Vortex Turbulence in Linear Schroedinger Wave Mechanics

Quantum turbulence that exhibits vortex creation, annihilation and interactions is demonstrated as an exact solution of the time-dependent, free-particle Schr\"odinger equation evolved from a smooth random-phased initial condition. Relaxed quantum turbulence in 2D and 3D exhibits universal scaling in the steady-state energy spectrum as k-1 in small scales. Due to the lack of dissipation, no evidence of the Kolmogorov-type forward energy cascade in 3D or the inverse energy cascade in 2D is found, but the rotational and potential flow components do approach equi-partition in the scaling regime. In addition, the 3D vortex line-line correlation exhibits universal behaviour, scaled as \Deltar^-2, where \Deltar is the separation between any two vortex line elements, in fully developed turbulence. We also show that the quantum vortex is not frozen to the matter, nor is the vortex motion induced by other vortices via Biot-Savart's law. Thus, the quantum vortex is actually a nonlinear wave, propagating at a speed very different from a classical vortex.Comment: 9 pages, 14 figure

High-Resolution Simulation on Structure Formation with Extremely Light Bosonic Dark Matter

An alternative bosonic dark matter model is examined in detail via high-resolution simulations. These bosons have particle mass of order $10^{-22}eV$ and are non-interacting. If they do exist and can account for structure formation, these bosons must be condensed into the Bose-Einstein state and described by a coherent wave function. This matter, also known as Fuzzy Dark Matter (Hu, Barkana & Gruzinov 2000),, is speculated to be able, first, to eliminate the sub-galactic halos to solve the problem of over-abundance of dwarf galaxies, and, second, to produce flat halo cores in galaxies suggested by some observations. Our simulation results show that although this extremely light bosonic dark matter indeed suppresses low-mass halos, it can, to the contrary of expectation, yield singular halo cores. The density profile of the singular halo is almost identical to the halo profile of Navarro, Frenk & White (1997). Such a profile seems to be universal, in that it can be produced via either accretion or merger.Comment: 21 pages, 10 figure

Effects of Preheated Clusters on the CMB Spectrum

Mounting evidence from $x$-ray observations reveals that bound objects should receive some form of energy in the past injected from non-gravitaional sources. We report that an instantaneous heating scheme, for which gases in dense regions were subjected to a temperature jump of 1keV at $z=2$ whereas those in rarified regions remained intact, can produce bound objects obeying the observed mass-temperature and luminosity-temperature relations. Such preheating lowers the peak Sunyaev-Zeldovich (SZ) power by a factor of 2 and exacerbates the need for the normalization of matter fluctuations $\sigma_8$ to assume an extreme high value $(\sim 1.1)$ for the SZ signals to account for the excess anisotropy on 5-arcminute scale detected by the Cosmic Background Imager in the cosmic microwave background radiation.Comment: 6 pages, 3 figs, submitted to ApJL. Corrected for a normalization problem and one more simulation result is included. Conclusion has been reversed. Motion pictures of simulations can be found at http://asweb.phys.ntu.edu.tw/~tseng/MEMO/SZE.htm

High Current-Induced Electron Redistribution in a CVD-Grown Graphene Wide Constriction

Investigating the charge transport behavior in one-dimensional quantum confined system such as the localized states and interference effects due to the nanoscale grain boundaries and merged domains in wide chemical vapor deposition graphene constriction is highly desirable since it would help to realize industrial graphene-based electronic device applications. Our data suggests a crossover from interference coherent transport to carriers flushing into grain boundaries and merged domains when increasing the current. Moreover, many-body fermionic carriers with disordered system in our case can be statistically described by mean-field Gross-Pitaevskii equation via a single wave function by means of the quantum hydrodynamic approximation. The novel numerical simulation method supports the experimental results and suggests that the extreme high barrier potential regions on graphene from the grain boundaries and merged domains can be strongly affected by additional hot charges. Such interesting results could pave the way for quantum transport device by supplying additional hot current to flood into the grain boundaries and merged domains in one-dimensional quantum confined CVD graphene, a great advantage for developing graphene-based coherent electronic devices

Experimental evidence for direct insulator-quantum Hall transition in multi-layer graphene

We have performed magnetotransport measurements on a multi-layer graphene flake. At the crossing magnetic field Bc, an approximately temperature-independent point in the measured longitudinal resistivity, which is ascribed to the direct insulator-quantum Hall (I-QH) transition, is observed. By analyzing the amplitudes of the magnetoresistivity oscillations, we are able to measure the quantum mobility of our device. It is found that at the direct I-QH transition, the product of the quantum mobility and is about 0.37 which is considerably smaller than 1. In contrast, at Bc, the longitudinal resistivity is close to the Hall resistivity, i.e., the product of the classical mobility and the crossing field is about 1. Therefore our results suggest that different mobilities need to be introduced for the direct I-QH transition observed in multi-layered graphene. Combined with existing experimental results obtained in various material systems, our data obtained on graphene suggest that the direct I-QH transition is a universal effect in 2D.Comment: 4 figure

High Resolution Simulation on Structure Formation with Extremely Light Bosonic Dark Matter

在本篇論文中，我們假設暗物質為質量超輕的波色子，並利用薛丁格-泊松方程式解此問體。並分析暗物質暈的質量分佈及能量分佈。An alternative bosonic dark matter model is examined in detail via high-resolution simulations. These bosons have particle mass of order 10¡22eV and are non-interacting.f they do exist and can account for structure formation, these bosons must be condensed into the Bose-Einstein state and described by a coherent wave function.his matter, also known as Fuzzy Dark Matter (Hu, Barkana & Gruzinov, 2000),s speculated to be able, ¯rst, to eliminate the sub-galactic halos to solve the prob-em of over-abundance of dwarf galaxies, and, second, to produce °at halo coresn galaxies suggested by some observations. Due to the limited dynamical range,ur 10243 simulation literarily addresses cluster-size halos in an 100 h¡1Mpc box,ather than galaxy-size halos in an 1 h¡1Mpc box, by adopting 10¡26eV boson mass.owever, since the SchrÄodinger-Poisson model studied in this work is a scale-freeystem, our results can be rescaled to a simulation box 100 times smaller. The sim-lation results show that although this extremely light bosonic dark matter indeeduppresses low-mass halos, it can, to the contrary of expectation, yield singular haloores. The density pro¯le of the singular halo is almost identical to the halo pro¯lef Navarro, Frenk & White (1997). Such a pro¯le seems to be independent of theormation processes via accretion or merger. We shall stress a caveat for rescalingrom 100 h¡1Mpc to 1 h¡1Mpc box. The background density averaged over 100 h¡1Mpc is usually considered to represent the true background, but that averagedver 1 h¡1Mpc can be subject to large sample variance. Though our simulation,fter rescaling, correspond to one of the many background densities, or e®ectively one of the many background cosmologies, we believe that the general trend obtained in this work remains valid in di®erent cosmologies.1. INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1. THEORY : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4.1 Bose-Einstein Condensate . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Basic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Numerical Scheme and Simulation : : : : : : : : : : : : : : : : : : : : : : : 10.1 Numerical Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Simulation Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. RESULTS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13.1 Validity of Linear Perturbation Theory . . . . . . . . . . . . . . . . . 13.2 Weakly Nonlinearity Regime . . . . . . . . . . . . . . . . . . . . . . . 15.3 Strong Nonlinearity Regime . . . . . . . . . . . . . . . . . . . . . . . 16. CONCLUSIONS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 21. Additional Chapter: Turbulent Structure within a Dark Halo Formed byLBDM : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.2 The Turbulent Flow of the Quantum Fluid . . . . . . . . . . . . . . . 25.3 Energy Analysis in Halos . . . . . . . . . . . . . . . . . . . . . . . . . 30.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32ontents 3ppendix 33. SchrÄodinger-Poisson System : : : : : : : : : : : : : : : : : : : : : : : : : : 34. Step by Step Derivation of Dimensionless SchrÄodinger-Poisson Equation : : 36. Pseudo-spectral Method : : : : : : : : : : : : : : : : : : : : : : : : : : : : 38.0.1 The Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39. Other Numerical Scheme: A.D.I. : : : : : : : : : : : : : : : : : : : : : : : 40. Why so mysterious? The Universal Pro¯le - N.F.W. Theory : : : : : : : : 41IST OF FIGURES.1 The solution of the linear perturbation given by Eq.(6). The verticaline labels the location of squared scaled Jean''s wavenumber at x = 6. 8.2 The linear evolution of the power spectrum from z = 100 to z = 10n an 100 h¡1Mpc box. The low-k power obeys the linear scaling / a2. 9.1 Evolution of 4jRkj2(z) and 4jIkj2(z) to check against the linear theory.eviation from the linear theory is evident from z=200 on. Black dotsre j(I2)kj2 at z = 100 constructed from few low-k modes to show theancellation between 2Rk and (I2)k so as to make nk ¿ 2Rk. . . . . 14.2 The weakly nonlinear evolution of the power spectrum from z = 10o z = 1:5, where the high-k modes are seen to be nonlinearly excited. 15.3 Two-dimensional projections of density in real space in a 100h¡1Mpcomoving box at z=3 (left panel) and z=0 (right panel). Halo A and are at the top left and bottom left. . . . . . . . . . . . . . . . . . . 16.4 The nonlinear evolution of the power spectrum from z = 1:5 to z =:0. The highest-k modes acquire their full power after z = 0:4,ndicative of the creation of singular halo cores. . . . . . . . . . . . . 17.5 The comparison of the halo power spectrum Ph(blue), the backgroundower spectrum Pb(green) and the full power spectrum P (red) at = 0. Ph matches P at high k and Pb matches P at low k. . . . . . 17.6 Waves are sent out from the collapsing halo A at z = 1 (left panel);t develops an oblate singular halo at z = 0 (right panel). . . . . . . 18ist of Figures 5.7 Halo B is subject to major merger at z = 0:7. The left panel revealshe progenitors at z = 1 and the right panel shows a singular haloith high degree of spherical symmetry at z = 0. . . . . . . . . . . . 19.8 Density pro¯les of two massive halos at z=0. The left panel plots thero¯le of halo A and the right panel the pro¯le of halo B. In bothanels green lines and blue lines denote the power law of indices ¡1:4nd ¡2:5, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . 20.1 A crosscut image of the halo A . . . . . . . . . . . . . . . . . . . . . 26.2 The crosscut velocity ¯eld of halo A, in the physical frame. . . . . . . 27.3 A crosscut image of the halo B . . . . . . . . . . . . . . . . . . . . . 28.4 The crosscut velocity ¯eld of halo B, in the physical frame. . . . . . . 29.5 This panel shows the quantum pressure (blue line), kinetic energyn comoving coordinate(red line) and kinetic energy in physical co-rdinate (pink line) versus radius of halo A & B in the comovingoordinate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3