A Dynamical System with Q-deformed Phase Space Represented in Ordinary Variable Spaces

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a difference operator instead of the differential operator. Then, using the path integral representation for such a dynamical system, we derive an effective short-time action, which contains interaction terms even for a free particle with q-deformed phase space. Analysis is also made on the eigenvalue problem for a particle with q-deformed phase space confined in a compact space. Under some boundary conditions of the compact space, there arises fairly different structures from $q=1$ case in the energy spectrum of the particle and in the corresponding eigenspace .Comment: 17page, 2 figure

5 Dimensional Spacetime with q-deformed Extra Space

An attempt to get a non-trivial-mass structure of particles in a Randall-Sundrum type of 5-dimensional spacetime with q-deformed extra dimension is discussed. In this spacetime, the fifth dimensional space is boundary free, but there areises an elastic potential preventing free motion toward the fifth direction. The q-deformation is, then, introduced in such a way that the spacetime coordinates become non-commutative between 4-dimensional components and the fifth component. As a result of this q-deformation, there arises naturally an ultraviolet-cutoff effect for the propagators of particles embedded in this spacetime.Comment: 14 pages, Latex file, 2 eps figure

Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length `a' is computed for given particle density `n.' Variational perturbation theory is used to resum the corresponding perturbative series for Delta/Nu in a classical three-dimensional scalar field theory with coupling `u' and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop perturbative coefficients, extending earlier work by one loop order.Comment: 8 pages; typos and errors of presentation fixed; beautifications; results unchange

AA-cation control of magnetoelectric quadrupole order in AA(TiO)Cu4_4(PO4_4)4_4 (AA = Ba, Sr, and Pb)

Ferroic magnetic quadrupole order exhibiting macroscopic magnetoelectric activity is discovered in the novel compound $A$(TiO)Cu$_4$(PO$_4$)$_4$ with $A$ = Pb, which is in contrast with antiferroic quadrupole order observed in the isostructural compounds with $A$ = Ba and Sr. Unlike the famous lone-pair stereochemical activity which often triggers ferroelectricity as in PbTiO$_3$, the Pb$^{2+}$ cation in Pb(TiO)Cu$_4$(PO$_4$)$_4$ is stereochemically inactive but dramatically alters specific magnetic interactions and consequently switches the quadrupole order from antiferroic to ferroic. Our first-principles calculations uncover a positive correlation between the degree of $A$-O bond covalency and a stability of the ferroic quadrupole order.Comment: 7 pages, 4 figure

Quantum mechanical virial theorem in systems with translational and rotational symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of Theoretical Physic

Research into the Retention Force of Electroformed Secondary Bar

INTRODUCTION: Electroformed metals are known to present good adaptability and biocompatibilities, but it is not yet known if the retention force of the electroformed secondary bar frame (ESBF) can endure long use. To clarify this point, the retention force between the primary cast bar and ESBF were measured. MATERIAL AND METHODS: An edentulous model was prepared and four implants (Frialit 2) were embedded. The fabrication of the primary bar was cast from pure titanium. We coated the completed titanium bar with silver lacquer and applied 0.3mm thick electrodeposite. The ESBF was attached to the cast titanium primary bar, cyclical tests performed for 15000 cycles and the retention force measured each time. The retention forces were measured in 37°C distilled water . RESULTS: The retention force value dropped as the number of reseating increased. It was 22N after 1000, 19N after 5000, 18N after 10000 and 16N after 15000 cycles. The hysteresis curve indicated that the resistance during cyclical testing was constant and stable up until the completion of 15000 cycles. CONCLUSION: The results confirmed that the retention force dropped gradually as the number of cycles increased, but that the stress imposed on the implants due to attaching and removal was low. This may be due to the excellent adaptation accuracy. In the case when repetition of attaching and removing for a long period is considerered, we need an attachment to enable the provision of a stable retention force Supported by Wieland Edelmetalle