Conditional Symmetries, the True Degree of Freedom and G.C.T. Invariant Wave functions for the general Bianchi Type II Vacuum Cosmology

The quantization of the most general Bianchi Type II geometry -with all six scale factors, as well as the lapse function and the shift vector, present- is considered. In an earlier work, a first reduction of the initial 6-dimensional configuration space, to a 4-dimensional one, has been achieved by the usage of the information furnished by the quantum form of the linear constraints. Further reduction of the space in which the wave function -obeying the Wheeler-DeWitt equation- lives, is accomplished by unrevealling the extra symmetries of the Hamiltonian. These symmetries appear in the form of -linear in momenta- first integrals of motion. Most of these symmetries, correspond to G.C.T.s through the action of the automorphism group. Thus, a G.C.T. invariant wave function is found, which depends on the only true degree of freedom, i.e. the unique curvature invariant, characterizing the hypersurfaces t=const.Comment: 10 pages, no figures, LaTeX2e Typesetting syste

Automorphism Inducing Diffeomorphisms, Invariant Characterization of Homogeneous 3-Spaces and Hamiltonian Dynamics of Bianchi Cosmologies

An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented, by considering the action of the Automorphism Group on the configuration space of the real, symmetric, positive definite, $3\times 3$ matrices. Thus, the gauge degrees of freedom are removed and the remaining (gauge invariant) degrees, are the --up to 3-- curvature invariants. An apparent discrepancy between this Kinematics and the Quantum Hamiltonian Dynamics of the lower Class A Bianchi Types, occurs due to the existence of the Outer Automorphism Subgroup. This discrepancy is satisfactorily removed by exploiting the quantum version of some classical integrals of motion (conditional symmetries) which are recognized as corresponding to the Outer Automorphisms.Comment: 18 pages, LaTeX2e, no figures, one table, to appear in Communications in Mathematical Physic

Locally Homogeneous Spaces, Induced Killing Vector Fields and Applications to Bianchi Prototypes

An answer to the question: Can, in general, the adoption of a given symmetry induce a further symmetry, which might be hidden at a first level? has been attempted in the context of differential geometry of locally homogeneous spaces. Based on E. Cartan's theory of moving frames, a methodology for finding all symmetries for any n dimensional locally homogeneous space is provided. The analysis is applied to 3 dimensional spaces, whereby the embedding of them into a 4 dimensional Lorentzian manifold is examined and special solutions to Einstein's field equations are recovered. The analysis is mainly of local character, since the interest is focused on local structures based on differential equations (and their symmetries), rather than on the implications of, e.g., the analytic continuation of their solution(s) and their dynamics in the large.Comment: 27 pages, no figues, no tables, one reference added, spelling and punctuation issues correcte

Investigating laser induced phase engineering in MoS2 transistors

Phase engineering of MoS2 transistors has recently been demonstrated and has led to record low contact resistances. The phase patterning of MoS2 flakes with laser radiation has also been realized via spectroscopic methods, which invites the potential of controlling the metallic and semiconducting phases of MoS2 transistors by simple light exposure. Nevertheless, the fabrication and demonstration of laser patterned MoS2 devices starting from the metallic polymorph has not been demonstrated yet. Here, we study the effects of laser radiation on 1T/1T'-MoS2 transistors with the prospect of driving an in-situ phase transition to the 2H-polymorph through light exposure. We find that although the Raman peaks of 2H-MoS2 become more prominent and the ones from the 1T/1T' phase fade after the laser exposure, the semiconducting properties of the laser patterned devices are not fully restored and the laser treatment ultimately leads to degradation of the transport channel