518 research outputs found
The Eastwood-Singer gauge in Einstein spaces
Electrodynamics in curved spacetime can be studied in the Eastwood--Singer
gauge, which has the advantage of respecting the invariance under conformal
rescalings of the Maxwell equations. Such a construction is here studied in
Einstein spaces, for which the Ricci tensor is proportional to the metric. The
classical field equations for the potential are then equivalent to first
solving a scalar wave equation with cosmological constant, and then solving a
vector wave equation where the inhomogeneous term is obtained from the gradient
of the solution of the scalar wave equation. The Eastwood--Singer condition
leads to a field equation on the potential which is preserved under gauge
transformations provided that the scalar function therein obeys a fourth-order
equation where the highest-order term is the wave operator composed with
itself. The second-order scalar equation is here solved in de Sitter spacetime,
and also the fourth-order equation in a particular case, and these solutions
are found to admit an exponential decay at large time provided that
square-integrability for positive time is required. Last, the vector wave
equation in the Eastwood-Singer gauge is solved explicitly when the potential
is taken to depend only on the time variable.Comment: 13 pages. Section 6, with new original calculations, has been added,
and the presentation has been improve
Topics in Cubic Special Geometry
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic
special Kaehler geometries. Imposing the invariance under axion-shifts, all
such corrections (but the imaginary constant one) can be introduced or removed
through suitable, lower unitriangular symplectic transformations, dubbed
Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to
the d=4 U-duality group G4, in symmetric cases they generally have a
non-trivial action on the unique quartic invariant polynomial I4 of the charge
representation R of G4. This leads to interesting phenomena in relation to
theory of extremal black hole attractors; namely, the possibility to make
transitions between different charge orbits of R, with corresponding change of
the supersymmetry properties of the supported attractor solutions. Furthermore,
a suitable action of PQ transformations can also set I4 to zero, or vice versa
it can generate a non-vanishing I4: this corresponds to transitions between
"large" and "small" charge orbits, which we classify in some detail within the
"special coordinates" symplectic frame. Finally, after a brief account of the
action of PQ transformations on the recently established correspondence between
Cayley's hyperdeterminant and elliptic curves, we derive an equivalent,
alternative expression of I4, with relevant application to black hole entropy.Comment: 1+39 page
Entanglement in a Valence-Bond-Solid State
We study entanglement in Valence-Bond-Solid state. It describes the ground
state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model
has a gap and open boundary conditions. We calculate an entropy of a subsystem
(continuous block of spins). It quantifies the entanglement of this block with
the rest of the ground state. We prove that the entanglement approaches a
constant value exponentially fast as the size of the subsystem increases.
Actually we proved that the density matrix of the continuous block of spins
depends only on the length of the block, but not on the total size of the chain
[distance to the ends also not essential]. We also study reduced density
matrices of two spins both in the bulk and on the boundary. We evaluated
concurrencies.Comment: 4pages, no figure
Thermodynamics of Photon Gas with an Invariant Energy Scale
Quantum Gravity framework motivates us to find new theories in which an
observer independent finite energy upper bound (preferably Planck Energy)
exists. We have studied the modifications in the thermodynamical properties of
a photon gas in such a scenario where we have an invariant energy scale. We
show that the density of states and the entropy in such a framework are less
than the corresponding quantities in Einstein's Special Relativity (SR) theory.
This result can be interpreted as a consequence of the deformed Lorentz
symmetry present in the particular model we have considered.Comment: 17 pages, 3 figure files, some addition in text as well as in
references, the scaling of figures have been modifie
Solving relativistic hydrodynamic equation in presence of magnetic field for phase transition in a neutron star
Hadronic to quark matter phase transition may occur inside neutron stars (NS)
having central densities of the order of 3-10 times normal nuclear matter
saturation density (). The transition is expected to be a two-step
process; transition from hadronic to 2-flavour matter and two-flavour to
equilibrated charge neutral three-flavour matter. In this paper we
concentrate on the first step process and solve the relativistic hydrodynamic
equations for the conversion front in presence of high magnetic field. Lorentz
force due to magnetic field is included in the energy momentum tensor by
averaging over the polar angles. We find that for an initial dipole
configuration of the magnetic field with a sufficiently high value at the
surface, velocity of the front increases considerably.Comment: 16 pages, 4 figures, same as published version of JPG, J. Phys. G:
Nucl. Part. Phys. 39 (2012) 09520
Factorizations and Physical Representations
A Hilbert space in M dimensions is shown explicitly to accommodate
representations that reflect the prime numbers decomposition of M.
Representations that exhibit the factorization of M into two relatively prime
numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)),
and related representations termed representations (together with
their conjugates) are analysed, as well as a representation that exhibits the
complete factorization of M. In this latter representation each quantum number
varies in a subspace that is associated with one of the prime numbers that make
up M
Quantum Impurity Entanglement
Entanglement in J_1-J_2, S=1/2 quantum spin chains with an impurity is
studied using analytic methods as well as large scale numerical density matrix
renormalization group methods. The entanglement is investigated in terms of the
von Neumann entropy, S=-Tr rho_A log rho_A, for a sub-system A of size r of the
chain. The impurity contribution to the uniform part of the entanglement
entropy, S_{imp}, is defined and analyzed in detail in both the gapless, J_2 <=
J_2^c, as well as the dimerized phase, J_2>J_2^c, of the model. This quantum
impurity model is in the universality class of the single channel Kondo model
and it is shown that in a quite universal way the presence of the impurity in
the gapless phase, J_2 <= J_2^c, gives rise to a large length scale, xi_K,
associated with the screening of the impurity, the size of the Kondo screening
cloud. The universality of Kondo physics then implies scaling of the form
S_{imp}(r/xi_K,r/R) for a system of size R. Numerical results are presented
clearly demonstrating this scaling. At the critical point, J_2^c, an analytic
Fermi liquid picture is developed and analytic results are obtained both at T=0
and T>0. In the dimerized phase an appealing picure of the entanglement is
developed in terms of a thin soliton (TS) ansatz and the notions of impurity
valence bonds (IVB) and single particle entanglement (SPE) are introduced. The
TS-ansatz permits a variational calculation of the complete entanglement in the
dimerized phase that appears to be exact in the thermodynamic limit at the
Majumdar-Ghosh point, J_2=J_1/2, and surprisingly precise even close to the
critical point J_2^c. In appendices the relation between the finite temperature
entanglement entropy, S(T), and the thermal entropy, S_{th}(T), is discussed
and and calculated at the MG-point using the TS-ansatz.Comment: 62 pages, 27 figures, JSTAT macro
Attractor Flows in st^2 Black Holes
Following the same treatment of Bellucci et.al., we obtain the hitherto
unknown general solutions of the radial attractor flow equations for extremal
black holes, both for non-BPS with non-vanishing and vanishing central charge Z
for the so-called st^2 model, the minimal rank-2 N=2 symmetric supergravity in
d=4 space-time dimensions.
We also make useful comparisons with results that already exist in
literature,and introduce the fake supergravity (first-order) formalism to be
used in our analysis. An analysis of the BPS bound all along the non-BPS
attractor flows and of the marginal stability of corresponding D-brane charge
configurations has also been presented.Comment: 59 pages,Latex. arXiv admin note: substantial text overlap with
arXiv:0807.3503 by other author
Nerve growth factor induces neurite outgrowth of PC12 cells by promoting Gβγ-microtubule interaction
Background: Assembly and disassembly of microtubules (MTs) is critical for neurite outgrowth and differentiation. Evidence suggests that nerve growth factor (NGF) induces neurite outgrowth from PC12 cells by activating the receptor tyrosine kinase, TrkA. G protein-coupled receptors (GPCRs) as well as heterotrimeric G proteins are also involved in regulating neurite outgrowth. However, the possible connection between these pathways and how they might ultimately converge to regulate the assembly and organization of MTs during neurite outgrowth is not well understood. Results: Here, we report that Gβγ, an important component of the GPCR pathway, is critical for NGF-induced neuronal differentiation of PC12 cells. We have found that NGF promoted the interaction of Gβγ with MTs and stimulated MT assembly. While Gβγ-sequestering peptide GRK2i inhibited neurite formation, disrupted MTs, and induced neurite damage, the Gβγ activator mSIRK stimulated neurite outgrowth, which indicates the involvement of Gβγ in this process. Because we have shown earlier that prenylation and subsequent methylation/demethylation of γ subunits are required for the Gβγ-MTs interaction in vitro, small-molecule inhibitors (L-28 and L-23) targeting prenylated methylated protein methyl esterase (PMPMEase) were tested in the current study. We found that these inhibitors disrupted Gβγ and ΜΤ organization and affected cellular morphology and neurite outgrowth. In further support of a role of Gβγ-MT interaction in neuronal differentiation, it was observed that overexpression of Gβγ in PC12 cells induced neurite outgrowth in the absence of added NGF. Moreover, overexpressed Gβγ exhibited a pattern of association with MTs similar to that observed in NGF-differentiated cells. Conclusions: Altogether, our results demonstrate that βγ subunit of heterotrimeric G proteins play a critical role in neurite outgrowth and differentiation by interacting with MTs and modulating MT rearrangement. Electronic supplementary material The online version of this article (doi:10.1186/s12868-014-0132-4) contains supplementary material, which is available to authorized users
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