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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 added

In cluster physics a single particle potential to determine the microscopic part of the total energy of a collective configuration is necessary to calculate the shell- and pairing effects. In this paper we investigate the properties of the Riesz fractional integrals and compare their properties with the standard Coulomb and Yukawa potentials commonly used. It is demonstrated, that Riesz potentials may serve as a promising extension of standard potentials and may be reckoned as a smooth transition from Coulomb to Yukawa like potentials, depending of the fractional parameter $\alpha$. For the macroscopic part of the total energy the Riesz potentials treat the Coulomb-, symmetry- and pairing-contributions from a generalized point of view, since they turn out to be similar realizations of the same fractional integral at distinct $\alpha$ values., Comment: final version

Polymeric methyltrioxorhenium, {(CH_{3})_{0.92}ReO_{3}}_{\infty} (poly-MTO), is the first member of a new class of organometallic hybrids which adopts the structural pattern and physical properties of classical perovskites in two dimensions (2D). We demonstrate how the electronic structure of poly-MTO can be tailored by intercalation of organic donor molecules, such as tetrathiafulvalene (TTF) or bis-(ethylendithio)-tetrathiafulvalene (BEDT-TTF), and by the inorganic acceptor SbF$_3$. Integration of donor molecules leads to a more insulating behavior of poly-MTO, whereas SbF$_3$ insertion does not cause any significant change in the resistivity. The resistivity data of pure poly-MTO is remarkably well described by a two-dimensional electron system. Below 38 K an unusual resistivity behavior, similar to that found in doped cuprates, is observed: The resistivity initially increases approximately as $\rho \sim$ ln$(1/T$) before it changes into a $\sqrt{T}$ dependence below 2 K. As an explanation we suggest a crossover from purely two-dimensional charge-carrier diffusion within the \{ReO$_2$\}$_{\infty}$ planes at high temperatures to three-dimensional diffusion at low temperatures in a disorder-enhanced electron-electron interaction scenario (Altshuler-Aronov correction). Furthermore, a linear positive magnetoresistance was found in the insulating regime, which is caused by spatial localization of itinerant electrons at some of the Re atoms, which formally adopt a $5d^1$ electronic configuration. X-ray diffraction, IR- and ESR-studies, temperature dependent magnetization and specific heat measurements in various magnetic fields suggest that the electronic structure of poly-MTO can safely be approximated by a purely 2D conductor., Comment: 15 pages, 16 figures, 2 tables

The definition of the standard differential operator is extended from integer steps to arbitrary stepsize. The classical, nonrelativistic Hamiltonian is quantized, using these new continuous operators. The resulting Schroedinger type equation generates free particle solutions, which are confined in space. The angular momentum eigenvalues are calculated algebraically. It is shown, that the charmonium spectrum may be classified by the derived angular momentum eigenvalues for stepsize=2/3., Comment: 11 pages, 2 figures

Polymeric methyltrioxorhenium (poly-MTO) represents the first example of an inherent conducting organometallic oxide. It adopts the structural motives and transport properties of some classical perovskites in two dimensions. In this study we present resistivity data down to 30 mK which exhibit a crossover from a metallic (d$\rho$/d$T >$ 0) to an insulating (d$\rho$/d$T <$ 0) behavior at about 30 K. Below 30 K an unusual resistivity behavior, similar to that of some doped cuprate systems, is observed: initially the resistivity increases approximately as $\rho \sim$ log$(1/T$) before it starts to saturate below 2 K. Furthermore, a linear positive magnetoresistance is found (up to 7 T). Temperature dependent magnetization and specific heat measurements in various magnetic fields indicate that the unusual resistivity behavior may be driven by spatial localization of the d$^1$ moments at the Re atoms., Comment: 2 pages, 2 figures

Polymeric methyltrioxorhenium (poly-MTO) is the first member of a new class of organometallic hybrids which adopts the structural motives and physical properties of classical perowskites in two dimensions. In this study we demonstrate how the electronic structure of poly-MTO can be tailored by intercalation of organic donor molecules such as tetrathiafulvalene (TTF). With increasing donor intercalation the metallic behavior of the parent compound, (CH$_{3}$)$_{0.92}$ReO$_{3} \cdot x%$ TTF ($x = 0$) becomes suppressed leading to an insulator at donor concentrations $x$ larger than 50. Specific heat, electric resistance and magnetic susceptibility studies indicate that an increasing amount of TTF causes the itinerant electrons of the poly-MTO matrix to localize., Comment: 2 pages, 3 figures, SCES04