449 research outputs found
Strongly correlated phases in rapidly rotating Bose gases
We consider a system of trapped spinless bosons interacting with a repulsive
potential and subject to rotation. In the limit of rapid rotation and small
scattering length, we rigorously show that the ground state energy converges to
that of a simplified model Hamiltonian with contact interaction projected onto
the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue
of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles,
we also prove convergence of states; in particular, in a certain regime we show
convergence towards the bosonic Laughlin wavefunction. This is the first
rigorous justification of the effective FQHE Hamiltonian for rapidly rotating
Bose gases. We review previous results on this effective Hamiltonian and
outline open problems.Comment: AMSLaTeX, 23 page
The excitation spectrum for weakly interacting bosons in a trap
We investigate the low-energy excitation spectrum of a Bose gas confined in a
trap, with weak long-range repulsive interactions. In particular, we prove that
the spectrum can be described in terms of the eigenvalues of an effective
one-particle operator, as predicted by the Bogoliubov approximation.Comment: LaTeX, 32 page
The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating
Bose-Einstein condensate on the unit disc in two dimensions. Writing the
coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps
\to 0 with the angular velocity proportional to
(\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0
(\eps^2|\log\eps|)^{-1} and then a minimizer of
the GP energy functional has no zeros in an annulus at the boundary of the disc
that contains the bulk of the mass. The vorticity resides in a complementary
`hole' around the center where the density is vanishingly small. Moreover, we
prove a lower bound to the ground state energy that matches, up to small
errors, the upper bound obtained from an optimal giant vortex trial function,
and also that the winding number of a GP minimizer around the disc is in accord
with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To
be published in Commun. Math. Phy
Anisotropic transport in unidirectional lateral superlattice around half-filling of the second Landau level
We have observed marked transport anisotropy in short period (a=92 nm)
unidirectional lateral superlattices around filling factors nu=5/2 and 7/2:
magnetoresistance shows a sharp peak for current along the modulation grating
while a dip appears for current across the grating. By altering the ratio a/l
(with l=sqrt{hbar/eB_perp} the magnetic length) via changing the electron
density n_e, it is shown that the nu=5/2 anisotropic features appear in the
range 6.6 alt a/l alt 7.2 varying their intensities, becoming most conspicuous
at a/l simeq 6.7. The peak/dip broadens with temperature roughly preserving its
height/depth up to 250 mK. Tilt experiments reveal that the structures are
slightly enhanced by an in-plane magnetic field B_| perpendicular to the
grating but are almost completely destroyed by B_| parallel to the grating. The
observations suggest the stabilization of a unidirectional charge-density-wave
or stripe phase by weak external periodic modulation at the second Landau
level.Comment: REVTeX, 5 pages, 3 figures, Some minor revisions, Added notes and
reference
New insulating phases of two-dimensional electrons in high Landau levels: observation of sharp thresholds to conduction
The intriguing re-entrant integer quantized Hall states recently discovered
in high Landau levels of high-mobility 2D electron systems are found to exhibit
extremely non-linear transport. At small currents these states reflect
insulating behavior of the electrons in the uppermost Landau level. At larger
currents, however, a discontinuous and hysteretic transition to a conducting
state is observed. These phenomena, found only in very narrow magnetic field
ranges, are suggestive of the depinning of a charge density wave state, but
other explanations can also be constructed.Comment: 5 pages, 5 figure
Theory of the Quantum Hall Smectic Phase II: Microscopic Theory
We present a microscopic derivation of the hydrodynamic theory of the Quantum
Hall smectic or stripe phase of a two-dimensional electron gas in a large
magnetic field. The effective action of the low energy is derived here from a
microscopic picture by integrating out high energy excitations with a scale of
the order the cyclotron energy.The remaining low-energy theory can be expressed
in terms of two canonically conjugate sets of degrees of freedom: the
displacement field, that describes the fluctuations of the shapes of the
stripes, and the local charge fluctuations on each stripe.Comment: 20 pages, RevTex, 3 figures, second part of cond-mat/0105448 New and
improved Introduction. Final version as it will appear in Physical Review
A cluster theory for a Janus fluid
Recent Monte Carlo simulations on the Kern and Frenkel model of a Janus fluid
have revealed that in the vapour phase there is the formation of preferred
clusters made up of a well-defined number of particles: the micelles and the
vesicles. A cluster theory is developed to approximate the exact clustering
properties stemming from the simulations. It is shown that the theory is able
to reproduce the micellisation phenomenon.Comment: 27 pages, 8 figures, 6 table
The Effects of Disorder on the Quantum Hall State
A disorder-averaged Hartree-Fock treatment is used to compute the density of
single particle states for quantum Hall systems at filling factor . It
is found that transport and spin polarization experiments can be simultaneously
explained by a model of mostly short-range effective disorder. The slope of the
transport gap (due to quasiparticles) in parallel field emerges as a result of
the interplay between disorder-induced broadening and exchange, and has
implications for skyrmion localization.Comment: 4 pages, 3 eps figure
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