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

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 A4A_4 symmetry

We study the lepton sector in the model based on the local gauge group $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ which do not contain particles with exotic electric charges. The seesaw mechanism and discrete $A_4$ 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 $V_{e3}$ 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 $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. 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