1,647 research outputs found
Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences
Compressive sensing (CS) has recently emerged as a framework for efficiently
capturing signals that are sparse or compressible in an appropriate basis.
While often motivated as an alternative to Nyquist-rate sampling, there remains
a gap between the discrete, finite-dimensional CS framework and the problem of
acquiring a continuous-time signal. In this paper, we attempt to bridge this
gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a
collection of functions that trace back to the seminal work by Slepian, Landau,
and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's
form a highly efficient basis for sampled bandlimited functions; by modulating
and merging DPSS bases, we obtain a dictionary that offers high-quality sparse
approximations for most sampled multiband signals. This multiband modulated
DPSS dictionary can be readily incorporated into the CS framework. We provide
theoretical guarantees and practical insight into the use of this dictionary
for recovery of sampled multiband signals from compressive measurements
Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models
We analyze the point-group symmetries of generic multiband tight-binding
models with respect to the transformation properties of the effective
interactions. While the vertex functions in the orbital language may transform
non-trivially under point-group operations, their point-group behavior in the
band language can be simplified by choosing a suitable Bloch basis.We first
give two analytically accessible examples. Then we show that, for a large class
of models, a natural Bloch basis exists, in which the vertex functions in the
band language transform trivially under all point-group operations. As a
consequence, the point-group symmetries can be used to reduce the computational
effort in perturbative many-particle approaches such as the functional
renormalization group.Comment: revised version: 38 pages, 4 figure
Theory of Raman scattering from Leggett's collective mode in a multiband superconductor: Application to MgB
In 1966 Leggett used a two-band superconductor to show that a new collective
mode could exist at low temperatures, corresponding to a counter-flow of the
superconducting condensates in each band. Here, the theory of electronic Raman
scattering in a superconductor by Klein and Dierker (1984) is extended to a
multiband superconductor. Raman scattering creates particle/hole pairs. In the
relevant \ symmetry, the attraction that produces pairing necessarily
couples excitations of superconducting pairs to these p/h excitations. In the
Appendix it is shown that for zero wave vector transfer this coupling
modifies the Raman response and makes the long-range Coulomb correction null.
The 2-band result is applied to MgB where this coupling activates
Leggett's collective mode. His simple limiting case is obtained when the
interband attractive potential is decreased to a value well below that given by
LDA theory. The peak from Leggett's mode is studied as the potential is
increased through the theoretical value: With realistic MgB\ parameters,
the peak broadens through decay into the continuum above the smaller (
band) superconducting gap. Finite effects are also taken into account,
yielding a Raman peak that agrees well in energy with the experimental result
by Blumberg \textit{et el.} (2007). This approach is also applied to the ,
2-band model of the Fe-pnictides considered by Chubukov \textit{et al.}(2009).Comment: 10 pages, 3 figures. To appear in Physical Review
Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model
We perform an instability analysis of the Emery three-band model at hole
doping and weak coupling within a channel-decomposed functional renormalization
group flow proposed in Phys. Rev. B 79, 195125 (2009). In our approach,
momentum dependences are taken into account with improved precision compared to
previous studies of related models. Around a generic parameter set, we find a
strong competition of antiferromagnetic and d-wave Cooper instabilities with a
smooth behavior under a variation of doping and additional hopping parameters.
For increasingly incommensurate ordering tendencies in the magnetic channel,
the d-wave pairing gap is deformed at its maxima. Comparing our results for the
Emery model to those obtained for the two-dimensional one-band Hubbard model
with effective parameters, we find that, despite considerable qualitative
agreement, multi-orbital effects have a significant impact on a quantitative
level.Comment: revised version: 22 pages, 11 figure
Spin dynamics of low-dimensional excitons due to acoustic phonons
We investigate the spin dynamics of excitons interacting with acoustic
phonons in quantum wells, quantum wires and quantum disks by employing a
multiband model based on the Luttinger Hamiltonian. We also use the
Bir-Pikus Hamiltonian to model the coupling of excitons to both longitudinal
acoustic phonons and transverse acoustic phonons, thereby providing us with a
realistic framework in which to determine details of the spin dynamics of
excitons. We use a fractional dimensional formulation to model the excitonic
wavefunctions and we demonstrate explicitly the decrease of spin relaxation
time with dimensionality. Our numerical results are consistent with
experimental results of spin relaxation times for various configurations of the
GaAs/AlGaAs material system. We find that longitudinal and
transverse acoustic phonons are equally significant in processes of exciton
spin relaxations involving acoustic phonons.Comment: 24 pages, 3 figure
Theory of nonequilibrium dynamics of multiband superconductors
We study the nonequilibrium dynamics of multiband BCS superconductors
subjected to ultrashort pump pulses. Using density-matrix theory, the time
evolution of the Bogoliubov quasiparticle densities and the superconducting
order parameters are computed as a function of pump pulse frequency, duration,
and intensity. Focusing on two-band superconductors, we consider two different
model systems. The first one, relevant for iron-based superconductors,
describes two-band superconductors with a repulsive interband interaction
which is much larger than the intraband pairing terms. The second
model, relevant for MgB, deals with the opposite limit where the intraband
interactions are dominant and the interband pair scattering is weak
but attractive. For ultrashort pump pulses, both of these models exhibit a
nonadiabatic behavior which is characterized by oscillations of the
superconducting order parameters. We find that for nonvanishing , the
superconducting gap on each band exhibits two oscillatory frequencies which are
determined by the long-time asymptotic values of the gaps. The relative
strength of these two frequency components depends sensitively on the magnitude
of the interband interaction .Comment: 6 pages, 3 figure
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