133 research outputs found
Wave Function Shredding by Sparse Quantum Barriers
We discuss a model in which a quantum particle passes through
potentials arranged in an increasingly sparse way. For infinitely many barriers
we derive conditions, expressed in terms ergodic properties of wave function
phases, which ensure that the point and absolutely continuous parts are absent
leaving a purely singularly continuous spectrum. For a finite number of
barriers, the transmission coefficient shows extreme sensitivity to the
particle momentum with fluctuation in many different scales. We discuss a
potential application of this behavior for erasing the information carried by
the wave function.Comment: 4 pages ReVTeX with 3 epsf figure
Anomalous Behavior of the Zero Field Susceptibility of the Ising Model on the Cayley Tree
It is found that the zero field susceptibility chi of the Ising model on the
Cayley tree exhibits unusually weak divergence at the critical point Tc. The
susceptibility amplitude is found to diverge at Tc proportionally to the tree
generation level n, while the behavior of chi is otherwise analytic in the
vicinity of Tc, with the critical exponent gamma=0.Comment: 3 pages, 2 figure
Anderson localization in bipartite lattices
We study the localization properties of a disordered tight-binding
Hamiltonian on a generic bipartite lattice close to the band center. By means
of a fermionic replica trick method, we derive the effective non-linear
-model describing the diffusive modes, which we analyse by using the
Wilson--Polyakov renormalization group. In addition to the standard parameters
which define the non-linear -model, namely the conductance and the
external frequency, a new parameter enters, which may be related to the
fluctuations of the staggered density of states. We find that, when both the
regular hopping and the disorder only couple one sublattice to the other, the
quantum corrections to the Kubo conductivity vanish at the band center, thus
implying the existence of delocalized states. In two dimensions, the RG
equations predict that the conductance flows to a finite value, while both the
density of states and the staggered density of states fluctuations diverge. In
three dimensions, we find that, for arbitrarily weak disorder, sufficiently
close to the band center, all states are extended. We also discuss the role of
various symmetry breaking terms, as a regular hopping between same sublattices,
or an on-site disorder.Comment: 51 pages, RevTex style. New version, with corrections and
enlargments, prepared to be submitted in Nuclear Physics
Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists
We review critically the concepts and the applications of Cayley Trees and
Bethe Lattices in statistical mechanics in a tentative effort to remove
widespread misuse of these simple, but yet important - and different - ideal
graphs. We illustrate, in particular, two rigorous techniques to deal with
Bethe Lattices, based respectively on self-similarity and on the Kolmogorov
consistency theorem, linking the latter with the Cavity and Belief Propagation
methods, more known to the physics community.Comment: 10 pages, 2 figure
Spin Models on Thin Graphs
We discuss the utility of analytical and numerical investigation of spin
models, in particular spin glasses, on ordinary ``thin'' random graphs (in
effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two
dimensional gravity. We highlight the similarity with Bethe lattice
calculations and the advantages of the thin graph approach both analytically
and numerically for investigating mean field results.Comment: Contribution to Parallel Session at Lattice95, 4 pages. Dodgy
compressed ps file replaced with uuencoded LaTex original + ps figure
Electronic states of metallic and semiconducting carbon nanotubes with bond and site disorder
Disorder effects on the density of states in carbon nanotubes are analyzed by
a tight binding model with Gaussian bond or site disorder. Metallic armchair
and semiconducting zigzag nanotubes are investigated. In the strong disorder
limit, the conduction and valence band states merge, and a finite density of
states appears at the Fermi energy in both of metallic and semiconducting
carbon nanotubes. The bond disorder gives rise to a huge density of states at
the Fermi energy differently from that of the site disorder case. Consequences
for experiments are discussed.Comment: Phys. Rev. B: Brief Reports (to be published). Related preprints can
be found at http://www.etl.go.jp/~harigaya/NEW.htm
Complex random matrix models with possible applications to spin- impurity scattering in quantum Hall fluids
We study the one-point and two-point Green's functions in a complex random
matrix model to sub-leading orders in the large N limit. We take this complex
matrix models as a model for the two-state scattering problem, as applied to
spin dependent scattering of impurities in quantum Hall fluids. The density of
state shows a singularity at the band center due to reflection symmetry. We
also compute the one-point Green's function for a generalized situation by
putting random matrices on a lattice of arbitrary dimensions.Comment: 20P, (+4 figures not included
Anderson transition of three dimensional phonon modes
Anderson transition of the phonon modes is studied numerically. The critical
exponent for the divergence of the localization length is estimated using the
transfer matrix method, and the statistics of the modes is analyzed. The latter
is shown to be in excellent agreement with the energy level statistics of the
disrodered electron system belonging to the orthogonal universality class.Comment: 2 pages and another page for 3 figures, J. Phys. Soc. Japa
Spectral and Transport Properties of Quantum Wires with Bond Disorder
Systems with bond disorder are defined through lattice Hamiltonians that are
of pure nearest neighbour hopping type, i.e. do not contain on-site
contributions. Previous analyses based on the Dorokhov-Mello-Pereyra-Kumar
(DMPK) transfer matrix technique have shown that both spectral and transport
properties of quasi one-dimensional systems belonging to this category are
highly unusual. Notably, regimes with absence of exponential Anderson
localization are observed, the single particle density of states exhibits
singular structure in the vicinity of the band centre, and the manifestation of
these phenomena depends in an apparently topological manner on the even- or
oddness of the channel number. In this paper we re-consider the problem from
the complementary perspective of the non-linear sigma-model. Relying on the
standard analogy between one-dimensional statistical field theories and
zero-dimensional quantum mechanics, we will relate the problem to the behaviour
of a quantum point particle subject to an Aharonov-Bohm flux. We will re-derive
previous DMPK results, identify a new class of even/odd staggering phenomena
and trace back the anomalous behaviour of the bond disordered system to a
simple physical mechanism, viz. the flux periodicity of the quantum
Aharonov-Bohm system. We will also touch upon connections to the low energy
physics of other lattice systems, notably disordered chiral systems in 0 and 2
dimensions and antiferromagnetic spin chains.Comment: 55 pages, 2 figures include
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