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

A New Clustering Method for Landsat Images Using Local Maximums of a Multidimensional Histogram

This paper describes a new clustering method for a huge satellite image. This method is composed of two major schemes, a multi-layered hashing scheme for multi-dimensional histogram (MDH) and a histogram clustering scheme using MDH. The MDH construction scheme works in 3 stages. In the 1st stage it constructs a few histogram layers for each part of an image, and in the 2nd and 3rd stages histogram layers are combined into one histogram. The clustering scheme searches for local maximums of MDH, and decides clusters around local maximums as sets of hyperrectangles. The major parameters of the clustering scheme are briefly discussed, and some results are also shown

Superconductivity under pressure in the Dirac semimetal PdTe2

The Dirac semimetal PdTe$_2$ was recently reported to be a type-I superconductor ($T_c =$1.64 K, $\mu_0 H_c (0) = 13.6$ mT) with unusual superconductivity of the surface sheath. We here report a high-pressure study, $p \leq 2.5$ GPa, of the superconducting phase diagram extracted from ac-susceptibility and transport measurements on single crystalline samples. $T_c (p)$ shows a pronounced non-monotonous variation with a maximum $T_c =$1.91 K around 0.91 GPa, followed by a gradual decrease to 1.27 K at 2.5 GPa. The critical field of bulk superconductivity in the limit $T \rightarrow 0$, $H_c(0,p)$, follows a similar trend and consequently the $H_c(T,p)$-curves under pressure collapse on a single curve: $H_c(T,p)=H_c(0,p)[1-(T/T_c(p))^2]$. Surface superconductivity is robust under pressure as demonstrated by the large superconducting screening signal that persists for applied dc-fields $H_a > H_c$. Surprisingly, for $p \geq 1.41$ GPa the superconducting transition temperature at the surface $T_c^S$ is larger than $T_c$ of the bulk. Therefore surface superconductivity may possibly have a non-trivial nature and is connected to the topological surface states detected by ARPES. We compare the measured pressure variation of $T_c$ with recent results from band structure calculations and discuss the importance of a Van Hove singularity.Comment: manuscript 9 pages with 8 figures + supplemental material 3 pages with 6 figure