4,472 research outputs found
Indecomposable representations and oscillator realizations of the exceptional Lie algebra G_2
In this paper various representations of the exceptional Lie algebra G_2 are
investigated in a purely algebraic manner, and multi-boson/multi-fermion
realizations are obtained. Matrix elements of the master representation, which
is defined on the space of the universal enveloping algebra of G_2, are
explicitly determined. From this master representation, different
indecomposable representations defined on invariant subspaces or quotient
spaces with respect to these invariant subspaces are discussed. Especially, the
elementary representations of G_2 are investigated in detail, and the
corresponding six-boson realization is given. After obtaining explicit forms of
all twelve extremal vectors of the elementary representation with the highest
weight {\Lambda}, all representations with their respective highest weights
related to {\Lambda} are systematically discussed. For one of these
representations the corresponding five-boson realization is constructed.
Moreover, a new three-fermion realization from the fundamental representation
(0,1) of G_2 is constructed also.Comment: 29 pages, 4 figure
Electron-nuclear entanglement in the cold lithium gas
We study the ground-state entanglement and thermal entanglement in the
hyperfine interaction of the lithium atom. We give the relationship between the
entanglement and both temperature and external magnetic fields.Comment: 7 pages, 3 figure
The Role of Chaos in One-Dimensional Heat Conductivity
We investigate the heat conduction in a quasi 1-D gas model with various
degree of chaos. Our calculations indicate that the heat conductivity
is independent of system size when the chaos of the channel is strong enough.
The different diffusion behaviors for the cases of chaotic and non-chaotic
channels are also studied. The numerical results of divergent exponent
of heat conduction and diffusion exponent are in consistent with the
formula . We explore the temperature profiles numerically and
analytically, which show that the temperature jump is primarily attributed to
superdiffusion for both non-chaotic and chaotic cases, and for the latter case
of superdiffusion the finite-size affects the value of remarkably.Comment: 6 pages, 7 figure
Heat conductivity in the presence of a quantized degree of freedom
We propose a model with a quantized degree of freedom to study the heat
transport in quasi-one dimensional system. Our simulations reveal three
distinct temperature regimes. In particular, the intermediate regime is
characterized by heat conductivity with a temperature exponent much
greater than 1/2 that was generally found in systems with point-like particles.
A dynamical investigation indicates the occurrence of non-equipartition
behavior in this regime. Moreover, the corresponding Poincar\'e section also
shows remarkably characteristic patterns, completely different from the cases
of point-like particles.Comment: 7 pages, 4 figure
Reducing the Tension Between the BICEP2 and the Planck Measurements: A Complete Exploration of the Parameter Space
A large inflationary tensor-to-scalar ratio is reported by the BICEP2 team based on their B-mode
polarization detection, which is outside of the confidence level of the
Planck best fit model. We explore several possible ways to reduce the tension
between the two by considering a model in which ,
, and the neutrino parameters and
are set as free parameters. Using the Markov Chain
Monte Carlo (MCMC) technique to survey the complete parameter space with and
without the BICEP2 data, we find that the resulting constraints on
are consistent with each other and the apparent tension
seems to be relaxed. Further detailed investigations on those fittings suggest
that probably plays the most important role in reducing the
tension. We also find that the results obtained from fitting without adopting
the consistency relation do not deviate much from the consistency relation.
With available Planck, WMAP, BICEP2 and BAO datasets all together, we obtain
, ,
, and
; if the consistency relation is
adopted, we get .Comment: 8 pages, 4 figures, submitted to PL
Two Polyak-Type Step Sizes for Mirror Descent
We propose two Polyak-type step sizes for mirror descent and prove their
convergences for minimizing convex locally Lipschitz functions. Both step
sizes, unlike the original Polyak step size, do not need the optimal value of
the objective function.Comment: 13 page
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