3,515 research outputs found

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

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    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=1q=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

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    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

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    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)

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    Ferroic magnetic quadrupole order exhibiting macroscopic magnetoelectric activity is discovered in the novel compound AA(TiO)Cu4_4(PO4_4)4_4 with AA = Pb, which is in contrast with antiferroic quadrupole order observed in the isostructural compounds with AA = Ba and Sr. Unlike the famous lone-pair stereochemical activity which often triggers ferroelectricity as in PbTiO3_3, the Pb2+^{2+} cation in Pb(TiO)Cu4_4(PO4_4)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 AA-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

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    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
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