On the origin of space

Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension $d$ of space evolves smoothly with time in the range 0 <= d(t) <=3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.Comment: 14 pages 3 figures, some clarifications adde

Quantum properties of two-dimensional electron gas in the inversion layer of Hg1−xCdxTe bicyrstals

The electronic and magnetotransport properties of conduction electrons in the grain boundary interface of p-type Hg1−xCdxTe bicrystals are investigated. The results clearly demonstrate the existence of a two-dimensional degenerate n-type inversion layer in the vicinity of the grain boundary. Hydrostatic pressure up to 103 MPa is used to characterize the properties of the two-dimensional electron gas in the inversion layer. At atmospheric pressure three series of quantum oscillations are revealled, indicating that tthree electric subbands are occupied. From quantum oscilations of the magnetoresistivity the characteristics parameters of the electric subbands (subband populations nsi, subband energies EF−Ei, effective electron masses m*ci) and their pressure dependences are established. A strong decrease of the carrier concentration in the inversion layer and of the corresponding subband population is observed when pressure is applied A simple theoretical model based on the triangular-well approximation and taking into account the pressure dependence of the energy band structure of Hg1−xCdxTe is use to calculate the energy band diagram of the quantum well and the pressure dependence of the subband parameters

Time-resolved Microwave Conductivity. Part 2.-Quantum-sized TiO_2 and the Effect of Adsorbates and Light Intensity on Charge-carrier Dynamics

Charge-carrier recombination dynamics after a pulsed laser excitation are investigated by time-resolved microwave conductivity (TRMC) for quantum-sized (Q-) TiO_2 and P25, a bulk-phase TiO_2. Adsorbed scavengers such as HNO_3, HC, HCIO_4, isopropyl alcohol, trans-decalin, tetranitromethane, and methyl viologen dichloride result in different charge-carrier recombination dynamics for Q-TiO_2 and P25. The differences include a current doubling with isopropyl alcohol for which electron injection into Q-TiO_2 is much slower than into P25 and relaxation of the selection rules of an indirect-bandgap semiconductor due to size quantization. However, the faster interfacial charge transfer predicted for Q-TiO_2 due to a 0. 2 eV gain in redox overpotentials is not observed. The effect of light intensity is also investigated. Above a critical injection level, fast recombination channels are opened, which may be a major factor resulting in the dependence of the steady-state photolysis quantum yields on l^(–1/2). The fast recombination channels are opened at lower injection levels for P25 than for Q-TiO_2, and a model incorporating the heterogeneity of surface-hole traps is presented