Anderson localization in generalized discrete time quantum walks

We study Anderson localization in a generalized discrete time quantum walk - a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and kinetic energy, and external and internal synthetic flux. Such quantum coins can be engineered with microwave pulses in qubit chains. The ordered case yields a two-band eigenvalue structure on the unit circle which becomes completely flat in the limit of vanishing kinetic energy. Disorder in the external magnetic field does not impact localization. Disorder in all the remaining angles yields Anderson localization. In particular, kinetic energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. Strong disorder in potential and internal magnetic field energies allows to obtain analytical expressions for spectrally independent localization length which is highly useful for various applications.Comment: 11 pages, 14 figure

Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.Comment: 6 pages, LaTeX 2.09, 3 PostScript figure

Dependence of the flux creep activation energy on current density and magnetic field for MgB2 superconductor

Systematic ac susceptibility measurements have been performed on a MgB$_2$ bulk sample. We demonstrate that the flux creep activation energy is a nonlinear function of the current density $U(j)\propto j^{-0.2}$, indicating a nonlogarithmic relaxation of the current density in this material. The dependence of the activation energy on the magnetic field is determined to be a power law $U(B)\propto B^{-1.33}$, showing a steep decline in the activation energy with the magnetic field, which accounts for the steep drop in the critical current density with magnetic field that is observed in MgB$_2$. The irreversibility field is also found to be rather low, therefore, the pinning properties of this new material will need to be enhanced for practical applications.Comment: 11 pages, 6 figures, Revtex forma

Radiative and Collisional Jet Energy Loss in a Quark-Gluon Plasma

We calculate radiative and collisional energy loss of hard partons traversing the quark-gluon plasma created at RHIC and compare the respective size of these contributions. We employ the AMY formalism for radiative energy loss and include additionally energy loss by elastic collisions. Our treatment of both processes is complete at leading order in the coupling, and accounts for the probabilistic nature of jet energy loss. We find that a solution of the Fokker-Planck equation for the probability density distributions of partons is necessary for a complete calculation of the nuclear modification factor $R_{AA}$ for pion production in heavy ion collisions. It is found that the magnitude of $R_{AA}$ is sensitive to the inclusion of both collisional and radiative energy loss, while the average energy is less affected by the addition of collisional contributions. We present a calculation of $R_{AA}$ for $\pi^0$ at RHIC, combining our energy loss formalism with a relativistic (3+1)-dimensional hydrodynamic description of the thermalized medium.Comment: 4 pages, 4 figures, contributed to Quark Matter 2008, Jaipur, Indi

Morphology and Orientation Selection of Non-Metallic Inclusions in Electrified Molten Metal

The effect of electric current on morphology and orientation selection of non-metallic inclusions in molten metal has been investigated using theoretical modelling and numerical calculation. Two geometric factors, namely the circularity (fc) and alignment ratio (fe) were introduced to describe the inclusions shape and configuration. Electric current free energy was calculated and the values were used to determine the thermodynamic preference between different microstructures. Electric current promotes the development of inclusion along the current direction by either expatiating directional growth or enhancing directional agglomeration. Reconfiguration of the inclusions to reduce the system electric resistance drives the phenomena. The morphology and orientation selection follows the routine to reduce electric free energy. The numerical results are in agreement with our experimental observations