2,119 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

    Critical Level Statistics of the Fibonacci Model

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    We numerically analyze spectral properties of the Fibonacci model which is a one-dimensional quasiperiodic system. We find that the energy levels of this model have the distribution of the band widths ww obeys PB(w)wαP_B(w)\sim w^{\alpha} (w0)(w\to 0) and PB(w)eβwP_B(w) \sim e^{-\beta w} (w)(w\to\infty), the gap distribution PG(s)sδP_G(s)\sim s^{-\delta} (s0)(s\to 0) (α,β,δ>0\alpha,\beta,\delta >0) . We also compare the results with those of multi-scale Cantor sets. We find qualitative differences between the spectra of the Fibonacci model and the multi-scale Cantor sets.Comment: 7 page
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