5,011 research outputs found
The generalized modified Bessel function at and Humbert functions
Recently Dixit, Kesarwani, and Moll introduced a generalization
of the modified Bessel function and showed that it satisfies an
elegant theory similar to . In this paper, we show that while
is an elementary function, can be
written in the form of an infinite series of Humbert functions. As an
application of this result, we generalize the transformation formula for the
logarithm of the Dedekind eta function .Comment: 14 pages, submitted for publicatio
Weierstrass-Enneper representation for Maximal Surfaces in Hodographic coordinates
We obtain the Weierstrass-Enneper representation for maximal graphs(whose
Gauss map is one-one) in Lorentz-Minkowski space. For this we use the method of
Barbishov and Chernikov, which they have used to find the solutions of
Born-Infeld equation in hodographic coordinates. We could use their method in
our case, because we realized that the maximal surface equation and Born-Infeld
equation are related via a wick rotation in the first variable of the
parametrising domain.Comment: 9 pages, 0 figure, Additional Affiliation adde
Heavy Vector and Axial-Vector Mesons in Asymmetric Strange Hadronic Matter
We calculate the effects of finite density of isospin asymmetric strange
hadronic matter, for different strangeness fractions, on the in-medium
properties of vector and axial-vector mesons using chiral hadronic SU(3) model and QCD sum rules. We
focus on the evaluation of in-medium mass-shift and shift of decay constant of
above vector and axial vector mesons. In QCD sum rule approach the properties
e.g. masses and decay constants of vector and axial vector mesons are written
in terms of quark and gluon condensates. These quarks and gluon condensates are
evaluated in the present work using chiral SU(3) model through the medium
modification of scalar-isoscalar fields and , the
scalar-isovector field
and scalar dilaton field in strange hadronic medium which
includes both nucleons as well as hyperons. As we shall see in detail the
masses and decay constants of heavy vector and axial vector mesons are affected
significantly due to isospin asymmetry and strangeness fraction of the medium
and these modifications may influence the experimental observables produced in
heavy ion collision experiments. The results of present investigations of
in-medium properties of vector and axial-vector mesons at finite density of
strange hadronic medium may be helpful for understanding the experimental data
from heavy-ion collision experiments in-particular for the Compressed Baryonic
Matter (CBM) experiment of FAIR facility at GSI, Germany.Comment: 43 pages, 15 figure
Entanglement like properties in Spin-Orbit Coupled Ultra Cold Atom and violation of Bell like Inequality
We show that the general quantum state of synthetically spin-orbit coupled
ultra cold bosonic atom whose condensate was experimentally created recently (
Y. J. Lin {\it et al.}, Nature, {\bf 471}, 83, (2011)), shows entanglement
between motional degrees of freedom ( momentum) and internal degrees of freedom
(hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH)
for such states that provides a unique opportunity to verify fundamental
principle like quantum non-contextuality for commutating observables which are
not spatially separated. We analyze in detail the Rabi oscillation executed by
such atom-laser system and how that influneces quantities like entanglement
entropy, violation of Bell like Inequality etc. We also discuss the implication
of our result in testing the quantum non-contextuality and Bell's Inequality
vioaltion by macroscopic quantum object like Bose-Einstein Condensate of ultra
cold atoms.Comment: Latex file with 4 pdf figure
Masses and decay widths of scalar and mesons in strange hadronic medium
Masses and decay constants of scalar and mesons in isospin
asymmetric strange hadronic matter at finite temperature are evaluated using
QCD sum rules and chiral SU(3) model. In-medium light quark condensates,
and , the strange quark condensates, , and the gluon condensates, ,
needed in QCD sum rule calculations are evaluated using chiral SU(3) model. As
an application, we calculate the in-medium partial decay width of scalar
() meson decaying to + (+) pseudoscalar mesons
using model. The medium effects in their decay widths are assimilated
through the modification in the masses of these mesons. These results may be
helpful to understand the possible outcomes of the future experiments like CBM
and PANDA under the FAIR facility where the study of charmed hadrons is one of
major goal.Comment: 28 pages, 8 figure
A note on pairs of rings with same prime ideals
We study the ring extensions R \subseteq T having the same set of prime
ideals provided Nil(R) is a divided prime ideal. Some conditions are given
under which no such T exist properly containing R. Using idealization theory,
the examples are also discussed to strengthen the results.Comment: 10 page
Flat bands with local Berry curvature in multilayer graphene
We demonstrate that flat bands with local Berry curvature arise naturally in
chiral (ABC) multilayer graphene placed on a boron nitride (BN) substrate. The
degree of flatness can be tuned by varying the number of graphene layers N. For
N = 7 the bands become nearly flat, with a small bandwidth of 3.6 meV. The two
nearly flat bands coming from the K and K' valleys cross along lines in the
reduced zone. Weak intervalley tunneling turns the bandcrossing into an avoided
crossing, producing two nearly flat bands with global Chern number zero, but
with local Berry curvature. The flatness of the bands suggests that many body
effects will dominate the physics, while the local Berry curvature of the bands
endows the system with a nontrivial quantum geometry. The quantum geometry
effects manifest themselves through the quantum distance (Fubini-Study) metric,
rather than the more conventional Chern number. Multilayer graphene on BN thus
provides a platform for investigating the effect of interactions in a system
with a non-trivial quantum distance metric, without the complication of
non-zero Chern numbers. We note in passing that flat bands with non-zero Chern
number can also be realized by making use of magnetic adatoms, and explicitly
breaking time reversal symmetry
Comment on "Two notes on imbedded prime divisors"
In this note, we show that a part of [5, Remark 2.2] is not correct. Some
conditions are given under which the same holds
Superimposing theta structure on a generalized modular relation
A generalized modular relation of the form ,
where and , is obtained in the course of
evaluating an integral involving the Riemann -function. It is a
two-variable generalization of a transformation found on page of
Ramanujan's Lost Notebook. This modular relation involves a surprising
generalization of the Hurwitz zeta function , which we denote by
. While is essentially a product of confluent
hypergeometric function and the Riemann zeta function, for
is an interesting new special function. We show that
satisfies a beautiful theory generalizing that of albeit the
properties of are much harder to derive than those of . In particular, it is shown that for and ,
can be analytically continued to Re except for a simple
pole at . This is done by obtaining a generalization of Hermite's formula
in the context of . The theory of functions reciprocal in the
kernel ,
where and and
are the Bessel functions, is worked out. So is the theory of a new
generalization of , namely, . Both these theories as
well as that of are essential to obtain the generalized modular
relation.Comment: 78 pages, submitted for publication. Comments are welcom
Heavy Vector and Axial-Vector Mesons in Hot and Dense Asymmetric Strange Hadronic Matter
We calculate the effects of finite density and temperature of isospin
asymmetric strange hadronic matter, for different strangeness fractions, on the
in-medium properties of vector and axial-vector mesons, using chiral hadronic SU(3) model and QCD sum rules. We
focus on the evaluation of in-medium mass-shift and shift in decay constant of
above vector and axial-vector mesons. In QCD sum rule approach, the properties,
e.g., the masses and decay constants of vector and axial-vector mesons are
written in terms of quark and gluon condensates. These quark and gluon
condensates are evaluated in the present work within chiral SU(3) model,
through the medium modification of, scalar-isoscalar fields and
, the scalar-isovector field and scalar dilaton field ,
in the strange hadronic medium which includes both nucleons as well as
hyperons. As we shall see in detail, the masses and decay constants of heavy
vector and axial-vector mesons are affected significantly due to isospin
asymmetry and strangeness fraction of the medium and these modifications may
influence the experimental observables produced in heavy ion collision
experiments. The results of present investigations of in-medium properties of
vector and axial-vector mesons at finite density and temperature of strange
hadronic medium may be helpful for understanding the experimental data from
heavy-ion collision experiments in-particular for the Compressed Baryonic
Matter (CBM) experiment of FAIR facility at GSI, Germany.Comment: 36 pages and 9 figures. arXiv admin note: substantial text overlap
with arXiv:1506.0211
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