7,585 research outputs found
Hear the Sound of Weyl Fermions
Quasiparticles and collective modes are two fundamental aspects that
characterize a quantum matter in addition to its ground state features. For
example, the low energy physics for Fermi liquid phase in He-III was featured
not only by Fermionic quasiparticles near the chemical potential but also by
fruitful collective modes in the long-wave limit, including several different
sound waves that can propagate through it under different circumstances. On the
other hand, it is very difficult for sound waves to be carried by the electron
liquid in the ordinary metals, due to the fact that long-range Coulomb
interaction among electrons will generate plasmon gap for ordinary electron
density fluctuation and thus prohibits the propagation of sound waves through
it. In the present paper, we propose a unique type of acoustic collective modes
in Weyl semimetals under the magnetic field called chiral zero sound. The
chiral zero sound can be stabilized under so-called "chiral limit", where the
intra-valley scattering time is much shorter than the inter-valley one, and
only propagates along an external magnetic field for Weyl semimetals with
multiple-pairs of Weyl points. The sound velocity of the chiral zero sound is
proportional to the field strength in the weak field limit, whereas it
oscillates dramatically in the strong field limit, generating an entirely new
mechanism for quantum oscillations through the dynamics of neutral bosonic
excitation, which may manifest itself in the thermal conductivity measurements
under magnetic field.Comment: 9+16 pages, 2+0 figures, a new appendix added, accepted in PR
Test for bandedness of high-dimensional covariance matrices and bandwidth estimation
Motivated by the latest effort to employ banded matrices to estimate a
high-dimensional covariance , we propose a test for being
banded with possible diverging bandwidth. The test is adaptive to the "large
, small " situations without assuming a specific parametric distribution
for the data. We also formulate a consistent estimator for the bandwidth of a
banded high-dimensional covariance matrix. The properties of the test and the
bandwidth estimator are investigated by theoretical evaluations and simulation
studies, as well as an empirical analysis on a protein mass spectroscopy data.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1002 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Two sample tests for high-dimensional covariance matrices
We propose two tests for the equality of covariance matrices between two
high-dimensional populations. One test is on the whole variance--covariance
matrices, and the other is on off-diagonal sub-matrices, which define the
covariance between two nonoverlapping segments of the high-dimensional random
vectors. The tests are applicable (i) when the data dimension is much larger
than the sample sizes, namely the "large , small " situations and (ii)
without assuming parametric distributions for the two populations. These two
aspects surpass the capability of the conventional likelihood ratio test. The
proposed tests can be used to test on covariances associated with gene ontology
terms.Comment: Published in at http://dx.doi.org/10.1214/12-AOS993 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
On the approximate maximum likelihood estimation for diffusion processes
The transition density of a diffusion process does not admit an explicit
expression in general, which prevents the full maximum likelihood estimation
(MLE) based on discretely observed sample paths. A\"{\i}t-Sahalia [J. Finance
54 (1999) 1361--1395; Econometrica 70 (2002) 223--262] proposed asymptotic
expansions to the transition densities of diffusion processes, which lead to an
approximate maximum likelihood estimation (AMLE) for parameters. Built on
A\"{\i}t-Sahalia's [Econometrica 70 (2002) 223--262; Ann. Statist. 36 (2008)
906--937] proposal and analysis on the AMLE, we establish the consistency and
convergence rate of the AMLE, which reveal the roles played by the number of
terms used in the asymptotic density expansions and the sampling interval
between successive observations. We find conditions under which the AMLE has
the same asymptotic distribution as that of the full MLE. A first order
approximation to the Fisher information matrix is proposed.Comment: Published in at http://dx.doi.org/10.1214/11-AOS922 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Tests for High Dimensional Generalized Linear Models
We consider testing regression coefficients in high dimensional generalized
linear models. An investigation of the test of Goeman et al. (2011) is
conducted, which reveals that if the inverse of the link function is unbounded,
the high dimensionality in the covariates can impose adverse impacts on the
power of the test. We propose a test formation which can avoid the adverse
impact of the high dimensionality. When the inverse of the link function is
bounded such as the logistic or probit regression, the proposed test is as good
as Goeman et al. (2011)'s test. The proposed tests provide p-values for testing
significance for gene-sets as demonstrated in a case study on an acute
lymphoblastic leukemia dataset.Comment: The research paper was stole by someone last November and illegally
submitted to arXiv by a person named gong zi jiang nan. We have asked arXiv
to withdraw the unfinished paper [arXiv:1311.4043] and it was removed last
December. We have collected enough evidences to identify the person and
Peking University has begun to investigate the plagiarize
Thermal effects on bipartite and multipartite correlations in fiber coupled cavity arrays
We investigate the thermal influence of fibers on the dynamics of bipartite
and multipartite correlations in fiber coupled cavity arrays where each cavity
is resonantly coupled to a two-level atom. The atom-cavity systems connected by
fibers can be considered as polaritonic qubits. We first derive a master
equation to describe the evolution of the atom-cavity systems. The bipartite
(multipartite) correlations is measured by concurrence and discord (spin
squeezing). Then, we solve the master equation numerically and study the
thermal effects on the concurrence, discord, and spin squeezing of qubits. On
the one hand, at zero temperature, there are steady-state bipartite and
multipartite correlations. One the other hand, the thermal fluctuations of a
fiber may blockade the generation of entanglement of two qubits connected
directly by the fiber while the discord can be generated and stored for a long
time. This thermal-induced blockade effects of bipartite correlations may be
useful for quantum information processing. The bipartite correlations of a
longer chain of qubits is more robust than a shorter one in the presence of
thermal fluctuations
A goodness-of-fit test for parametric and semi-parametric models in multiresponse regression
We propose an empirical likelihood test that is able to test the goodness of
fit of a class of parametric and semi-parametric multiresponse regression
models. The class includes as special cases fully parametric models;
semi-parametric models, like the multiindex and the partially linear models;
and models with shape constraints. Another feature of the test is that it
allows both the response variable and the covariate be multivariate, which
means that multiple regression curves can be tested simultaneously. The test
also allows the presence of infinite-dimensional nuisance functions in the
model to be tested. It is shown that the empirical likelihood test statistic is
asymptotically normally distributed under certain mild conditions and permits a
wild bootstrap calibration. Despite the large size of the class of models to be
considered, the empirical likelihood test enjoys good power properties against
departures from a hypothesized model within the class.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ208 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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