11,707 research outputs found
Hybrid Quantum Cosmology: Combining Loop and Fock Quantizations
As a necessary step towards the extraction of realistic results from Loop
Quantum Cosmology, we analyze the physical consequences of including
inhomogeneities. We consider in detail the quantization of a gravitational
model in vacuo which possesses local degrees of freedom, namely, the linearly
polarized Gowdy cosmologies with the spatial topology of a three-torus. We
carry out a hybrid quantization which combines loop and Fock techniques. We
discuss the main aspects and results of this hybrid quantization, which include
the resolution of the cosmological singularity, the polymeric quantization of
the internal time, a rigorous definition of the quantum constraints and the
construction of their solutions, the Hilbert structure of the physical states,
and the recovery of a conventional Fock quantization for the inhomogeneities.Comment: 24 pages, published in International Journal of Modern Physics A,
Special Issue: Proceedings of the Second Workshop on Quantum Gravity and
Noncommutative Geometry (Lisbon, Portugal
Short periodic orbits theory for partially open quantum maps
We extend the semiclassical theory of short periodic orbits [Phys. Rev. E
{\bf 80}, 035202(R) (2009)] to partially open quantum maps. They correspond to
classical maps where the trajectories are partially bounced back due to a
finite reflectivity . These maps are representative of a class that has many
experimental applications. The open scar functions are conveniently redefined,
providing a suitable tool for the investigation of these kind of systems. Our
theory is applied to the paradigmatic partially open tribaker map. We find that
the set of periodic orbits that belong to the classical repeller of the open
map () are able to support the set of long-lived resonances of the
partially open quantum map in a perturbative regime. By including the most
relevant trajectories outside of this set, the validity of the approximation is
extended to a broad range of values. Finally, we identify the details of
the transition from qualitatively open to qualitatively closed behaviour,
providing an explanation in terms of short periodic orbits.Comment: 6 pages, 4 figure
Further Improvements in the Understanding of Isotropic Loop Quantum Cosmology
The flat, homogeneous, and isotropic universe with a massless scalar field is
a paradigmatic model in Loop Quantum Cosmology. In spite of the prominent role
that the model has played in the development of this branch of physics, there
still remain some aspects of its quantization which deserve a more detailed
discussion. These aspects include the kinematical resolution of the
cosmological singularity, the precise relation between the solutions of the
densitized and non-densitized versions of the quantum Hamiltonian constraint,
the possibility of identifying superselection sectors which are as simple as
possible, and a clear comprehension of the Wheeler-DeWitt (WDW) limit
associated with the theory in those sectors. We propose an alternative operator
to represent the Hamiltonian constraint which is specially suitable to deal
with these issues in a satisfactory way. In particular, with our constraint
operator, the singularity decouples in the kinematical Hilbert space and can be
removed already at this level. Thanks to this fact, we can densitize the
quantum Hamiltonian constraint in a rigorous manner. Besides, together with the
physical observables, this constraint superselects simple sectors for the
universe volume, with a support contained in a single semiaxis of the real line
and for which the basic functions that encode the information about the
geometry possess optimal physical properties. Namely, they provide a
no-boundary description around the cosmological singularity and admit a
well-defined WDW limit in terms of standing waves. Both properties explain the
presence of a generic quantum bounce replacing the singularity at a fundamental
level, in contrast with previous studies where the bounce was proved in
concrete regimes and focusing on states with a marked semiclassical behavior.Comment: 13 pages, version accepted for publication in Physical Review
The scar mechanism revisited
Unstable periodic orbits are known to originate scars on some eigenfunctions
of classically chaotic systems through recurrences causing that some part of an
initial distribution of quantum probability in its vicinity returns
periodically close to the initial point. In the energy domain, these
recurrences are seen to accumulate quantum density along the orbit by a
constructive interference mechanism when the appropriate quantization (on the
action of the scarring orbit) is fulfilled. Other quantized phase space
circuits, such as those defined by homoclinic tori, are also important in the
coherent transport of quantum density in chaotic systems. The relationship of
this secondary quantum transport mechanism with the standard mechanism for
scarring is here discussed and analyzed.Comment: 6 pages, 6 figure
The role of short periodic orbits in quantum maps with continuous openings
We apply a recently developed semiclassical theory of short periodic orbits
to the continuously open quantum tribaker map. In this paradigmatic system the
trajectories are partially bounced back according to continuous reflectivity
functions. This is relevant in many situations that include optical
microresonators and more complicated boundary conditions. In a perturbative
regime, the shortest periodic orbits belonging to the classical repeller of the
open map - a cantor set given by a region of exactly zero reflectivity - prove
to be extremely robust in supporting a set of long-lived resonances of the
continuously open quantum maps. Moreover, for step like functions a significant
reduction in the number needed is obtained, similarly to the completely open
situation. This happens despite a strong change in the spectral properties when
compared to the discontinuous reflectivity case.Comment: 6 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1604.0181
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