18,865 research outputs found
Realization of effective super Tonks-Girardeau gases via strongly attractive one-dimensional Fermi gases
A significant feature of the one-dimensional super Tonks-Girardeau gas is its
metastable gas-like state with a stronger Fermi-like pressure than for free
fermions which prevents a collapse of atoms. This naturally suggests a way to
search for such strongly correlated behaviour in systems of interacting
fermions in one dimension. We thus show that the strongly attractive Fermi gas
without polarization can be effectively described by a super Tonks-Girardeau
gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A
natural description of such super Tonks-Girardeau gases is provided by Haldane
generalized exclusion statistics. In particular, we find that they are
equivalent to ideal particles obeying more exclusive statistics than
Fermi-Dirac statistics.Comment: 4 pages, 2 figure
Reduced pattern training based on task decomposition using pattern distributor
Task Decomposition with Pattern Distributor (PD) is a new task decomposition method for multilayered feedforward neural networks. Pattern distributor network is proposed that implements this new task decomposition method. We propose a theoretical model to analyze the performance of pattern distributor network. A method named Reduced Pattern Training is also introduced, aiming to improve the performance of pattern distribution. Our analysis and the experimental results show that reduced pattern training improves the performance of pattern distributor network significantly. The distributor module’s classification accuracy dominates the whole network’s performance. Two combination methods, namely Cross-talk based combination and Genetic Algorithm based combination, are presented to find suitable grouping for the distributor module. Experimental results show that this new method can reduce training time and improve network generalization accuracy when compared to a conventional method such as constructive backpropagation or a task decomposition method such as Output Parallelism
Fermionization and fractional statistics in the strongly interacting one-dimensional Bose gas
We discuss recent results on the relation between the strongly interacting
one-dimensional Bose gas and a gas of ideal particles obeying nonmutual
generalized exclusion statistics (GES). The thermodynamic properties considered
include the statistical profiles, the specific heat and local pair
correlations. In the strong coupling limit , the
Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation
from Fermi statistics during boson fermionization for finite but large
interaction strength is described by the relation , where is a measure of the GES. This gives a quantitative
description of the fermionization process. In this sense the recent
experimental measurement of local pair correlations in a 1D Bose gas of
Rb atoms also provides a measure of the deviation of the GES parameter
away from the pure Fermi statistics value . Other
thermodynamic properties, such as the distribution profiles and the specific
heat, are also sensitive to the statistics. They also thus provide a way of
exploring fractional statistics in the strongly interacting 1D Bose gas.Comment: 7 pages, 4 figure
Task decomposition using pattern distributor
In this paper, we propose a new task decomposition method for multilayered feedforward neural networks, namely Task Decomposition with Pattern Distributor in order to shorten the training time and improve the generalization accuracy of a network under training. This new method uses the combination of modules (small-size feedforward network) in parallel and series, to produce the overall solution for a complex problem. Based on a “divide-and-conquer” technique, the original problem is decomposed into several simpler sub-problems by a pattern distributor module in the network, where each sub-problem is composed of the whole input vector and a fraction of the output vector of the original problem. These sub-problems are then solved by the corresponding groups of modules, where each group of modules is connected in series with the pattern distributor module and the modules in each group are connected in parallel. The design details and implementation of this new method are introduced in this paper. Several benchmark classification problems are used to test this new method. The analysis and experimental results show that this new method could reduce training time and improve generalization accuracy
Modeling the environmental controls on tree water use at different temporal scales
Acknowledgements This study is part of the first author’s PhD projects in 2010–2014, co-funded by the National Centre for Groundwater Research and Training in Australia and the China Scholarship Council. We give thanks to Zijuan Deng and Xiang Xu for their assistance in the field. Constructive comments and suggestion from the anonymous reviewers are appreciated for significant improvement of the manuscript.Peer reviewedPostprin
Generalized exclusion statistics and degenerate signature of strongly interacting anyons
We show that below the degenerate temperature the distribution profiles of
strongly interacting anyons in one dimension coincide with the most probable
distributions of ideal particles obeying generalized exclusion statistics
(GES). In the strongly interacting regime the thermodynamics and the local
two-particle correlation function derived from the GES are seen to agree for
low temperatures with the results derived for the anyon model using the
thermodynamic Bethe Ansatz. The anyonic and dynamical interactions implement a
continuous range of GES, providing a signature of strongly interacting anyons,
including the strongly interacting one-dimensional Bose gas.Comment: 7 pages, 3 figures, expanded versio
Ferromagnetic behaviour in the strongly interacting two-component Bose gas
We investigate the low temperature behaviour of the integrable 1D
two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find
that for strong coupling the characteristics of the thermodynamics at low
temperatures are quantitatively affected by the spin ferromagnetic states,
which are described by an effective ferromagnetic Heisenberg chain. The free
energy, specific heat, susceptibility and local pair correlation function are
calculated for various physical regimes in terms of temperature and interaction
strength. These thermodynamic properties reveal spin effects which are
significantly different than those of the spinless Bose gas. The zero-field
susceptibility for finite strong repulsion exceeds that of a free spin
paramagnet. The critical exponents of the specific heat and
the susceptibility are indicative of the ferromagnetic
signature of the two-component spinor Bose gas. Our analytic results are
consistent with general arguments by Eisenberg and Lieb for polarized spinor
bosons.Comment: 15 pages, 6 figures, revised version, references added, minor
correction
Yang-Yang method for the thermodynamics of one-dimensional multi-component interacting fermions
Using Yang and Yang's particle-hole description, we present a thorough
derivation of the thermodynamic Bethe ansatz equations for a general
fermionic system in one-dimension for both the repulsive and
attractive regimes under the presence of an external magnetic field. These
equations are derived from Sutherland's Bethe ansatz equations by using the
spin-string hypothesis. The Bethe ansatz root patterns for the attractive case
are discussed in detail. The relationship between the various phases of the
magnetic phase diagrams and the external magnetic fields is given for the
attractive case. We also give a quantitative description of the ground state
energies for both strongly repulsive and strongly attractive regimes.Comment: 22 pages, 2 figures, slight improvements, some extra reference
Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
We investigate pairing and quantum phase transitions in the one-dimensional
two-component Fermi atomic gas in an external field. The phase diagram,
critical fields, magnetization and local pairing correlation are obtained
analytically via the exact thermodynamic Bethe ansatz solution. At zero
temperature, bound pairs of fermions with opposite spin states form a singlet
ground state when the external field . A completely ferromagnetic
phase without pairing occurs when the external field . In the
region we observe a mixed phase of matter in which paired
and unpaired atoms coexist. The phase diagram is reminiscent of that of type II
superconductors. For temperatures below the degenerate temperature and in the
absence of an external field, the bound pairs of fermions form hard-core bosons
obeying generalized exclusion statistics.Comment: 9 pages, 5 figures, expanded version with additional text, references
and figure
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
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