Dispersion Relations for Waves propagating in Composite Fermion Gases

The discrete Uehling-Uhlenbeck equations are solved to study the propagation of plane (sound) waves in a system of composite fermionic particles with hard-sphere interactions and the filling factor ($\nu$) being 1/2. The Uehling-Uhlenbeck collision sum, as it is highly nonlinear, is linearized firstly and then decomposed by using the plane wave assumption. We compare the dispersion relations thus obtained by the relevant Pauli-blocking parameter $B$ which describes the different-statistics particles for the quantum analog of the discrete Boltzmann system when $B$ is positive (Bose gases), zero (Boltzmann gases), and negative (Fermi Gases). We found, as the effective magnetic field being zero ($\nu$=1/2 using the composite fermion formulation), the electric and fluctuating (induced) magnetic fields effect will induce anomalous dispersion relations.Comment: 13 pages with 2 figure

Phantom Thermodynamics Revisited

Although generalized Chaplygin phantom models do not show any big rip singularities, we investigated k-essence models together with noncanonical kinetic energy for which there might be a big rip future singularity in the phantom region. We present our results by finely tuning the parameter ($\beta$) which is closely related to the canonical kinetic term in $k$-essence formalism. The scale factor $a(t)$ could be negative and decreasing within a specific range of $\beta$ during the initial evolutional period. There will be no singularity for the scale factor for all times once $\beta$ is carefully selected.Comment: 4 pages; 1 figur

Possible Pressure Effect for Superconductors

We make an estimate of the possible range of $\Delta T_c$ induced by high-pressure effects in post-metallic superconductors by using the theory of {\it extended irreversible/reversible thermodynamics} and Pippard's length scale. The relationship between the increment of the superconducting temperature and the increase of the pressure is parabolic.Comment: 6 pages; 1999-March result

Stability of Quantum Fluids : Wavy Interface Effect

A numerical investigation for the stability of the incompressible slip flow of normal quantum fluids (above the critical phase transition temperature) inside a microslab where surface acoustic waves propagate along the walls is presented. Governing equations and associated slip velocity and wavy interface boundary conditions for the flow of normal fluids confined between elastic wavy interfaces are obtained. The numerical approach is an extension (with a complex matrix pre-conditioning) of the spectral method. We found that the critical Reynolds number ($Re_{cr}$ or the critical velocity) decreases significantly once the slip velocity and wavy interface effects are present and the latter is dominated ($Re_{cr}$ mainly depends on the wavy interfaces).Comment: 4 Figures; 2004-Jan work

Note on the Zero-Energy-Limit Solution for the Modified Gross-Pitaevskii Equation

The modified Gross-Pitaevskii equation was derived and solved to obtain the 1D solution in the zero-energy limit. This stationary solution could account for the dominated contributions due to the kinetic effect as well as the chemical potential in inhomogeneous Bose gases.Comment: 4 pages in total; 2002-May complete

Possible Negative Pressure States in the Evolution of the Universe

Hydrodynamic derivation of the entrainment of matter induced by a surface elastic wave propagating along the flexible vacuum-matter interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. The critical reflux values associated with the product of the second-order (unit) body forcing and the Reynolds number (representing the viscous dissipations) decrease as the Knudsen number (representing the rarefaction measure) increases from zero to 0.1. We obtained the critical bounds for matter-freezed or zero-volume-flow-rate states corresponding to specific Reynolds numbers (ratio of wave inertia and viscous dissipation effects) and wave numbers which might be linked to the evolution of the Universe. Our results also show that for positive evolution of the matter (the maximum speed of the matter (gas) appears at the center-line) there might be existence of negative pressure.Comment: 4 Figures in tota

Stationary Ballistic 'V' States for Preferred Motions of Many Particles

We use the discrete kinetic theory with the free-orientation parameter being fixed ($\pi/4$) to derive the macroscopic velocity field for many particles flowing through a microdomain. Our results resemble qualitatively other hydrodynamical solutions. The V-shaped velocity field changes as the dominant physical parameter (Knudsen number) varies. We also briefly discuss the possible mechanism due to the entropy production along the boundaries.Comment: 1999-Works; two figure

Comments on "Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators"

We make comments on Gaidarzhy {\it et al.}'s [{\it Phys. Rev. Lett.} 94, 030402 (2005)] letter.Comment: 3 page

Note on the 818_{18}-Knot

We define some physical variables associated with the traversing sequences of electrons along the orbit which is a 2D projection of 8$_{18}$-knot. The configuration is regular but the resulting contributions, which are related to the physical variable, of those combinations from all the possible states to the fixed spatial sites show certain irregular behavior near the over- or under-crossing points of this knot. The possible explanation for this kind of direct geometric consequences is made to linked to the physical insight.Comment: One Table and Two Figures; 1999-Feb. complete

Resonant States of Wave Propagation in Disordered System of Bosonic Particles

We demonstrate the effects of an induced disorder (or a free-orientation : $\theta$ which is related to the relative direction of scattering of particles w.r.t. to the normal of the propagating plane-wave front) upon the possible resonance of the plane (sound) wave propagating in Bose gases by using the quantum kinetic equations. We firstly present the diverse dispersion relations obtained by the relevant Pauli-blocking parameter $B$ (which describes the Bose particles when $B$ is positive) and the free-orientation $\theta$ and then, based on the acoustic analog, address the possible resonant states.Comment: 7 Figures; 2004-March complete