14,587 research outputs found
Relative Severi inequality for fibrations of maximal Albanese dimension over curves
Let be a relatively minimal fibration of maximal Albanese
dimension from a variety of dimension to a curve defined over
an algebraically closed field of characteristic zero. We prove that , which was conjectured by Barja in [2]. Via the strategy
outlined in [5], it also leads to a new proof of the Severi inequality for
varieties of maximal Albanese dimension. Moreover, when the equality holds and
, we prove that the general fiber of has to satisfy the
Severi equality that . We also prove
some sharper results of the same type under extra assumptions.Comment: Comments are welcom
Deforming black holes with even multipolar differential rotation boundary
Motivated by the novel asymptotically global AdS solutions with deforming
horizon in [JHEP {\bf 1802}, 060 (2018)], we analyze the boundary metric with
even multipolar differential rotation and numerically construct a family of
deforming solutions with quadrupolar differential rotation boundary, including
two classes of solutions: solitons and black holes. In contrast to solutions
with dipolar differential rotation boundary, we find that even though the norm
of Killing vector becomes spacelike for certain regions of polar
angle when , solitons and black holes with quadrupolar
differential rotation still exist and do not develop hair due to superradiance.
Moreover, at the same temperature, the horizonal deformation of quadrupolar
rotation is smaller than that of dipolar rotation. Furthermore, we also study
the entropy and quasinormal modes of the solutions, which have the analogous
properties to that of dipolar rotation.Comment: 18 pages, 21 figure
Dynamical Mean Field Theory for the Bose-Hubbard Model
The dynamical mean field theory (DMFT), which is successful in the study of
strongly correlated fermions, was recently extended to boson systems [Phys.
Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT
to study the Bose-Hubbard model which describes on-site interacting bosons in a
lattice. Using exact diagonalization as the impurity solver, we get the DMFT
solutions for the Green's function, the occupation density, as well as the
condensate fraction on a Bethe lattice. Various phases are identified: the Mott
insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At
finite temperatures, we obtain the crossover between the Mott-like regime and
the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams
on the plane and on the plane are
produced ( is the scaled hopping amplitude). We compare our results
with the previous ones, and discuss the implication of these results to
experiments.Comment: 11 pages, 8 figure
Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems
Hybrid massive MIMO structures with lower hardware complexity and power
consumption have been considered as a potential candidate for millimeter wave
(mmWave) communications. Channel covariance information can be used for
designing transmitter precoders, receiver combiners, channel estimators, etc.
However, hybrid structures allow only a lower-dimensional signal to be
observed, which adds difficulties for channel covariance matrix estimation. In
this paper, we formulate the channel covariance estimation as a structured
low-rank matrix sensing problem via Kronecker product expansion and use a
low-complexity algorithm to solve this problem. Numerical results with uniform
linear arrays (ULA) and uniform squared planar arrays (USPA) are provided to
demonstrate the effectiveness of our proposed method
Matrix Completion-Based Channel Estimation for MmWave Communication Systems With Array-Inherent Impairments
Hybrid massive MIMO structures with reduced hardware complexity and power
consumption have been widely studied as a potential candidate for millimeter
wave (mmWave) communications. Channel estimators that require knowledge of the
array response, such as those using compressive sensing (CS) methods, may
suffer from performance degradation when array-inherent impairments bring
unknown phase errors and gain errors to the antenna elements. In this paper, we
design matrix completion (MC)-based channel estimation schemes which are robust
against the array-inherent impairments. We first design an open-loop training
scheme that can sample entries from the effective channel matrix randomly and
is compatible with the phase shifter-based hybrid system. Leveraging the
low-rank property of the effective channel matrix, we then design a channel
estimator based on the generalized conditional gradient (GCG) framework and the
alternating minimization (AltMin) approach. The resulting estimator is immune
to array-inherent impairments and can be implemented to systems with any array
shapes for its independence of the array response. In addition, we extend our
design to sample a transformed channel matrix following the concept of
inductive matrix completion (IMC), which can be solved efficiently using our
proposed estimator and achieve similar performance with a lower requirement of
the dynamic range of the transmission power per antenna. Numerical results
demonstrate the advantages of our proposed MC-based channel estimators in terms
of estimation performance, computational complexity and robustness against
array-inherent impairments over the orthogonal matching pursuit (OMP)-based CS
channel estimator.Comment: This work has been submitted to the IEEE for possible publication.
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