27,528 research outputs found
Matrix models without scaling limit
In the context of hermitean one--matrix models we show that the emergence of
the NLS hierarchy and of its reduction, the KdV hierarchy, is an exact result
of the lattice characterizing the matrix model. Said otherwise, we are not
obliged to take a continuum limit to find these hierarchies. We interpret this
result as an indication of the topological nature of them. We discuss the
topological field theories associated with both and discuss the connection with
topological field theories coupled to topological gravity already studied in
the literature.Comment: Latex, SISSA-ISAS 161/92/E
The (N,M)-th KdV hierarchy and the associated W algebra
We discuss a differential integrable hierarchy, which we call the (N, M)MW_N$ algebra. We show
that there exist M distinct reductions of the (N, M)--th KdV hierarchy, which
are obtained by imposing suitable second class constraints. The most drastic
reduction corresponds to the (N+M)--th KdV hierarchy. Correspondingly the W(N,
M) algebra is reduced to the W_{N+M} algebra. We study in detail the
dispersionless limit of this hierarchy and the relevant reductions.Comment: 40 pages, LaTeX, SISSA-171/93/EP, BONN-HE-46/93, AS-IPT-49/9
Sensitivity of Coronal Loop Sausage Mode Frequencies and Decay Rates to Radial and Longitudinal Density Inhomogeneities: A Spectral Approach
Fast sausage modes in solar magnetic coronal loops are only fully contained
in unrealistically short dense loops. Otherwise they are leaky, losing energy
to their surrounds as outgoing waves. This causes any oscillation to decay
exponentially in time. Simultaneous observations of both period and decay rate
therefore reveal the eigenfrequency of the observed mode, and potentially
insight into the tubes' nonuniform internal structure. In this article, a
global spectral description of the oscillations is presented that results in an
implicit matrix eigenvalue equation where the eigenvalues are associated
predominantly with the diagonal terms of the matrix. The off-diagonal terms
vanish identically if the tube is uniform. A linearized perturbation approach,
applied with respect to a uniform reference model, is developed that makes the
eigenvalues explicit. The implicit eigenvalue problem is easily solved
numerically though, and it is shown that knowledge of the real and imaginary
parts of the eigenfrequency is sufficient to determine the width and density
contrast of a boundary layer over which the tubes' enhanced internal densities
drop to ambient values. Linearized density kernels are developed that show
sensitivity only to the extreme outside of the loops for radial fundamental
modes, especially for small density enhancements, with no sensitivity to the
core. Higher radial harmonics do show some internal sensitivity, but these will
be more difficult to observe. Only kink modes are sensitive to the tube
centres. {Variation in internal and external Alfv\'en speed along the loop is
shown to have little effect on the fundamental dimensionless eigenfrequency,
though the associated eigenfunction becomes more compact at the loop apex as
stratification increases, or may even displace from the apex.Comment: Accepted J. Phys. A: Math. Theor. (Oct 31 2017). 20 pages, 12 figure
Turbulent convection model in the overshooting region: II. Theoretical analysis
Turbulent convection models are thought to be good tools to deal with the
convective overshooting in the stellar interior. However, they are too complex
to be applied in calculations of stellar structure and evolution. In order to
understand the physical processes of the convective overshooting and to
simplify the application of turbulent convection models, a semi-analytic
solution is necessary.
We obtain the approximate solution and asymptotic solution of the turbulent
convection model in the overshooting region, and find some important properties
of the convective overshooting:
I. The overshooting region can be partitioned into three parts: a thin region
just outside the convective boundary with high efficiency of turbulent heat
transfer, a power law dissipation region of turbulent kinetic energy in the
middle, and a thermal dissipation area with rapidly decreasing turbulent
kinetic energy. The decaying indices of the turbulent correlations ,
, and are only determined by the parameters of the
TCM, and there is an equilibrium value of the anisotropic degree .
II. The overshooting length of the turbulent heat flux is
about ().
III. The value of the turbulent kinetic energy at the convective boundary
can be estimated by a method called \textsl{the maximum of diffusion}.
Turbulent correlations in the overshooting region can be estimated by using
and exponentially decreasing functions with the decaying indices.Comment: 32 pages, 9 figures, Accepted by The Astrophysical Journa
Vibration Induced Non-adiabatic Geometric Phase and Energy Uncertainty of Fermions in Graphene
We investigate geometric phase of fermion states under relative vibrations of
two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation
using Floquet scheme. In a period of vibration the fermions acquire different
geometric phases depending on their momenta. There are two regions in the
momentum space: the adiabatic region where the geometric phase can be
approximated by the Berry phase and the chaotic region where the geometric
phase drastically fluctuates in changing parameters. The energy of fermions due
to vibrations shows spikes in the chaotic region. The results suggest a
possible dephasing mechanism which may cause classical-like transport
properties in graphene.Comment: 9 pages, 5 figure
Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate
The particle-number fluctuations originated from collective excitations are
investigated for a three-dimensional, repulsively interacting Bose-Einstein
condensate (BEC) confined in a harmonic trap. The contribution due to the
quantum depletion of the condensate is calculated and the explicit expression
of the coefficient in the formulas denoting the particle-number fluctuations is
given. The results show that the particle-number fluctuations of the condensate
follow the law and the fluctuations vanish when
temperature approaches to the BEC critical temperature.Comment: RevTex, 4 page
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