Affine Quantization on the Half Line

The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of conventional quantum mechanics over Rn but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half-line. We formulate and solve some simple models, the free particle and the harmonic oscillator.

Transitions to Equilibrium State in Classical φ4 Lattice

Statistical behavior of a classical φ4 Hamiltonian lattice is investigated from microscopic dynamics. Thelargest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system.It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitionsto equipartitions, and the scaling behaviors of these lower and upper critical couplings vs. the system size are numericallyobtained.

Low-temperature catalytic methane deep oxidation over sol-gel derived mesoporous hausmannite (Mn_(3)O_(4)) spherical particles

In this study,Mn_(3)O_(4) spherical particles(SPs)were synthesized by the sol-gel process,after which they were thermally annealed at 400℃,and comprehensively characterized.X-ray Diffraction(XRD)revealed that Mn_(3)O_(4) exhibited a tetragonal spinel structure,and Fourier transformed infrared(FTIR)spectroscopy identified surfaceadsorbed functional groups.Scanning electron microscopy(SEM)and the specific surface area analyses by Brunauer−Emmett−Teller(BET)revealed a porous,homogeneous surface composed of strongly agglomerated spherical grains with an estimated average particle size of∼35 nm,which corresponded to a large specific surface area of∼81.5 m^(2)/g.X-ray photoelectron spectroscopy(XPS)analysis indicated that Mn_(3)O_(4) was composed of metallic cations(Mn^(4+),Mn^(3)+,and Mn^(2+))and oxygen species(O_(2)−,OH−and CO_(3)^(2−)).The optical bandgap energy is∼2.55 eV.Assessment of the catalytic performance of the Mn_(3)O_(4) SPs indicated T90 conversion of CH4 to CO_(2) and H_(2)O at 398℃ for gas hourly space velocity(GHSV)of 72000 mL^(3) g^(−1) h^(−1).This observed performance can be attributed to the cooperative effects of the smallest spherical grain size with a mesoporous structure,which is responsible for the larger specific surface area and available surface-active oxygenated species.The cooperative effect of the good reducibility,higher ratio of active species(OLat/OAds),and results of density functional theory(DFT)calculations suggested that the total oxidation of CH_(4) over the mesoporous Mn_(3)O_(4) SPs might take place via a two-term process in which both the Langmuir−Hinshelwood and Mars−van Krevelen mechanisms are cooperatively involved.