14,384 research outputs found
Interactions suppress Quasiparticle Tunneling at Hall Bar Constrictions
Tunneling of fractionally charged quasiparticles across a two-dimensional
electron system on a fractional quantum Hall plateau is expected to be strongly
enhanced at low temperatures. This theoretical prediction is at odds with
recent experimental studies of samples with weakly-pinched
quantum-point-contact constrictions, in which the opposite behavior is
observed. We argue here that this unexpected finding is a consequence of
electron-electron interactions near the point contact.Comment: 4 page
Asymptotically exact trial wave functions for yrast states of rotating Bose gases
We revisit the composite fermion (CF) construction of the lowest angular
momentum yrast states of rotating Bose gases with weak short range interaction.
For angular momenta at and below the single vortex, , the overlaps
between these trial wave functions and the corresponding exact solutions {\it
increase} with increasing system size and appear to approach unity in the
thermodynamic limit. In the special case , this remarkable behaviour was
previously observed numerically. Here we present methods to address this point
analytically, and find strongly suggestive evidence in favour of similar
behaviour for all . While not constituting a fully conclusive proof
of the converging overlaps, our results do demonstrate a striking similarity
between the analytic structure of the exact ground state wave functions at , and that of their CF counterparts. Results are given for two different
projection methods commonly used in the CF approach
Vortex Lattice Structure of Fulde-Ferrell-Larkin-Ovchinnikov Superconductors
In superconductors with singlet pairing, the inhomogeneous
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is expected to be stabilized by a
large Zeeman splitting. We develop an efficient method to evaluate the
Landau-Ginzburg free energies of FFLO-state vortex lattices and use it to
simplify the considerations that determine the optimal vortex configuration at
different points in the phasediagram. We demonstrate that the order parameter
spatial profile is completely determined, up to a uniform translation, by its
Landau level index n and the vortex Lattice structure and derive an explicit
expression for the order parameter spatial profile that can be used to
determine n from experimental data.Comment: 6 pages with one embedded color figure. Minor changes. Final version
as publishe
Edge State Tunneling in a Split Hall Bar Model
In this paper we introduce and study the correlation functions of a chiral
one-dimensional electron model intended to qualitatively represent narrow Hall
bars separated into left and right sections by a penetrable barrier. The model
has two parameters representing respectively interactions between top and
bottom edges of the Hall bar and interactions between the edges on opposite
sides of the barrier. We show that the scaling dimensions of tunneling
processes depend on the relative strengths of the interactions, with repulsive
interactions across the Hall bar tending to make breaks in the barrier
irrelevant. The model can be solved analytically and is characterized by a
difference between the dynamics of even and odd Fourier components. We address
its experimental relevance by comparing its predictions with those of a more
geometrically realistic model that must be solved numerically.Comment: 13 pages, including 4 figures,final version as publishe
Effective order strong stability preserving Runge–Kutta methods
We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of effective order methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods—like classical order five methods—require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge–Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice
Modulation Doping near Mott-Insulator Heterojunctions
We argue that interesting strongly correlated two-dimensional electron
systems can be created by modulation doping near a heterojunction between Mott
insulators. Because the dopant atoms are remote from the carrier system, the
electronic system will be weakly disordered. We argue that the competition
between different ordered states can be engineered by choosing appropriate
values for the dopant density and the setback distance of the doping layer. In
particular larger setback distances favor two-dimensional antiferromagnetism
over ferromagnetism. We estimate some key properties of modulation-doped Mott
insulator heterojunctions by combining insights from Hartree-Fock-Theory and
Dynamical-Mean-Field-Theory descriptions and discuss potentially attractive
material combinations.Comment: 9 pages, 9 figures, submitte
Quantitative Probe of Pairing Correlations in a Cold Fermionic Atom Gas
A quantitative measure of the pairing correlations present in a cold gas of
fermionic atoms can be obtained by studying the dependence of RF spectra on
hyperfine state populations. This proposal follows from a sum rule that relates
the total interaction energy of the gas to RF spectrum line positions. We argue
that this indicator of pairing correlations provides information comparable to
that available from the spin-susceptibility and NMR measurements common in
condensed-matter systems.Comment: 5 pages, 1 figur
Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
We consider a series of massive scaling limits m_1 -> infty, q -> 0, lim m_1
q = Lambda_{3} followed by m_4 -> infty, Lambda_{3} -> 0, lim m_4 Lambda_{3} =
(Lambda_2)^2 of the beta-deformed matrix model of Selberg type (N_c=2, N_f=4)
which reduce the number of flavours to N_f=3 and subsequently to N_f=2. This
keeps the other parameters of the model finite, which include n=N_L and
N=n+N_R, namely, the size of the matrix and the "filling fraction". Exploiting
the method developed before, we generate instanton expansion with finite g_s,
epsilon_{1,2} to check the Nekrasov coefficients (N_f =3,2 cases) to the lowest
order. The limiting expressions provide integral representation of irregular
conformal blocks which contains a 2d operator lim frac{1}{C(q)} : e^{(1/2)
\alpha_1 \phi(0)}: (int_0^q dz : e^{b_E phi(z)}:)^n : e^{(1/2) alpha_2 phi(q)}:
and is subsequently analytically continued.Comment: LaTeX, 21 pages; v2: a reference adde
Quantized Casimir Force
We investigate the Casimir effect between two-dimensional electron systems
driven to the quantum Hall regime by a strong perpendicular magnetic field. In
the large separation (d) limit where retardation effects are essential we find
i) that the Casimir force is quantized in units of 3\hbar c \alpha^2/(8\pi^2
d^4), and ii) that the force is repulsive for mirrors with same type of
carrier, and attractive for mirrors with opposite types of carrier. The sign of
the Casimir force is therefore electrically tunable in ambipolar materials like
graphene. The Casimir force is suppressed when one mirror is a charge-neutral
graphene system in a filling factor \nu=0 quantum Hall state.Comment: 4.2 page
Three-point density correlation functions in the fractional quantum Hall regime
In this paper we consider the three-particle density correlation function for
a fractional quantum Hall liquid. The study of this object is motivated by
recent experimental studies of fractional quantum Hall systems using inelastic
light scattering and phonon absorption techniques. Symmetry properties of the
correlation function are noted. An exact sum-rule is derived which this
quantity must obey. This sum-rule is used to assess the convolution
approximation that has been used to estimate the matrix elements for such
experiments. PACS Numbers: 73.40.Hm, 73.20.Mf, 72.10.DiComment: 12 pages + 1 (PS) figur
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