43,472 research outputs found
Exactly solvable models and ultracold Fermi gases
Exactly solvable models of ultracold Fermi gases are reviewed via their
thermodynamic Bethe Ansatz solution. Analytical and numerical results are
obtained for the thermodynamics and ground state properties of two- and
three-component one-dimensional attractive fermions with population imbalance.
New results for the universal finite temperature corrections are given for the
two-component model. For the three-component model, numerical solution of the
dressed energy equations confirm that the analytical expressions for the
critical fields and the resulting phase diagrams at zero temperature are highly
accurate in the strong coupling regime. The results provide a precise
description of the quantum phases and universal thermodynamics which are
applicable to experiments with cold fermionic atoms confined to one-dimensional
tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16
pages, 6 figure
Schema Independent Relational Learning
Learning novel concepts and relations from relational databases is an
important problem with many applications in database systems and machine
learning. Relational learning algorithms learn the definition of a new relation
in terms of existing relations in the database. Nevertheless, the same data set
may be represented under different schemas for various reasons, such as
efficiency, data quality, and usability. Unfortunately, the output of current
relational learning algorithms tends to vary quite substantially over the
choice of schema, both in terms of learning accuracy and efficiency. This
variation complicates their off-the-shelf application. In this paper, we
introduce and formalize the property of schema independence of relational
learning algorithms, and study both the theoretical and empirical dependence of
existing algorithms on the common class of (de) composition schema
transformations. We study both sample-based learning algorithms, which learn
from sets of labeled examples, and query-based algorithms, which learn by
asking queries to an oracle. We prove that current relational learning
algorithms are generally not schema independent. For query-based learning
algorithms we show that the (de) composition transformations influence their
query complexity. We propose Castor, a sample-based relational learning
algorithm that achieves schema independence by leveraging data dependencies. We
support the theoretical results with an empirical study that demonstrates the
schema dependence/independence of several algorithms on existing benchmark and
real-world datasets under (de) compositions
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Sequence Classification Restricted Boltzmann Machines With Gated Units
For the classification of sequential data, dynamic Bayesian networks and recurrent neural networks (RNNs) are the preferred models. While the former can explicitly model the temporal dependences between the variables, and the latter have the capability of learning representations. The recurrent temporal restricted Boltzmann machine (RTRBM) is a model that combines these two features. However, learning and inference in RTRBMs can be difficult because of the exponential nature of its gradient computations when maximizing log likelihoods. In this article, first, we address this intractability by optimizing a conditional rather than a joint probability distribution when performing sequence classification. This results in the ``sequence classification restricted Boltzmann machine'' (SCRBM). Second, we introduce gated SCRBMs (gSCRBMs), which use an information processing gate, as an integration of SCRBMs with long short-term memory (LSTM) models. In the experiments reported in this article, we evaluate the proposed models on optical character recognition, chunking, and multiresident activity recognition in smart homes. The experimental results show that gSCRBMs achieve the performance comparable to that of the state of the art in all three tasks. gSCRBMs require far fewer parameters in comparison with other recurrent networks with memory gates, in particular, LSTMs and gated recurrent units (GRUs)
Magnetism and Charge Dynamics in Iron Pnictides
In a wide variety of materials, such as copper oxides, heavy fermions,
organic salts, and the recently discovered iron pnictides, superconductivity is
found in close proximity to a magnetically ordered state. The character of the
proximate magnetic phase is thus believed to be crucial for understanding the
differences between the various families of unconventional superconductors and
the mechanism of superconductivity. Unlike the AFM order in cuprates, the
nature of the magnetism and of the underlying electronic state in the iron
pnictide superconductors is not well understood. Neither density functional
theory nor models based on atomic physics and superexchange, account for the
small size of the magnetic moment. Many low energy probes such as transport,
STM and ARPES measured strong anisotropy of the electronic states akin to the
nematic order in a liquid crystal, but there is no consensus on its physical
origin, and a three dimensional picture of electronic states and its relations
to the optical conductivity in the magnetic state is lacking. Using a first
principles approach, we obtained the experimentally observed magnetic moment,
optical conductivity, and the anisotropy of the electronic states. The theory
connects ARPES, which measures one particle electronic states, optical
spectroscopy, probing the particle hole excitations of the solid and neutron
scattering which measures the magnetic moment. We predict a manifestation of
the anisotropy in the optical conductivity, and we show that the magnetic phase
arises from the paramagnetic phase by a large gain of the Hund's rule coupling
energy and a smaller loss of kinetic energy, indicating that iron pnictides
represent a new class of compounds where the nature of magnetism is
intermediate between the spin density wave of almost independent particles, and
the antiferromagnetic state of local moments.Comment: 4+ pages with additional one-page supplementary materia
Universal Tomonaga-Luttinger liquid phases in one-dimensional strongly attractive SU(N) fermionic cold atoms
A simple set of algebraic equations is derived for the exact low-temperature
thermodynamics of one-dimensional multi-component strongly attractive fermionic
atoms with enlarged SU(N) spin symmetry and Zeeman splitting. Universal
multi-component Tomonaga-Luttinger liquid (TLL) phases are thus determined. For
linear Zeeman splitting, the physics of the gapless phase at low temperatures
belongs to the universality class of a two-component asymmetric TLL
corresponding to spin-neutral N-atom composites and spin-(N-1)/2 single atoms.
The equation of states is also obtained to open up the study of multi-component
TLL phases in 1D systems of N-component Fermi gases with population imbalance.Comment: 12 pages, 3 figure
Neutrino mixing matrix in the 3-3-1 model with heavy leptons and symmetry
We study the lepton sector in the model based on the local gauge group
which do not contain particles with
exotic electric charges. The seesaw mechanism and discrete symmetry are
introduced into the model to understand why neutrinos are especially light and
the observed pattern of neutrino mixing. The model provides a method for
obtaining the tri-bimaximal mixing matrix in the leading order. A non-zero
mixing angle presents in the modified mixing matrix.Comment: 10 page
Universal local pair correlations of Lieb-Liniger bosons at quantum criticality
The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system
featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion
quantum criticality. We analytically calculate finite temperature local pair
correlations for the strong coupling Bose gas at quantum criticality using the
polylog function in the framework of the Yang-Yang thermodynamic equations. We
show that the local pair correlation has the universal value in the quantum critical regime, the TLL phase and the
quasi-classical region, where is the pressure per unit length rescaled by
the interaction energy with interaction
strength and linear density . This suggests the possibility to test
finite temperature local pair correlations for the TLL in the relativistic
dispersion regime and to probe quantum criticality with the local correlations
beyond the TLL phase. Furthermore, thermodynamic properties at high
temperatures are obtained by both high temperature and virial expansion of the
Yang-Yang thermodynamic equation.Comment: 8 pages, 6 figures, additional text and reference
The earliest high-fired glazed ceramics in China: the composition of the proto-porcelain from Zhejiang during the Shang and Zhou periods (c. 1700-221 BC)
Bodies and glazes of 54 proto-porcelain sherds and 18 non proto-porcelain samples from Shang and Zhou periods production sites in Deqing, Zhejiang province were analysed by EPMA-WDS. The results indicate that the bodies of all samples were made from local raw material porcelain stone, with the proto-porcelain samples being made from clay of higher quality. Wood ashes, high in lime and low in potash, were intentionally applied to the proto-porcelain samples, resulting in the formation of lime-rich glazes whose compositions were determined by a temperature-controlled mechanism. In contrast, kiln fragments and furniture show a potash-rich fuel vapour glaze, which formed unintentionally during use of the kiln. The firing temperature for most of the proto-porcelain glazes is around the maturing temperature for typical more recent lime glazes, showing that the potters were already at such an early time able to attain sufficiently high temperature in their kilns
Wilson ratio of Fermi gases in one dimension
We calculate the Wilson ratio of the one-dimensional Fermi gas with spin
imbalance. The Wilson ratio of attractively interacting fermions is solely
determined by the density stiffness and sound velocity of pairs and of excess
fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio
exhibits anomalous enhancement at the two critical points due to the sudden
change in the density of states. Despite a breakdown of the quasiparticle
description in one dimension, two important features of the Fermi liquid are
retained, namely the specific heat is linearly proportional to temperature
whereas the susceptibility is independent of temperature. In contrast to the
phenomenological TLL parameter, the Wilson ratio provides a powerful parameter
for testing universal quantum liquids of interacting fermions in one, two and
three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine
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