424 research outputs found
Branched Polymers on the Given-Mandelbrot family of fractals
We study the average number A_n per site of the number of different
configurations of a branched polymer of n bonds on the Given-Mandelbrot family
of fractals using exact real-space renormalization. Different members of the
family are characterized by an integer parameter b, b > 1. The fractal
dimension varies from to 2 as b is varied from 2 to infinity. We
find that for all b > 2, A_n varies as , where
and are some constants, and . We determine the
exponent , and the size exponent (average diameter of polymer
varies as ), exactly for all b > 2. This generalizes the earlier results
of Knezevic and Vannimenus for b = 3 [Phys. Rev {\bf B 35} (1987) 4988].Comment: 24 pages, 8 figure
A Model for Quantum Stochastic Absorption in Absorbing Disordered Media
Wave propagation in coherently absorbing disordered media is generally
modeled by adding a complex part to the real part of the potential. In such a
case, it is already understood that the complex potential plays a duel role; it
acts as an absorber as well as a reflector due to the mismatch of the phase of
the real and complex parts of the potential. Although this model gives expected
results for weakly absorbing disordered media, it gives unphysical results for
the strong absorption regime where it causes the system to behave like a
perfect reflector. To overcome this issue, we develop a model here using
stochastic absorption for the modeling of absorption by "fake", or "side",
channels obviating the need for a complex potential. This model of stochastic
absorption eliminates the reflection that is coupled with the absorption in the
complex potential model and absorption is proportional to the magnitude of the
absorbing parameter. Solving the statistics of the reflection coefficient and
its phase for both the models, we argue that stochastic absorption is a
potentially better way of modeling absorbing disordered media.Comment: 5 pages, 4 figure
Hofstadter butterflies of bilayer graphene
We calculate the electronic spectrum of bilayer graphene in perpendicular
magnetic fields nonperturbatively. To accommodate arbitrary displacements
between the two layers, we apply a periodic gauge based on singular flux
vortices of phase . The resulting Hofstadter-like butterfly plots show a
reduced symmetry, depending on the relative position of the two layers against
each other. The split of the zero-energy relativistic Landau level differs by
one order of magnitude between Bernal and non-Bernal stacking.Comment: updated to refereed and edited versio
Random-phase reservoir and a quantum resistor: The Lloyd model
We introduce phase disorder in a 1D quantum resistor through the formal
device of `fake channels' distributed uniformly over its length such that the
out-coupled wave amplitude is re-injected back into the system, but with a
phase which is random. The associated scattering problem is treated via
invariant imbedding in the continuum limit, and the resulting transport
equation is found to correspond exactly to the Lloyd model. The latter has been
a subject of much interest in recent years. This conversion of the random phase
into the random Cauchy potential is a notable feature of our work. It is
further argued that our phase-randomizing reservoir, as distinct from the well
known phase-breaking reservoirs, induces no decoherence, but essentially
destroys all interference effects other than the coherent back scattering.Comment: 4 pages,5 figure
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
Scaling of Hamiltonian walks on fractal lattices
We investigate asymptotical behavior of numbers of long Hamiltonian walks
(HWs), i.e. self-avoiding random walks that visit every site of a lattice, on
various fractal lattices. By applying an exact recursive technique we obtain
scaling forms for open HWs on 3-simplex lattice, Sierpinski gasket, and their
generalizations: Given-Mandelbrot (GM), modified Sierpinski gasket (MSG) and
n-simplex fractal families. For GM, MSG and n-simplex lattices with odd values
of n, number of open HWs , for the lattice with sites, varies as
. We explicitly calculate exponent for several
members of GM and MSG families, as well as for n-simplices with n=3,5, and 7.
For n-simplex fractals with even n we find different scaling form: , where is fractal dimension of the lattice,
which also differs from the formula expected for homogeneous lattices. We
discuss possible implications of our results on studies of real compact
polymers.Comment: 19 pages, 13 figures, RevTex4; extended Introduction, several
references added; one figure added in section II; corrected typos; version
accepted for publication in Phys.Rev.
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 ), while it is shown that BEC
always occurs for .Comment: 4 pages, 10 figure
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
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
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