N-fold Parasupersymmetry

We find a new type of non-linear supersymmetries, called N-fold parasupersymmetry, which is a generalization of both N-fold supersymmetry and parasupersymmetry. We provide a general formulation of this new symmetry and then construct a second-order N-fold parasupersymmetric quantum system where all the components of N-fold parasupercharges are given by type A N-fold supercharges. We show that this system exactly reduces to the Rubakov-Spiridonov model when N=1 and admits a generalized type C 2N-fold superalgebra. We conjecture the existence of other `N-fold generalizations' such as N-fold fractional supersymmetry, N-fold orthosupersymmetry, and so on.Comment: 10 pages, no figures; Intro. expande

Hands-on Physical Science Course at Radford University

Most students in our introductory physical science course are elementary education majors. We are faced with several obstacles in teaching basic science to these students. For example, they lack interest in science, logical thinking, and necessary data gathering and analysis skills, among others. Many of those obstacles could be traced back to the science courses they had taken in the past. Those courses put more emphasis on memorizing scientific facts than understanding natural phenomena or experiencing scientific methods. As a result, the students tend to have a negative attitude toward science in general. In order to reverse this attitude, We have been developing a hands-on, experience based physical science course. In each class students are asked to perform several experiments which require observation, data gathering, and analysis. The instructor provides necessary scientific background and explanation on the experiments as they go. One of the experiments the students enjoyed a lot is the measurement of average speeds of cars. They actually go out on the street and take data. Through this course students can experience how science works and learn that science could be more exciting than just memorizing

DECIGO/BBO as a probe to constrain alternative theories of gravity

We calculate how strongly one can constrain the alternative theories of gravity with deci-Hz gravitational wave interferometers such as DECIGO and BBO. Here we discuss Brans-Dicke theory and massive graviton theories as typical examples. We consider the inspiral of compact binaries composed of a neutron star (NS) and an intermediate mass black hole (IMBH) for Brans-Dicke (BD) theory and those composed of a super massive black hole (SMBH) and a black hole (SMBH) for massive graviton theories. Using the restricted 2PN waveforms including spin effects and taking the spin precession into account, we perform the Monte Carlo simulations of $10^4$ binaries to estimate the determination accuracy of binary parameters including the Brans-Dicke parameter $\omega_{\mathrm{BD}}$ and the graviton Compton length $\lambda_g$. Assuming a $(1.4, 10)M_{\odot}$ NS/BH binary of SNR=$\sqrt{200}$, the constraint on $\omega_{\mathrm{BD}}$ is obtained as $\omega_{\mathrm{BD}}>2.32\times 10^6$, which is 300 times stronger than the estimated constraint from LISA observation. Furthermore, we find that, due to the expected large merger rate of NS/BH binaries of $O(10^4)$ yr$^{-1}$, a statistical analysis yields $\omega_{\mathrm{BD}}>3.77\times10^8$, which is 4 orders of magnitude stronger than the current strongest bound obtained from the solar system experiment. For massive graviton theories, assuming a $(10^6, 10^5)M_{\odot}$ BH/BH binary at 3Gpc, one can put a constraint $\lambda_g>3.35\times10^{20}$cm, on average. This is three orders of magnitude stronger than the one obtained from the solar system experiment. From these results, it is understood that DECIGO/BBO is a very powerful tool for constraining alternative theories of gravity, too.Comment: 4 pages, 3 figures; Accepted to Prog. Theor. Phys. Letters; Many interpretations and some references have been added; Some Coding errors being corrected and the final constraints came out stronge

Theory of AC Anomalous Hall Conductivity in d-electron systems

To elucidate the intrinsic nature of anomalous Hall effect (AHE) in $d$-electron systems, we study the AC anomalous Hall conductivity (AHC) in a tight-binding model with ($d_{xz},d_{yz}$)-orbitals. We drive a general expression for the AC AHC $\sigma_{xy}(\omega)$, which is valid for finite quasiparticle damping rate $\gamma$=$\hbar/2\tau$, and find that the AC AHC is strongly dependent on $\gamma$. When $\gamma=+0$, the AC AHC shows a spiky peak at finite energy $\Delta$ that originates from the interband particle-hole excitation, where $\Delta$ represents the minimum band-splitting measured from the Fermi level. In contrast, we find that this spiky peak is quickly suppressed when $\gamma$ is finite. By using a realistic value of $\gamma(\omega)$ at $\omega=\Delta/2$ in $d$-electron systems, the spiky peak is considerably suppressed. In the present model, the obtained results also represents the AC spin Hall conductivity in a paramagnetic state.Comment: 13pages, 9 figure