54,770 research outputs found
The Lanczos algorithm with selective orthogonalization
A new stable and efficient implementation of the Lanczos algorithm is presented. The algorithm is a powerful method for finding a few eigenvalues and eigenvectors at one or both ends of the spectrum of a symmetric matrix A. The algorithm is particularly effective if A is large and sparse in that the only way in which A enters the calculation is through a subroutine which computes Av for any vector v. Thus the user is free to take advantage of any sparsity structure in A and A need not even be represented as a matrix et al
Composite fermions in bands with N-fold rotational symmetry
We study the effect of band anisotropy with discrete rotational symmetry
(where ) in the quantum Hall regime of two-dimensional electron
systems. We focus on the composite Fermi liquid (CFL) at half filling of the
lowest Landau level. We find that the magnitude of anisotropy transferred to
the composite fermions decreases very rapidly with . We demonstrate this by
performing density matrix normalization group calculations on the CFL, and
comparing the anisotropy of the composite fermion Fermi contour with that of
the (non-interacting) electron Fermi contour at zero magnetic field. We also
show that the effective interaction between the electrons after projecting into
a single Landau level is much less anisotropic than the band, a fact which does
not depend on filling and thus has implications for other quantum Hall states
as well. Our results confirm experimental observations on anisotropic bands
with warped Fermi contours, where the only detectable effect on the composite
Fermi contour is an elliptical distortion ().Comment: 6 pages + bibliography, 5 figure
Connection between Fermi contours of zero-field electrons and composite fermions in two-dimensional systems
We investigate the relation between the Fermi sea (FS) of zero-field carriers
in two-dimensional systems and the FS of the corresponding composite fermions
which emerge in a high magnetic field at filling , as the
kinetic energy dispersion is varied. We study cases both with and without
rotational symmetry, and find that there is generally no straightforward
relation between the geometric shapes and topologies of the two FSs. In
particular, we show analytically that the composite Fermi liquid (CFL) is
completely insensitive to a wide range of changes to the zero-field dispersion
which preserve rotational symmetry, including ones that break the zero-field FS
into multiple disconnected pieces. In the absence of rotational symmetry, we
show that the notion of `valley pseudospin' in many-valley systems is
generically not transferred to the CFL, in agreement with experimental
observations. We also discuss how a rotationally symmetric band structure can
induce a reordering of the Landau levels, opening interesting possibilities of
observing higher-Landau-level physics in the high-field regime.Comment: 7 pages + references, 7 figures. Added many-body DMRG calculatio
Surface-slip equations for multicomponent nonequilibrium air flow
Equations are presented for the surface-slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds number, high-altitude flight regime of a space vehicle. The equations are obtained from closed form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities were obtained in a form which can be employed in flowfield computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate, species-concentration boundary condition for a multicomponent mixture in absence of slip
- …