14,087 research outputs found
Faddeev-Skyrme Model and Rational Maps
The Faddeev-Skyrme model, a modified O(3) nonlinear sigma model in three
space dimensions, is known to admit topological solitons that are stabilized by
the Hopf charge. The Faddeev-Skyrme model is also related to the low-energy
limits of SU(2) Yang-Mills theory. Here, the model is reformulated into its
gauge-equivalent expression, which turns out to be Skyrme-like. The solitonic
solutions of this Skyrme-like model are analyzed by the rational map ansatz.
The energy function and the Bogomolny-type lower bound of the energy are
established. The generalized Faddeev-Skyrme model that originates from the
infrared limits of SU(N) Yang-Mills theory is presented.Comment: 12 pages, LaTex, minor typo correcte
Abelian Decomposition of SO(2N) Yang-Mills Theory
Faddeev and Niemi have proposed a decomposition of SU(N) Yang-Mills theory in
terms of new variables, appropriate for describing the theory in the infrared
limit. We extend this method to SO(2N) Yang-Mills theory. We find that the
SO(2N) connection decomposes according to irreducible representations of SO(N).
The low energy limit of the decomposed theory is expected to describe
soliton-like configurations with nontrivial topological numbers. How the method
of decomposition generalizes for Yang-Mills theory is also
discussed.Comment: 8 pages, no figur
A Relation between the Anomalous Dimensions and OPE Coefficients in Asymptotic Free Field Theories
In asymptotic free field theories we show that part of the OPE of the trace
of the stress-energy tensor and an arbitrary composite field is determined by
the anomalous dimension of the composite field. We take examples from the
two-dimensional O(N) non-linear sigma model.Comment: 6 pages, plain TeX, uses harvma
Analytical Results for Cold Asymmetrical Fermion Superfluids at the Mean-Field Level
We present the analytical results at the mean-field level for the
asymmetrical fermion system with attractive contact interaction at the zero
temperature. The results can be expressed in terms of linear combinations of
the elliptic integrals of the first and second kinds. In the limit of small gap
parameter, we discuss how the asymmetry in fermion species affects the phases
of the ground state. In the limit of large gap parameter, we show that two
candidate phases are competing for the system's ground state. The Sarma phase
containing a pure Fermi fluid and a mixed condensate is favored at large degree
of asymmetry. The separated phase consisting of a pure Fermi fluid and a boson
condensate supports the system at smaller degree of asymmetry. The two phases
are degenerate in the limit of infinite pairing gap.Comment: 23 pages, no figur
Application of Time-Fractional Order Bloch Equation in Magnetic Resonance Fingerprinting
Magnetic resonance fingerprinting (MRF) is one novel fast quantitative
imaging framework for simultaneous quantification of multiple parameters with
pseudo-randomized acquisition patterns. The accuracy of the resulting
multi-parameters is very important for clinical applications. In this paper, we
derived signal evolutions from the anomalous relaxation using a fractional
calculus. More specifically, we utilized time-fractional order extension of the
Bloch equations to generate dictionary to provide more complex system
descriptions for MRF applications. The representative results of phantom
experiments demonstrated the good accuracy performance when applying the
time-fractional order Bloch equations to generate dictionary entries in the MRF
framework. The utility of the proposed method is also validated by in-vivo
study.Comment: Accepted at 2019 IEEE 16th International Symposium on Biomedical
Imaging (ISBI 2019
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