1,842 research outputs found
Tensor models and hierarchy of n-ary algebras
Tensor models are generalization of matrix models, and are studied as models
of quantum gravity. It is shown that the symmetry of the rank-three tensor
models is generated by a hierarchy of n-ary algebras starting from the usual
commutator, and the 3-ary algebra symmetry reported in the previous paper is
just a single sector of the whole structure. The condition for the Leibnitz
rules of the n-ary algebras is discussed from the perspective of the invariance
of the underlying algebra under the n-ary transformations. It is shown that the
n-ary transformations which keep the underlying algebraic structure invariant
form closed finite n-ary Lie subalgebras. It is also shown that, in physical
settings, the 3-ary transformation practically generates only local
infinitesimal symmetry transformations, and the other more non-local
infinitesimal symmetry transformations of the tensor models are generated by
higher n-ary transformations.Comment: 13 pages, some references updated and correcte
Uniqueness of canonical tensor model with local time
Canonical formalism of the rank-three tensor model has recently been
proposed, in which "local" time is consistently incorporated by a set of first
class constraints. By brute-force analysis, this paper shows that there exist
only two forms of a Hamiltonian constraint which satisfies the following
assumptions: (i) A Hamiltonian constraint has one index. (ii) The kinematical
symmetry is given by an orthogonal group. (iii) A consistent first class
constraint algebra is formed by a Hamiltonian constraint and the generators of
the kinematical symmetry. (iv) A Hamiltonian constraint is invariant under time
reversal transformation. (v) A Hamiltonian constraint is an at most cubic
polynomial function of canonical variables. (vi) There are no disconnected
terms in a constraint algebra. The two forms are the same except for a slight
difference in index contractions. The Hamiltonian constraint which was obtained
in the previous paper and behaved oddly under time reversal symmetry can
actually be transformed to one of them by a canonical change of variables. The
two-fold uniqueness is shown up to the potential ambiguity of adding terms
which vanish in the limit of pure gravitational physics.Comment: 21 pages, 12 figures. The final result unchanged. Section 5 rewritten
for clearer discussions. The range of uniqueness commented in the final
section. Some other minor correction
The fluctuation spectra around a Gaussian classical solution of a tensor model and the general relativity
Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this
paper, I study numerically the fluctuation spectra around a Gaussian classical
solution of a tensor model, which represents a fuzzy flat space in arbitrary
dimensions. It is found that the momentum distribution of the low-lying
low-momentum spectra is in agreement with that of the metric tensor modulo the
general coordinate transformation in the general relativity at least in the
dimensions studied numerically, i.e. one to four dimensions. This result
suggests that the effective field theory around the solution is described in a
similar manner as the general relativity.Comment: 29 pages, 13 figure
Modeling peculiar velocities of dark matter halos
We present a simple model that accurately describes various statistical
properties of peculiar velocities of dark matter halos. We pay particular
attention to the following two effects; first, the evolution of the halo
peculiar velocity depends on the local matter density, instead of the global
density. Second, dark matter halos are biased tracers of the underlying mass
distribution, thus halos tend to be located preferentially at high density
regions. For the former, we develop an empirical model calibrated with N-body
simulations, while for the latter, we use a conventional halo bias models based
on the extended Press-Schechter model combined with an empirical log-normal
probability distribution function of the mass density distribution. We find
that compared with linear theory, the present model significantly improves the
accuracy of predictions of statistical properties of the halo peculiar velocity
field including the velocity dispersion, the probability distribution function,
and the pairwise velocity dispersion at large separations. Thus our model
predictions may be useful in analyzing future observations of the peculiar
velocities of galaxy clusters.Comment: This paper was published in MNRAS, 343, 1312 (2003). Owing to an
error in numerical computations, some incorrect results were presented there.
Erratum is to be published in MNRAS. Conclusions of the original version are
unaffected by the correction. This version supersedes the original versio
Detection of Excess Hard X-ray Emission from the Group of Galaxies HCG62
From the group of galaxies HCG62, we detected an excess hard X-ray emission
in energies above keV with \A SCA. The excess emission is spatially
extended up to from the group center, and somewhat enhanced toward
north. Its spectrum can be represented by either a power-law of photon index
0.8-2.7, or a Bremsstrahlung of temperature keV. In the 2-10 keV range,
the observed hard X-ray flux, erg cm
s, implies a luminosity of erg s for a
Hubble constant of 50 km s Mpc. The emission is thus too luminous
to be attributed to X-ray binaries in the memb er galaxies. We discuss possible
origin of the hard X-ray emission.Comment: 6 pages, 3 Postscript figures, uses emulateapj.sty. Accepted for
publication in the Astrophysical Journal Letter
Cranked Hartree-Fock-Bogoliubov Calculation for Rotating Bose-Einstein Condensates
A rotating bosonic many-body system in a harmonic trap is studied with the
3D-Cranked Hartree-Fock-Bogoliubov method at zero temperature, which has been
applied to nuclear many-body systems at high spin. This method is a variational
method extended from the Hartree-Fock theory, which can treat the pairing
correlations in a self-consistent manner. An advantage of this method is that a
finite-range interaction between constituent particles can be used in the
calculation, unlike the original Gross-Pitaevskii approach. To demonstrate the
validity of our method, we present a calculation for a toy model, that is, a
rotating system of ten bosonic particles interacting through the repulsive
quadrupole-quadrupole interaction in a harmonic trap. It is found that the
yrast states, the lowest-energy states for the given total angular momentum,
does not correspond to the Bose-Einstein condensate, except a few special
cases. One of such cases is a vortex state, which appears when the total
angular momentum is twice the particle number (i.e., ).Comment: accepted to Phys. Rev.
The lowest modes around Gaussian solutions of tensor models and the general relativity
In the previous paper, the number distribution of the low-lying spectra
around Gaussian solutions representing various dimensional fuzzy tori of a
tensor model was numerically shown to be in accordance with the general
relativity on tori. In this paper, I perform more detailed numerical analysis
of the properties of the modes for two-dimensional fuzzy tori, and obtain
conclusive evidences for the agreement. Under a proposed correspondence between
the rank-three tensor in tensor models and the metric tensor in the general
relativity, conclusive agreement is obtained between the profiles of the
low-lying modes in a tensor model and the metric modes transverse to the
general coordinate transformation. Moreover, the low-lying modes are shown to
be well on a massless trajectory with quartic momentum dependence in the tensor
model. This is in agreement with that the lowest momentum dependence of metric
fluctuations in the general relativity will come from the R^2-term, since the
R-term is topological in two dimensions. These evidences support the idea that
the low-lying low-momentum dynamics around the Gaussian solutions of tensor
models is described by the general relativity. I also propose a renormalization
procedure for tensor models. A classical application of the procedure makes the
patterns of the low-lying spectra drastically clearer, and suggests also the
existence of massive trajectories.Comment: 31 pages, 8 figures, Added references, minor corrections, a
misleading figure replace
A renormalization procedure for tensor models and scalar-tensor theories of gravity
Tensor models are more-index generalizations of the so-called matrix models,
and provide models of quantum gravity with the idea that spaces and general
relativity are emergent phenomena. In this paper, a renormalization procedure
for the tensor models whose dynamical variable is a totally symmetric real
three-tensor is discussed. It is proven that configurations with certain
Gaussian forms are the attractors of the three-tensor under the renormalization
procedure. Since these Gaussian configurations are parameterized by a scalar
and a symmetric two-tensor, it is argued that, in general situations, the
infrared dynamics of the tensor models should be described by scalar-tensor
theories of gravity.Comment: 20 pages, 3 figures, references added, minor correction
Clustering of dark matter halos on the light-cone: scale-, time- and mass-dependence of the halo biasing in the Hubble volume simulations
We develop a phenomenological model to predict the clustering of dark matter
halos on the light-cone by combining several existing theoretical models.
Assuming that the velocity field of halos on large scales is approximated by
linear theory, we propose an empirical prescription of a scale-, mass-, and
time-dependence of halo biasing. We test our model against the Hubble Volume
-body simulation and examine its validity and limitations. We find a good
agreement in two-point correlation functions of dark matter halos between the
phenomenological model predictions and measurements from the simulation for
Mpc both in the real and redshift spaces. Although calibrated on the
mass scale of groups and clusters and for redshifts up to , the model
is quite general and can be applied to a wider range of astrophysical objects,
such as galaxies and quasars, if the relation between dark halos and visible
objects is specified.Comment: 5 pages, 2 figures, ApJL accepted. New references adde
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