48,509 research outputs found
Special complex manifolds
We introduce the notion of a special complex manifold: a complex manifold
(M,J) with a flat torsionfree connection \nabla such that (\nabla J) is
symmetric. A special symplectic manifold is then defined as a special complex
manifold together with a \nabla-parallel symplectic form \omega . This
generalises Freed's definition of (affine) special K\"ahler manifolds. We also
define projective versions of all these geometries. Our main result is an
extrinsic realisation of all simply connected (affine or projective) special
complex, symplectic and K\"ahler manifolds. We prove that the above three types
of special geometry are completely solvable, in the sense that they are locally
defined by free holomorphic data. In fact, any special complex manifold is
locally realised as the image of a holomorphic 1-form \alpha : C^n \to T^* C^n.
Such a realisation induces a canonical \nabla-parallel symplectic structure on
M and any special symplectic manifold is locally obtained this way. Special
K\"ahler manifolds are realised as complex Lagrangian submanifolds and
correspond to closed forms \alpha. Finally, we discuss the natural geometric
structures on the cotangent bundle of a special symplectic manifold, which
generalise the hyper-K\"ahler structure on the cotangent bundle of a special
K\"ahler manifold.Comment: 24 pages, latex, section 3 revised (v2), modified Abstract and
Introduction, version to appear in J. Geom. Phy
Subspaces of a para-quaternionic Hermitian vector space
Let be a para-quaternionic Hermitian structure on the real
vector space . By referring to the tensorial presentation , we
give an explicit description, from an affine and metric point of view, of main
classes of subspaces of which are invariantly defined with respect to the
structure group of and respectively
Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench
At thermal equilibrium, the concept of effective central charge for massive
deformations of two-dimensional conformal field theories (CFT) is well
understood, and can be defined by comparing the partition function of the
massive model to that of a CFT. This temperature-dependent effective charge
interpolates monotonically between the central charge values corresponding to
the IR and UV fixed points at low and high temperatures, respectively. We
propose a non-equilibrium, time-dependent generalization of the effective
central charge for integrable models after a quantum quench, ,
obtained by comparing the return amplitude to that of a CFT quench. We study
this proposal for a large mass quench of a free boson, where the charge is seen
to interpolate between at , and at
, as is expected. We use our effective charge to define an "Ising
to Tricritical Ising" quench protocol, where the charge evolves from at , to at , the corresponding
values of the first two unitary minimal CFT models. We then argue that the
inverse "Tricritical Ising to Ising" quench is impossible with our methods.
These conclusions can be generalized for quenches between any two adjacent
unitary minimal CFT models. We finally study a large mass quench into the
"staircase model" (sinh-Gordon with a particular complex coupling). At short
times after the quench, the effective central charge increases in a discrete
"staircase" structure, where the values of the charge at the steps can be
computed in terms of the central charges of unitary minimal CFT models. When
the initial state is a pure state, one always finds that , though , generally
oscillates at finite times. We explore how this constraint may be related to RG
flow irreversibility.Comment: Some discussion modified. Title slightly modified. References added.
Scipost submissio
Confinement-Higgs Phase Crossover as a Lattice Artifact in 1+1 Dimensions
We examine the phase structure of massive Yang-Mills theory in 1+1
dimensions. This theory is equivalent to a gauged principal chiral sigma model.
It has been previously shown that the gauged theory has only a confined phase,
and no Higgs phase in the continuum, and at infinite volume. There are no
massive gluons, but only hadron-like bound states of sigma-model particles. The
reason is that the gluon mass diverges, being proportional to the two-point
correlation function of the renormalized field of the sigma model at . We
use exact large- results to show that after introducing a lattice
regularization and typical values of the coupling constants used in Monte Carlo
simulations, the gluon mass becomes finite, and even sometimes small. A smooth
crossover into a Higgs phase can then appear. For small volumes and large ,
we find an analytic expression for the gluon mass, which depends on the
coupling constants and the volume. We argue that this Higgs phase is
qualitatively similar to the one observed in lattice computations at .Comment: Version accepted for publication in JHEP. Improved discussion of
results, references adde
Raman Spectroscopy on Plasmonic Materials: Recent Advances and Applications in Molecular detection
Plasmonic Enhancement of the electric field is the basis of the Surface-enhanced Raman Scattering technique (SERS). This technique is based on the localization of light in the nanoscale occurring in plasmonic materials and provides the best conditions for molecular detection, even single-molecule detection. This can only be achieved by the use of spectroscopy in the nanoscale. The building of functional nanostructured devices to obtain sensitive and selective platforms, with specific applications in molecular detection, biodiagnosis and Cultural Heritage is presented. Plasmonic effects are highly activated in nanostructures substrates containing tips or in interparticle gaps. The nanofabrication of metal nanoparticles with special morphology, such as nanostars is presented here for the specific case of silver. The functionalization with bifunctional molecules gives rise to highly active gaps that can be employed in the molecular detection of pollutants. Another important application of these nanostructured platforms is the functionalization with biological molecules for bioanalytical applications and the detection of colorants with interest for the Cultural Heritage.Universidad de Málaga. Campus de Excelencia Internacional AndalucÃa Tech
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