9,967 research outputs found
The small-mass limit and white-noise limit of an infinite dimensional Generalized Langevin Equation
We study asymptotic properties of the Generalized Langevin Equation (GLE) in
the presence of a wide class of external potential wells with a power-law decay
memory kernel. When the memory can be expressed as a sum of exponentials, a
class of Markovian systems in infinite-dimensional spaces is used to represent
the GLE. The solutions are shown to converge in probability in the small-mass
limit and the white-noise limit to appropriate systems under minimal
assumptions, of which no Lipschitz condition is required on the potentials.
With further assumptions about space regularity and potentials, we obtain
convergence in the white-noise limit
Global estimates for quasilinear parabolic equations on Reifenberg flat domains and its applications to Riccati type parabolic equations with distributional data
In this paper, we prove global weighted Lorentz and Lorentz-Morrey estimates
for gradients of solutions to the quasilinear parabolic equations:
in a bounded
domain , under minimal regularity
assumptions on the boundary of domain and on nonlinearity . Then results
yields existence of a solution to the Riccati type parabolic equations:
where and is a bounded Radon
measure.Comment: to appear Calculus of Variations and Partial Differential Equation
Irreducible restrictions of Brauer characters of the Chevalley group G_2(q) to its proper subgroups
Let be the Chevalley group of type defined over a finite field
with q=p^n elements, where p is a prime number and is a positive integer.
In this paper, we determine when the restriction of an absolutely irreducible
representation of in characteristic other than p to a maximal subgroup of
is still irreducible. Similar results are obtained for and
.Comment: 30 page
Gradient estimates for singular quasilinear elliptic equations with measure data
In this paper, we prove -estimates for gradients of solutions to
singular quasilinear elliptic equations with measure data
in a bounded domain
, where , and is a Radon measure in Comment: 20 pages. arXiv admin note: text overlap with arXiv:1511.0621
Low-dimensional complex characters of the symplectic and orthogonal groups
We classify the irreducible complex characters of the symplectic groups
and the orthogonal groups , of
degrees up to the bound D, where for symplectic groups,
for orthogonal groups in odd dimension, and for
orthogonal groups in even dimension.Comment: 44 pages. Comm. Algebra, to appea
Characters of p'-degree and Thompson's character degree theorem
A classical theorem of John Thompson on character degrees asserts that if the
degree of every ordinary irreducible character of a finite group is 1 or
divisible by a prime , then has a normal -complement. We obtain a
significant improvement of this result by considering the average of
-degrees of irreducible characters. We also consider fields of character
values and prove several improvements of earlier related results.Comment: 23 page
On the importance of using exact pairing in the study of pygmy dipole resonance
The strength functions of giant dipole resonance (GDR) in oxygen O, calcium Ca, and tin Sn isotopes are calculated
within the phonon damping model under three approximations: without superfluid
pairing, including BCS pairing, and exact pairing gaps. The analysis of the
numerical results shows that exact pairing decreases the two-neutron separation
energy in light nuclei, but increases it in heavy nuclei as compared to that
obtained within the BCS theory. In neutron-rich medium and heavy nuclei, exact
pairing significantly enhances the strength located at the low-energy tail of
the GDR, which is usually associated with the pygmy dipole resonance. The line
shape of the GDR changes significantly with increasing the neutron number
within an isotopic chain if the model parameter is kept fixed at the value
determined for the stable isotope.Comment: 26 pages, 19 figures, to appear in Journal of Physics
Comment on arXiv:0709.3700 "Orientation dependence of the optical spectra in graphene at high frequencies"
Zhang et al. reported in [Phys. Rev. B 77, 241402(R) (2008)] a theoretical
study of the optical spectra of monolayer graphene employing the Kubo formula
within a tight-binding model. Their calculations predicted that at high
frequencies the optical conductivity of graphene becomes strongly anisotropic.
In particular, at frequencies comparable to the energy separation of the upper
and lower bands at the -point, the optical conductivity is strongly
suppressed if the field polarization is along the zigzag direction while it is
significantly high for the armchair one. We find that, unfortunately, this
result is just a consequence of the incorrect determination of the current
operator in k-space. Here, we present the standard scheme to obtain this
operator correctly. As a result, we show that the optical conductivity of
monolayer graphene is indeed isotropic, which is consistent with the results of
other (both theoretical and experimental) studies in the literature.Comment: submitte
Self-consistent quasiparticle RPA for multi-level pairing model
Particle-number projection within the Lipkin-Nogami (LN) method is applied to
the self-consistent quasiparticle random-phase approximation (SCQRPA), which is
tested in an exactly solvable multi-level pairing model. The SCQRPA equations
are numerically solved to find the energies of the ground and excited states at
various numbers of doubly degenerate equidistant levels. The use of
the LN method allows one to avoid the collapse of the BCS (QRPA) to obtain the
energies of the ground and excited states as smooth functions of the
interaction parameter . The comparison between results given by different
approximations such as the SCRPA, QRPA, LNQRPA, SCQRPA and LNSCQRPA is carried
out. While the use of the LN method significantly improves the agreement with
the exact results in the intermediate coupling region, we found that in the
strong coupling region the SCQRPA results are closest to the exact ones.Comment: Accepted by Phys. Rev.
Giant dipole resonance in Tl at low temperature
The thermal pairing gap obtained by embedding the exact solutions of the
pairing problem into the canonical ensemble is employed to calculate the width
and strength function of the giant dipole resonance (GDR) within the phonon
damping model. The results of calculations describe reasonably well the data
for the GDR width as well as the GDR linearized strength function, recently
obtained for Tl in the temperature region between 0.8 and 1.2 MeV,
which other approaches that neglect the effect of non-vanishing thermal pairing
fail to describe.Comment: 18 page, 4 figures, accepted for publication in Phys. Rev.
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