1,090 research outputs found
Ensemble Density Functional Theory for Inhomogeneous Fractional Quantum Hall Systems
The fractional quantum Hall effect (FQHE) occurs at certain magnetic field
strengths B*(n) in a two-dimensional electron gas of density n at strong
magnetic fields perpendicular to the plane of the electron gas. At these
magnetic fields strengths, the system is incompressible, i.e., there is a
finite cost in energy for creating charge density fluctuations in the bulk,
while the boundary of the electron gas has gapless modes of density waves. The
bulk energy gap arises because of the strong electron-electron interactions.
While there are very good models for infinite homogeneous systems and for the
gapless excitations of the boundary of the electron gas, computational methods
to accurately model finite, inhomogeneous systems with more then about ten
electrons have not been available until very recently. We will here review an
ensemble density functional approach to studying the ground state of large
inhomogeneous spin polarized FQHE systems.Comment: 23 pages (revtex), 6 Postscript figures. To be published in Int. J.
Quant. Chem. (invited talk at the 1996 Sanibel Symposium
Instability and wavelength selection during step flow growth of metal surfaces vicinal to fcc(001)
We study the onset and development of ledge instabilities during growth of
vicinal metal surfaces using kinetic Monte Carlo simulations. We observe the
formation of periodic patterns at [110] close packed step edges on surfaces
vicinal to fcc(001) under realistic molecular beam epitaxy conditions. The
corresponding wavelength and its temperature dependence are studied by
monitoring the autocorrelation function for step edge position. Simulations
suggest that the ledge instability on fcc(1,1,m) vicinal surfaces is controlled
by the strong kink Ehrlich-Schwoebel barrier, with the wavelength determined by
dimer nucleation at the step edge. Our results are in agreement with recent
continuum theoretical predictions, and experiments on Cu(1,1,17) vicinal
surfaces.Comment: 4 pages, 4 figures, RevTe
Lorentz shear modulus of fractional quantum Hall states
We show that the Lorentz shear modulus of macroscopically homogeneous
electronic states in the lowest Landau level is proportional to the bulk
modulus of an equivalent system of interacting classical particles in the
thermodynamic limit. Making use of this correspondence we calculate the Lorentz
shear modulus of Laughlin's fractional quantum Hall states at filling factor
( an odd integer) and find that it is equal to ,
where is the density of particles and the sign depends on the direction of
magnetic field. This is in agreement with the recent result obtained by Read in
arXiv:0805.2507 and corrects our previous result published in Phys. Rev. B {\bf
76}, 161305 (R) (2007).Comment: 8 pages, 3 figure
Morphology of ledge patterns during step flow growth of metal surfaces vicinal to fcc(001)
The morphological development of step edge patterns in the presence of
meandering instability during step flow growth is studied by simulations and
numerical integration of a continuum model. It is demonstrated that the kink
Ehrlich-Schwoebel barrier responsible for the instability leads to an invariant
shape of the step profiles. The step morphologies change with increasing
coverage from a somewhat triangular shape to a more flat, invariant steady
state form. The average pattern shape extracted from the simulations is shown
to be in good agreement with that obtained from numerical integration of the
continuum theory.Comment: 4 pages, 4 figures, RevTeX 3, submitted to Phys. Rev.
Conformal dimension and random groups
We give a lower and an upper bound for the conformal dimension of the
boundaries of certain small cancellation groups. We apply these bounds to the
few relator and density models for random groups. This gives generic bounds of
the following form, where is the relator length, going to infinity.
(a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model,
and
(b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at
densities .
In particular, for the density model at densities , as the relator
length goes to infinity, the random groups will pass through infinitely
many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to
density < 1/16. Many minor improvements. To appear in GAF
Vantaan toimeentulotuen palveluyhteistyökokeilu : Asiakkaiden ja työntekijöiden kokemuksia Kelan ja sosiaalitoimen palveluyhteistyöstä
Spin-ensemble density-functional theory for inhomogeneous quantum Hall systems
We have developed an ensemble density-functional theory that includes spin degrees of freedom for non-uniform quantum Hall systems. We have applied this theory using a local-spin-density approximation to study the edge reconstruction of parabolically confined quantum dots. For a Zeeman splitting below a certain critical value, the edge of a completely polarized maximum density droplet reconstructs into a spin-unpolarized structure. For larger Zeeman splittings, the edge remains polarized and develops an exchange hole
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
Electric-Field Breakdown of Absolute Negative Conductivity and Supersonic Streams in Two-Dimensional Electron Systems with Zero Resistance/Conductance States
We calculate the current-voltage characteristic of a two-dimensional electron
system (2DES) subjected to a magnetic field at strong electric fields. The
interaction of electrons with piezoelectric acoustic phonons is considered as a
major scattering mechanism governing the current-voltage characteristic. It is
shown that at a sufficiently strong electric field corresponding to the Hall
drift velocity exceeding the velocity of sound, the dissipative current
exhibits an overshoot. The overshoot of the dissipative current can result in a
breakdown of the absolute negative conductivity caused by microwave irradiation
and, therefore, substantially effect the formation of the domain structures
with the zero-resistance and zero-conductance states and supersonic electron
streams.Comment: 5 pages, 4 figure
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