dependent cut-off of the distribution of the number of connections and
find that its position differs from earlier estimates.Comment: 5 pages, 2 figure
The number of ways to label a structure
It has been observed that the number of different ways in which a graph with p points can be labelled is p ! divided by the number of symmetries, and that this holds regardless of the species of structure at hand. In this note, a simple group-theoretic proof is provided.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45724/1/11336_2005_Article_BF02289423.pd
Entanglement in Valence-Bond-Solid States
This article reviews the quantum entanglement in Valence-Bond-Solid (VBS)
states defined on a lattice or a graph. The subject is presented in a
self-contained and pedagogical way. The VBS state was first introduced in the
celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki
(abbreviation AKLT is widely used). It became essential in condensed matter
physics and quantum information (measurement-based quantum computation). Many
publications have been devoted to the subject. Recently entanglement was
studied in the VBS state. In this review we start with the definition of a
general AKLT spin chain and the construction of VBS ground state. In order to
study entanglement, a block subsystem is introduced and described by the
density matrix. Density matrices of 1-dimensional models are diagonalized and
the entanglement entropies (the von Neumann entropy and Renyi entropy) are
calculated. In the large block limit, the entropies also approach finite
limits. Study of the spectrum of the density matrix led to the discovery that
the density matrix is proportional to a projector.Comment: Published version, 80 pages, 8 figures; references update
Meeting the Expectations of Your Heritage Culture: Links between Attachment Style, Intragroup Marginalisation, and Psychological Adjustment
This article has been made available through the Brunel Open Access Publishing Fund.This article has been made available through the Brunel Open Access Publishing Fund.Do insecurely-attached individuals perceive greater rejection from their heritage culture? Few studies have examined the antecedents and outcomes of this perceived rejection – termed intragroup marginalisation – in spite of its implications for the adjustment of cultural migrants to the mainstream culture. The present study investigated whether anxious and avoidant attachment orientations among cultural migrants were associated with greater intragroup marginalisation and, in turn, with lower subjective well-being and flourishing, and higher acculturative stress. Anxious attachment was associated with heightened intragroup marginalisation from friends and, in turn, with increased acculturative stress; anxious attachment was also associated with increased intragroup marginalisation from family. Avoidant attachment was linked with increased intragroup marginalisation from family and, in turn, with decreased subjective well-being
L\'evy-type diffusion on one-dimensional directed Cantor Graphs
L\'evy-type walks with correlated jumps, induced by the topology of the
medium, are studied on a class of one-dimensional deterministic graphs built
from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a
standard random walk on the sets but is also allowed to move ballistically
throughout the empty regions. Using scaling relations and the mapping onto the
electric network problem, we obtain the exact values of the scaling exponents
for the asymptotic return probability, the resistivity and the mean square
displacement as a function of the topological parameters of the sets.
Interestingly, the systems undergoes a transition from superdiffusive to
diffusive behavior as a function of the filling of the fractal. The
deterministic topology also allows us to discuss the importance of the choice
of the initial condition. In particular, we demonstrate that local and average
measurements can display different asymptotic behavior. The analytic results
are compared with the numerical solution of the master equation of the process.Comment: 9 pages, 9 figure
Cutpoints in the conjunction of two graphs
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47480/1/13_2005_Article_BF01226435.pd
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