2,119 research outputs found

### 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

### Critical Level Statistics of the Fibonacci Model

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 $w$ obeys $P_B(w)\sim
w^{\alpha}$ $(w\to 0)$ and $P_B(w) \sim e^{-\beta w}$ $(w\to\infty)$, the gap
distribution $P_G(s)\sim s^{-\delta}$ $(s\to 0)$ ($\alpha,\beta,\delta >0$) .
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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