arXiv subjects

Orchidea Maria Lecian

Publications and source records attributed to Orchidea Maria Lecian.

At least 19 recordsLinked to original sources

arXiv2023

Cosmological-Billiards Groups and self-adjoint BKL Transfer Operators

Cosmological billiards arise as a map of the solution of the Einstein equations, when the most general symmetry for the metric tensor is hypothesized, and points are considered as spatially decoupled in the asymptotic limit towards the cosmological singularity, according to the BKL (Belinski Khalatnikov Lifshitz) paradigm. In $4=3+1$ dimensions, two kinds of cosmological billiards are considered: the so-called 'big billiard' which accounts for pure gravity, and the 'small billiard', which is a symmetry-reduced version of the previous one, and is obtained when the 'symmetry walls' are considered. The solution of Einstein field equations is this way mapped to the (discrete) Poincaré map of a billiard ball on the sides of a triangular billiard table, in the Upper Poincaré Half Plane (UPHP). The billiard modular group is the scheme within which the dynamics of classical chaotic systems on surfaces of constant negative curvature is analyzed. The periodic orbits of the two kinds of billiards are classified, according to the different symmetry-quotienting mechanisms. The differences with the description implied by the billiard modular group are investigated and outlined. In the quantum regime, the eigenvalues (i.e. the sign that wavefunctions acquire according to quantum BKL maps) for periodic phenomena of the BKL maps on the Maass wavefunctions are classified. The complete spectrum of the semiclassical operators which act as BKL map for periodic orbits is obtained. Differently form the case of the modular group, here it is shown that the semiclassical transfer operator for Cosmological Billiards is not only the adjoint operator of the one acting on the Maass waveforms, but that the two operators are the same \it{self-adjoint} operator, thus outlining a different approach to the Langlands Jaquet correspondence.

gr-qc↗

arXiv2023

Retrieval of phonemes and Kohonen algorithm

A phoneme-retrieval technique is proposed, which is due to the particular way of the construction of the network. An initial set of neurons is given. The number of these neurons is approximately equal to the number of typical structures of the data. For example if the network is built for voice retrieval then the number of neurons must be equal to the number of characteristic phonemes of the alphabet of the language spoken by the social group to which the particular person belongs. Usually this task is very complicated and the network can depend critically on the samples used for the learning. If the network is built for image retrieval then it works only if the data to be retrieved belong to a particular set of images. If the network is built for voice recognition it works only for some particular set of words. A typical example is the words used for the flight of airplanes. For example a command like the "airplane should make a turn of 120 degrees towards the east" can be easily recognized by the network if a suitable learning procedure is used.

cs.CL↗

arXiv2023

About some compression algorithms

We use neural network algorithms for finding compression methods of images in the framework of iterated function systems which is a collection of the transformations of the interval $(0, 1)$ satisfying suitable properties.

eess.IV↗

arXiv2023

Stellar dynamics within the virial theorem: asymptotic small-parameters time expansion of the Ermakov-Lewis-Leach invariant as an infinite series of conservation laws

The regime of undamped oscillations characterizing the stellar dynamics of virialised systems is analysed within the framework of a new approach to the study of the integrals of motion. The method is relevant as far as the cosmological implementation is concerned, as it applies to the calculations apt for any age of the evolution of the Universe starting from the epoch of non-Gaussianities until present time. The new method here developed is based on the asymptotic small-parameters expansion of the new expression of the Ermakov-Lewis-Leach integrals of motion; as a result, an infinite series of new conservation laws implies the uniqueness and existence of new integrals of motion; analytical examples are provided after the pulsed Plummer potential, the three instances of the pulsed Dehnen potentials, the pulsed harmonic potential, the Jaffe potential, the Hernquist potential, applied to the studied problem. Particular cases of complex potentials are therefore also comprehended in the analysis. The constants of motions descending from the conservation laws are demonstrated to depend on the virialised radius and on the virialised mass of the stellar system, independently of the potential used. Cosmological implementation is given within the framework of a generic Terzic'-Kandrup potential. Comparison with data analysis techniques are provided with.

math-ph↗

arXiv2019

Constraints on modified dispersion relations

Deviation from standard dispersion relations for electrons and photons in the form of an extra term proportional to an arbitrarily high power of momentum is studied. It is shown that observational constraints lead to a region in the parametric space that is similar in shape to the region obtained earlier in a theory in which the extra term was proportional to third power of momentum.

gr-qc↗

arXiv2018

Remarks on the Bojowald--Paily paper Deformed general relativity

A couple of technicalities in the paper M. Bojowald, G. Paily, Phys. Rev. D 87, 044044 (2013) are discussed. The explicit formula given there for the function entering the modified hypersurface-deformed algebra, which presumably originates in loop quantum gravity, seems to be oversimplified, and the embedding of deformed special relativity in deformed general relativity proposed there for spherically symmetric models raises some questions as well.

gr-qc↗

arXiv2018

Modular structures and extended-modular-group-structures after Hecke pairs

The simplices and the complexes arsing form the grading of the fundamental (desymmetrized) domain of arithmetical groups and non-arithmetical groups, as well as their extended (symmetrized) ones are described also for oriented manifolds in dim greater than 2. The conditions for the definition of fibers are summarized after Hamiltonian analysis, the latters can in some cases be reduced to those for sections for graded groups, such as the Picard groups and the Vinberg group.The cases for which modular structures rather than modular-groupstructure measures can be analyzed for non-arithmetic groups, i.e. also in the cases for which Gelfand triples (rigged spaces) have to be substituted by Hecke couples, as, for Hecke groups, the existence of intertwining operators after the calculation of the second commutator within the Haar measures for the operators of the correspondingly-generated C-[star] algebras is straightforward. The results hold also for (also non-abstract) groups with measures on (manifold) boundaries. The Poincaré invariance of the representation of Wigner-Bargmann (spin 1/2) particles is analyzed within the Fock-space interaction representation. The well-posed-ness of initial conditions and boundary ones for the connected (families of) equations is discussed. As an example, Picard-related equations can be classified according to the genus of the modular curve(s) attached to the solutions(s). From the Hamiltonian analysis, further results in the contraction of the congruence (extended sub-)groups for non-arithmetical groups for the construction of tori is provided as an alternative to the free diffeomorphism group. In addition, the presence of Poincaré complexes is found compatible with non-local interactions, i.e. both lattices interactions or spin-like ones.

math-ph↗

arXiv2018

Gedanken Tests for Correlated Michelson Interferometers (One- interferometer tests and two-interferometer tests: the role of cosmologically-implemented models including Poincaré particles)

The features of correlated Michelson interferometers are for describing the analysis of Einsteinian spacetime models, and the quantum geometries pertinent with descriptions of GR compatible with particle Physics. Such apparati allow for the spectral decomposition of fractional Planck-scale displacements correlations and fractional Plancktime- interval correlations for kinematical investigations in particle Physics on emerging Minkowski background, and for models which admit GR as a limit after cosmological implementations for Poincaré particles content.

gr-qc↗

arXiv2017

Geometry of the generical cosmological solution before the singularity limit

The generic cosmological solution is analyzed both for the non-asymptotic limit to the cosmological singularity and in the asymptotic limit analytically. The Bianchi I solution and the Bianchi IX solution, described as a sequence of Bianchi I reparameterized solutions, are analyzed with respect to the asymptotic symmetry implied by the space part of the metric tensor. Numerical studies are explained. The semiclassical regime is proposed by using the degrees of freedom for the initial conditions to the Einstein field equations, i.e. those which are not necessarily characterizing for a Bianchi scheme. The appropriate homegeneization techniques and the de-homogenization techniques referred to a generic system of PDE's are discussed and applied to the affine (Misner) space containing the dynamics pertinent to the Hamiltonian problem associated to the solution of the Hamiltonian constraint. The asymptotic limit to the cosmological singularity for the generic cosmological solution is implemented within the asymptotic Kasner parametrization of the BKL approach and for the Misner-Chitre formalism. The EFE in the Misner-Chitre approach imply constraints on the non-asymptotical degrees of freedom, which allow one to define classes of solutions on the anisotropy plane.

gr-qc↗

arXiv2017

Semiclassical Length Measure from a Quantum-Gravity Wave Function

The definition of a length operator in quantum cosmology is usually influenced by a~quantum theory for gravity considered. The semiclassical limit at the Planck age must meet the requirements implied in present observations. The features of a semiclassical wave-functional state are investigated, for which the modern measure(ment)s is consistent. The results of a length measurement at present times are compared with the same measurement operation at cosmological times. By this measure, it is possible to discriminate, within the same Planck-length expansion, the corrections to a Minkowski flat space possibly due to classicalization of quantum phenomena at the Planck time and those due to possible quantum-gravitational manifestations of present times. This~analysis and the comparison with the previous literature can be framed as a test for the verification of the time at which anomalies at present related to the gravitational field, and, in particular, whether they are ascribed to the classicalization epoch. Indeed, it allows to discriminate not only within the possible quantum features of the quasi (Minkowski) flat spacetime, but also from (possibly Lorentz violating) phenomena detectable at high-energy astrophysical scales. The results of two different (coordinate) length measures have been compared both at cosmological time and as a perturbation element on flat Minkowski spacetime. The differences for the components of the corresponding classical(ized) metric tensor have been analyzed at different orders of expansions. The comparison of the results of (straight) length measures in two different directions, in particular, can encode the pertinent information about the parameters defining the semiclassical wavefunctional for (semiclassicalized) gravitational field.

gr-qc↗

arXiv2016

Spacetime-noncommutativity regime of Loop Quantum Gravity

A recent study by Bojowald and Paily provided a path toward the identification of an effective quantum-spacetime picture of Loop Quantum Gravity, applicable in the "Minkowski regime", the regime where the large-scale (coarse-grained) spacetime metric is flat. A pivotal role in the analysis is played by Loop-Quantum-Gravity-based modifications to the hypersurface deformation algebra, which leave a trace in the Minkowski regime. We here show that the symmetry-algebra results reported by Bojowald and Paily are consistent with a description of spacetime in the Minkowski regime given in terms of the $κ$-Minkowski noncommutative spacetime, whose relevance for the study of the quantum-gravity problem had already been proposed for independent reasons.

gr-qc↗

arXiv2013

Semiclassical and quantum behavior of the Mixmaster model in the polymer approach

We analyze the quantum dynamics of the Bianchi Type IX model, as described in the so-called polymer representation of quantum mechanics, to characterize the modifications that a discrete na- ture in the anisotropy variables of the Universe induces on the morphology of the cosmological sin- gularity. We first perform a semiclassical analysis, to be regarded as the zeroth-order approximation of a WKB (Wentzel-Kramers-Brillouin) approximation of the quantum dynamics, and demonstrate how the features of polymer quantum mechanics are able to remove the chaotic properties of the Bianchi IX dynamics. Then, we address the study of the full quantum dynamics of this model in the polymer representation and analyze the two cases, in which the Bianchi IX spatial curvature does not affect the wave-packet behavior, as well as the instance, for which it plays the role of an infinite potential confining the dynamics of the anisotropic variables. The main development of this analysis consists of investigating how, differently from the standard canonical quantum evolution, the high quantum number states are not preserved arbitrarily close to the cosmological singularity. This property emerges as a consequence, on one hand, of the no longer chaotic features of the classical dynamics (on which the Misner analysis is grounded), and, on the other hand, of the impossibility to remove the quantum effect due to the spatial curvature. In the polymer picture, the quantum evolution of the Bianchi IX model remains always significantly far from the semiclassical behavior, as far as both the wave-packet spread and the occupation quantum numbers are concerned. As a result, from a quantum point of view, the Mixmaster dynamics loses any predictivity characterization for the discrete nature of the Universe anisotropy.

gr-qc↗

arXiv2013

Periodic orbits in cosmological billiards: the Selberg trace formula for asymptotic Bianchi IX universes, evidence for scars in the wavefunction of the quantum universe and large-scale structure anisotropies of the present universe

The Selberg trace formula is specified for cosmological billiards in $4=3+1$ spacetime dimensions. The spectral formula is rewritten as an exact sum over the initial conditions for the Einstein field equations for which periodic orbits are implied. For this, a suitable density of measure invariant under the billiard maps has been defined, within the statistics implied by the BKL paradigm. The trace formula has also been specified for the stochastic limit of the dynamics, where the sum over initial conditions has been demonstrated to be equivalent to a sum over suitable symmetry operations on the generators of the groups that define the billiard dynamics, and acquires different features for the different statistical maps. Evidence for scars at the quantum regime is provided. The validity of the Selberg trace formula at the classical level and in the quantum regime enforces the validity of the semiclassical descriptions of these systems, thus offering further elements for the comparison of quantum-gravity effects and the present observed structure of the universe. This procedure also constitutes a new approach in hyperbolic geometry for the application of the Selberg trace formula for a chaotic system whose orbits are associated to precise statistical distributions, for both billiard tables corresponding to the desymmetrized fundamental domain and to that a a congruence subgroup of it.

gr-qc↗

arXiv2013

Stochastization of BKL dynamics and Anisotropic Sky Patterns

The dynamics of cosmological billiards in $4=3+1$ spacetime dimensions is analyzed; the different statistical maps are characterized within the stochastic limit, reached after a large number of iterations of the billiard maps. New densities of invariant measures have been established, also for billiard systems which contain symmetry walls, according to the content of Weyl reflections in the maps, which account for the change of sign of the non-oscillating scale factors in the solution to the Einstein field equations. The statistical equivalence between the big billiard and the small billiard, posed in [Phys. Rev. D83, 044038 (2011)], is here proven by means of these new definitions of probabilities for the small billiard. Further new classes of BKL probabilities have also been defined especially for the one-variable map and for the two-variable map, for the early-time BKL dynamics, for a stochastizing BKL dynamics and for a completely stochastized dynamics, both for the big billiard and for the small billiard. The trajectories have been classified according to these new probabilties, and different specifications of probabilties comparing classes of initial conditions have been assigned for the stochastization of the dynamics. As a result, is is possible to establish a definition of BKL probabilities for the unquotiented dynamics of the big billiard, where the different patterns of Weyl reflections are encoded. The statistical description of BKL probabilities for the occurrence of a given number of epochs in each era are therefore further characterized by the most probable number of Weyl reflections contained in such eras, which is inferred from the implications of the billiard maps on the UPHP. These new constructions have been considered for the determination of the connection between the observed values of anisotropy by a stochastic limit of the BKL dynamics.

gr-qc↗

arXiv2013

BKL maps and Poincaré sections

Cosmological billiards arise as a map of the solution to the Einstein equations, when the most general symmetry of the metric tensor is implemented, under the BKL (named after Belinskii, Khalatnikov and Lifshitz) paradigm, for which points are spatially decoupled in the asymptotical limit close to the cosmological singularity. Cosmological billiards in $4=3+1$ dimensions for the case of pure gravity are analyzed for those features, for which the content of Weyl reflections in the BKL maps requires definition of a 3-dimensional restricted phase space. The role of Poincaré sections in these processes is outlined. The quantum regime is investigated within this framework: as a result, 1-epoch BKL eras are found to be the most probable configuration at which the wavefunctions have to be evaluated; furthermore, BKL eras containing $n>>1$ epochs are shown to be a less probable configuration for the wavefunctions. This description of the dynamics allows one to gain information about the connections between the statistical characterization of the maps which imply the different symmetry-quotienting mechanisms and the characterization of the semiclassical limit of the wavefunctions for the classical trajectories, for which the phenomenon of 'scars' on the wavefunction is found for other kinds of billiards.

gr-qc↗

arXiv2013

Reflections on the hyperbolic plane

The most general solution to the Einstein equations in $4=3+1$ dimensions in the asymptotical limit close to the cosmological singularity under the BKL (Belinski-Khalatnikov-Lifshitz) hypothesis, for which space gradients are neglected and time derivatives only are considered, can be visualized by the behavior of a billiard ball in a triangular domain on the Upper Poincaré Half Plane (UPHP). The behavior of the billiard system (named 'big billiard') can be schematized by dividing the succesions of trajectories according to Poincaré return map on the sides of the billiard table, according to the paradigms implemented by the BKL investigation and by the CB-LKSKS (Chernoff- Barrow- Lifshitz- Khalatnikov- Sinai- Khanin- Shchur) one. Different maps are obtained, according to different symmetry-quotienting mechanisms used to analyze the dynamics according to the symmetries of the billiard domain and to the features of the geodesics on the UPHP. In the inhomogenous case, new structures have been uncovered, such that, in this framework, the billiard table (named 'small billiard') consists of 1/6 of the previous one. The connections between the symmetry-quotienting mechanisms are further investigated on the UPHP. The relation between the complete billiard and the small billiard are also further explained according to the role of Weyl reflections. The quantum properties of the system are sketched as well, and the physical interpretation of the wavefunction is further developped. In particular, a physical interpretation for the symmetry-quotienting maps is proposed, according to the Fourier decomposition of the energy levels of the wavefunction of the universe, as far as the meaning of epochs and eras is concerned from a quantum point of view.

gr-qc↗

arXiv2013

Novel Analysis of Spinor Interactions and non-Riemannian Geometry

A novel analysis of the gauge theory of the local Lorentz group is implemented both in flat and in curved space-time, and the resulting dynamics is analyzed in view of the geometrical interpretation of the gauge potential. The Yang-Mills picture of local Lorentz transformations is first approached in a second-order formalism. For the Lagrangian approach to reproduce the second Cartan structure equation as soon as the Lorentz gauge connections are identified with the contortion tensor, an interaction term between the Lorentz gauge fields and the spin connections has to be postulated. The full picture involving gravity, torsion and spinors is described by a coupled set of field equations, which allows one to interpret both gravitational spin connections and matter spin density as the source term for the Yang-Mills equations. The contortion tensor acquires a propagating character, because of its non-Abelian feature, and the pure contact interaction is restored in the limit of vanishing Lorentz connections.

hep-th↗

arXiv2011

Non-analytical power law correction to the Einstein-Hilbert action: gravitational wave propagation

We analyze the features of the Minkowskian limit of a particular non-analytical f(R) model, whose Taylor expansion in the weak field limit does not hold, as far as gravitational waves (GWs) are concerned. We solve the corresponding Einstein equations and we find an explicit expression of the modified GWs as the sum of two terms, i.e. the standard one and a modified part. As a result, GWs in this model are not transverse, and their polarization is different from that of General Relativity. The velocity of the GW modified part depends crucially on the parameters characterizing the model, and it mostly results much smaller than the speed of light. Moreover, this investigation allows one to further test the viability of this particular f(R) gravity theory as far as interferometric observations of GWs are concerned.

gr-qc↗