1,803 research outputs found
Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness
The activation gaps for fractional quantum Hall states at filling fractions
are computed for heterojunction, square quantum well, as well as
parabolic quantum well geometries, using an interaction potential calculated
from a self-consistent electronic structure calculation in the local density
approximation. The finite thickness is estimated to make 30% correction
to the gap in the heterojunction geometry for typical parameters, which
accounts for roughly half of the discrepancy between the experiment and
theoretical gaps computed for a pure two dimensional system. Certain model
interactions are also considered. It is found that the activation energies
behave qualitatively differently depending on whether the interaction is of
longer or shorter range than the Coulomb interaction; there are indications
that fractional Hall states close to the Fermi sea are destabilized for the
latter.Comment: 32 pages, 13 figure
Composite fermion state of spin-orbit coupled bosons
We consider spinor Bose gas with the isotropic Rashba spin-orbit coupling in
2D. We argue that at low density its groundstate is a composite fermion state
with a Chern-Simons gauge field and filling factor one. The chemical potential
of such a state scales with the density as \mu \propto n^{3/2}. This is a lower
energy per particle than \mu \propto n for the earlier suggested groundstate
candidates: a condensate with broken time-reversal symmetry and a spin density
wave state.Comment: 15 pages, 7 figures, Revte
Segregation, precipitation, and \alpha-\alpha' phase separation in Fe-Cr alloys: a multi-scale modelling approach
Segregation, precipitation, and phase separation in Fe-Cr systems is
investigated. Monte Carlo simulations using semiempirical interatomic
potential, first-principles total energy calculations, and experimental
spectroscopy are used. In order to obtain a general picture of the relation of
the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and
interface regions several complementary methods has to be used. Using Exact
Muffin-Tin Orbitals method the effective chemical potential as a function of Cr
content (0-15 at.% Cr) is calculated for a surface, second atomic layer and
bulk. At ~10 at.% Cr in the alloy the reversal of the driving force of a Cr
atom to occupy either bulk or surface sites is obtained. The Cr containing
surfaces are expected when the Cr content exceeds ~10 at.%. The second atomic
layer forms about 0.3 eV barrier for the migration of Cr atoms between bulk and
surface atomic layer. To get information on Fe-Cr in larger scales we use
semiempirical methods. Using combined Monte Carlo molecular dynamics
simulations, based on semiempirical potential, the precipitation of Cr into
isolated pockets in bulk Fe-Cr and the upper limit of the solubility of Cr into
Fe layers in Fe/Cr layer system is studied. The theoretical predictions are
tested using spectroscopic measurements. Hard X-ray photoelectron spectroscopy
and Auger electron spectroscopy investigations were carried out to explore Cr
segregation and precipitation in Fe/Cr double layer and Fe_0.95Cr_0.05 and
Fe_0.85Cr_0.15 alloys. Initial oxidation of Fe-Cr was investigated
experimentally at 10^-8 Torr pressure of the spectrometers showing intense
Cr_2O_3 signal. Cr segregation and the formation of Cr rich precipitates were
traced by analysing the experimental spectral intensities with respect to
annealing time, Cr content, and kinetic energy of the exited electron.Comment: 16 pages, 14 figures, 52 reference
The Atomic Slide Puzzle: Self-Diffusion of an Impure Atom
In a series of recent papers van Gastel et al have presented first
experimental evidence that impure, Indium atoms, embedded into the first layer
of a Cu(001) surface, are not localized within the close-packed surface layers
but make concerted, long excursions visualized in a series of STM images. Such
excursions occur due to continuous reshuffling of the surface following the
position exchanges of both impure and host atoms with the naturally occuring
surface vacancies. Van Gastel et al have also formulated an original
lattice-gas type model with asymmetric exchange probabilities, whose numerical
solution is in a good agreement with the experimental data. In this paper we
propose an exact lattice solution of several versions of this model.Comment: Latex, 4 pages, 2 figures, to appear in Phys. Rev. E (RC
Universal Equilibrium Currents in the Quantum Hall Fluid
The equilibrium current distribution in a quantum Hall fluid that is
subjected to a slowly varying confining potential is shown to generally consist
of strips or channels of current, which alternate in direction, and which have
universal integrated strengths. A measurement of these currents would yield
direct independent measurements of the proper quasiparticle and quasihole
energies in the fractional quantum Hall states.Comment: 4 pages, Revte
Integral and fractional Quantum Hall Ising ferromagnets
We compare quantum Hall systems at filling factor 2 to those at filling
factors 2/3 and 2/5, corresponding to the exact filling of two lowest electron
or composite fermion (CF) Landau levels. The two fractional states are examples
of CF liquids with spin dynamics. There is a close analogy between the
ferromagnetic (spin polarization P=1) and paramagnetic (P=0) incompressible
ground states that occur in all three systems in the limits of large and small
Zeeman spin splitting. However, the excitation spectra are different. At
filling factor 2, we find spin domains at half-polarization (P=1/2), while
antiferromagnetic order seems most favorable in the CF systems. The transition
between P=0 and 1, as seen when e.g. the magnetic field is tilted, is also
studied by exact diagonalization in toroidal and spherical geometries. The
essential role of an effective CF-CF interaction is discussed, and the
experimentally observed incompresible half-polarized state is found in some
models
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
This paper is devoted to a deeper understanding of the heat flow and to the
refinement of calculus tools on metric measure spaces (X,d,m). Our main results
are:
- A general study of the relations between the Hopf-Lax semigroup and
Hamilton-Jacobi equation in metric spaces (X,d).
- The equivalence of the heat flow in L^2(X,m) generated by a suitable
Dirichlet energy and the Wasserstein gradient flow of the relative entropy
functional in the space of probability measures P(X).
- The proof of density in energy of Lipschitz functions in the Sobolev space
W^{1,2}(X,d,m).
- A fine and very general analysis of the differentiability properties of a
large class of Kantorovich potentials, in connection with the optimal transport
problem.
Our results apply in particular to spaces satisfying Ricci curvature bounds
in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the
doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4,
Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop.
4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6
simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients,
still equivalent to all other ones, has been propose
Quasiparticles and excitons for the Pfaffian quantum Hall state
We propose trial wave functions for quasiparticle and exciton excitations of
the Moore-Read Pfaffian fractional quantum Hall states, both for bosons and for
fermions, and study these numerically. Our construction of trial wave functions
employs a picture of the bosonic Moore-Read state as a symmetrized double layer
composite fermion state. We obtain the number of independent angular momentum
multiplets of quasiparticle and exciton trial states for systems of up to 20
electrons. We find that the counting for quasielectrons at large angular
momentum on the sphere matches that expected from the CFT which describes the
Moore-Read state's boundary theory. In particular, the counting for
quasielectrons is the same as for quasiholes, in accordance with the idea that
the CFT describing both sides of the FQH plateau should be the same. We also
show that our trial wave functions have good overlaps with exact wave functions
obtained using various interactions, including second Landau level Coulomb
interactions and the 3-body delta interaction for which the Pfaffian states and
their quasiholes are exact ground states. We discuss how these results relate
to recent work by Sreejith et al. on a similar set of trial wave functions for
excitations over the Pfaffian state as well as to earlier work by Hansson et
al., which has produced trial wave functions for quasiparticles based on
conformal field theory methods and by Bernevig and Haldane, which produced
trial wave functions based on clustering properties and `squeezing'.Comment: 22 pages, 18 figure
Maximum-entropy theory of steady-state quantum transport
We develop a theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of nonequilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the nonequilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely used scattering-state occupation schemes at the level of the self-consistent single-particle approximation. The latter schemes are shown not to maximize the entropy, except in certain limits
Island diffusion on metal fcc(100) surfaces
We present Monte Carlo simulations for the size and temperature dependence of
the diffusion coefficient of adatom islands on the Cu(100) surface. We show
that the scaling exponent for the size dependence is not a constant but a
decreasing function of the island size and approaches unity for very large
islands. This is due to a crossover from periphery dominated mass transport to
a regime where vacancies diffuse inside the island. The effective scaling
exponents are in good agreement with theory and experiments.Comment: 13 pages, 2 figures, to be published in Phys. Rev. Let
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