85 research outputs found
Resonant scattering on impurities in the Quantum Hall Effect
We develop a new approach to carrier transport between the edge states via
resonant scattering on impurities, which is applicable both for short and long
range impurities. A detailed analysis of resonant scattering on a single
impurity is performed. The results are used for study of the inter-edge
transport by multiple resonant hopping via different impurities' sites. It is
shown that the total conductance can be found from an effective Schroedinger
equation with constant diagonal matrix elements in the Hamiltonian, where the
complex non-diagonal matrix elements are the amplitudes of a carrier hopping
between different impurities. It is explicitly demonstrated how the complex
phase leads to Aharonov-Bohm oscillations in the total conductance. Neglecting
the contribution of self-crossing resonant-percolation trajectories, one finds
that the inter-edge carrier transport is similar to propagation in
one-dimensional system with off-diagonal disorder. We demonstrated that each
Landau band has an extended state , while all other states are
localized. The localization length behaves as .Comment: RevTex 41 pages; 3 Postscript figure on request; Final version
accepted for publication in Phys. Rev. B. A new section added contained a
comparison with other method
Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
We study a one-dimensional anisotropic exclusion process describing particles
injected at the origin, moving to the right on a chain of sites and being
removed at the (right) boundary. We construct the steady state and compute the
density profile, exact expressions for all equal-time n-point density
correlation functions and the time-dependent two-point function in the steady
state as functions of the injection and absorption rates. We determine the
phase diagram of the model and compare our results with predictions from
dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P
vacua states in heavy ion collisions in presence of dissipation and noise
We have studied possible formation of vacua states in heavy ion
collisions. Random phases of the chiral fields were evolved in a finite
temperature potential, incorporating the breaking of symmetry. Initial
random phases very quickly settle into oscillation around the values dictated
by the potential. The simulation study indicate that an initial =0
state do not evolve into a 0 state. However, an initial
0 state, if formed in heavy ion collision, can survive, as a
coherent superposition of a number of modes.Comment: 6 pages, 6 figure
Formation of an Edge Striped Phase in Fractional Quantum Hall Systems
We have performed an exact diagonalization study of up to N=12 interacting
electrons on a disk at filling for both Coulomb and
short-range interaction for which Laughlin wave function is the exact solution.
For Coulomb interaction and we find persistent radial oscillations
in electron density, which are not captured by the Laughlin wave function. Our
results srongly suggest formation of a chiral edge striped phase in quantum
Hall systems. The amplitude of the charge density oscillations decays slowly,
perhaps as a square root of the distance from the edge; thus the spectrum of
edge excitations is likely to be affected.Comment: 4 pages, 3 Figs. include
Universal structure of the edge states of the fractional quantum Hall states
We present an effective theory for the bulk fractional quantum Hall states on
the Jain sequences on closed surfaces and show that it has a universal form
whose structure does not change from fraction to fraction. The structure of
this effective theory follows from the condition of global consistency of the
flux attachment transformation on closed surfaces. We derive the theory of the
edge states on a disk that follows naturally from this globally consistent
theory on a torus. We find that, for a fully polarized two-dimensional electron
gas, the edge states for all the Jain filling fractions have
only one propagating edge field that carries both energy and charge, and two
non-propagating edge fields of topological origin that are responsible for the
statistics of the excitations. Explicit results are derived for the electron
and quasiparticle operators and for their propagators at the edge. We show that
these operators create states with the correct charge and statistics. It is
found that the tunneling density of states for all the Jain states scales with
frequency as .Comment: 10 page
Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
We present an effective Chern-Simons theory for the bulk fully polarized
fractional quantum Hall (FQH) hierarchical states constructed as daughters of
general states of the Jain series, {\it i. e.} as FQH states of the
quasi-particles or quasi-holes of Jain states. We discuss the stability of
these new states and present two reasonable stability criteria. We discuss the
theory of their edge states which follows naturally from this bulk theory. We
construct the operators that create elementary excitations, and discuss the
scaling behavior of the tunneling conductance in different situations. Under
the assumption that the edge states of these fully polarized hierarchical
states are unreconstructed and unresolved, we find that the differential
conductance for tunneling of electrons from a Fermi liquid into {\em any}
hierarchical Jain FQH states has the scaling behavior with the
universal exponent , where is the filling fraction of the
hierarchical state. Finally, we explore alternative ways of constructing FQH
states with the same filling fractions as partially polarized states, and
conclude that this is not possible within our approach.Comment: 10 pages, 50 references, no figures; formerly known as "Composite
Fermions: The Next Generation(s)" (title changed by the PRB thought police).
This version has more references and a discussion of the stability of the new
states. Published version. One erroneous reference is correcte
A new approach to the ground state of quantum-Hall systems
I present variational solutions of the many-body Schr\"odinger equation for a
two-dimensional electron system in strong magnetic fields, which have, at
, the energy about 46% lower than the energy of the Laughlin liquid. At
, I obtain the energy, about 29% lower than was reported so far.Comment: ReVTeX, 5 pages with 3 figures included; some formulas [eqs.
(6)-(9)], one figure (fig 2), some new refs. and new results are adde
Tight-binding g-Factor Calculations of CdSe Nanostructures
The Lande g-factors for CdSe quantum dots and rods are investigated within
the framework of the semiempirical tight-binding method. We describe methods
for treating both the n-doped and neutral nanostructures, and then apply these
to a selection of nanocrystals of variable size and shape, focusing on
approximately spherical dots and rods of differing aspect ratio. For the
negatively charged n-doped systems, we observe that the g-factors for
near-spherical CdSe dots are approximately independent of size, but show strong
shape dependence as one axis of the quantum dot is extended to form rod-like
structures. In particular, there is a discontinuity in the magnitude of
g-factor and a transition from anisotropic to isotropic g-factor tensor at
aspect ratio ~1.3. For the neutral systems, we analyze the electron g-factor of
both the conduction and valence band electrons. We find that the behavior of
the electron g-factor in the neutral nanocrystals is generally similar to that
in the n-doped case, showing the same strong shape dependence and discontinuity
in magnitude and anisotropy. In smaller systems the g-factor value is dependent
on the details of the surface model. Comparison with recent measurements of
g-factors for CdSe nanocrystals suggests that the shape dependent transition
may be responsible for the observations of anomalous numbers of g-factors at
certain nanocrystal sizes.Comment: 15 pages, 6 figures. Fixed typos to match published versio
Holographic description of strongly correlated electrons in external magnetic fields
We study the Fermi level structure of (2+1)-dimensional strongly interacting
electron systems in external magnetic field using the AdS/CFT correspondence.
The gravity dual of a finite density fermion system is a Dirac field in the
background of the dyonic AdS-Reissner-Nordstrom black hole. In the probe limit
the magnetic system can be reduced to the non-magnetic one, with
Landau-quantized momenta and rescaled thermodynamical variables. We find that
at strong enough magnetic fields, the Fermi surface vanishes and the
quasiparticle is lost either through a crossover to conformal regime or through
a phase transition to an unstable Fermi surface. In the latter case, the
vanishing Fermi velocity at the critical magnetic field triggers the non-Fermi
liquid regime with unstable quasiparticles and a change in transport properties
of the system. We associate it with a metal-"strange metal" phase transition.
We compute the DC Hall and longitudinal conductivities using the
gravity-dressed fermion propagators. As expected, the Hall conductivity is
quantized according to integer Quantum Hall Effect (QHE) at weak magnetic
fields. At strong magnetic fields, new plateaus typical for the fractional QHE
appear. Our pattern closely resembles the experimental results on graphite
which are described using the fractional filling factor proposed by Halperin.Comment: 39 pages, 11 figures, Ch. 21, Lect. Notes Phys. "Strongly interacting
matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner,
A. Schmitt, H.-U. Yee. arXiv admin note: substantial text overlap with
arXiv:1011.405
Quantum Mechanics and Thermodynamics of Particles with Distance Dependent Statistics
The general notion of distance dependent statistics in anyon-like systems is
discussed. The two-body problem for such statistics is considered, the general
formula for the second virial coefficient is derived and it is shown that in
the limiting cases it reproduces the known results for ideal anyons.Comment: 9 pages, LATEX Kiev Institute for Theoretical Physics preprint
ITP-93-5E, January 199
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