Resonant-state expansion of the Green's function of open quantum systems

Our series of recent work on the transmission coefficient of open quantum systems in one dimension will be reviewed. The transmission coefficient is equivalent to the conductance of a quantum dot connected to leads of quantum wires. We will show that the transmission coefficient is given by a sum over all discrete eigenstates without a background integral. An apparent "background" is in fact not a background but generated by tails of various resonance peaks. By using the expression, we will show that the Fano asymmetry of a resonance peak is caused by the interference between various discrete eigenstates. In particular, an unstable resonance can strongly skew the peak of a nearby resonance.Comment: 7 pages, 7 figures. Submitted to International Journal of Theoretical Physics as an article in the Proceedings for PHHQP 2010 (http://www.math.zju.edu.cn/wjd/

Extinction and the Radial Distribution of Supernova Properties in Their Parent Galaxies

We use a Monte Carlo technique and assumed spatial distributions of dust and supernova (SN) progenitors in a simple model of a characteristic SN--producing disk galaxy to explore the effects of extinction on the radial distributions of SN properties in their parent galaxies. The model extinction distributions and projected radial number distributions are presented for various SN types. Even though the model has no core-collapse SNe within three kpc of the center, a considerable fraction of the core-collapse SNe are projected into the inner regions of inclined parent galaxies owing to their small vertical scale height. The model predicts that because of extinction, SNe projected into the central regions should on average appear dimmer and have a much larger magnitude scatter than those in the outer regions. In particular, the model predicts a strong deficit of bright core-collapse events inside a projected radius of a few kpc. Such a deficit is found to be present in the observations. It is a natural consequence of the characteristic spatial distributions of dust and core-collapse SNe in galaxies, and it leads us to offer an alternative to the conventional interpretation of the Shaw effect.Comment: 14 pages, 4 figure

Vortex jamming in superconductors and granular rheology

We demonstrate that a highly frustrated anisotropic Josephson junction array(JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings along the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i. e. injection of external electric current at zero temperature. Current-voltage curves at various strength of the anisotropy exhibit universal scaling features around the jamming point much as do the flow curves in granular rheology, shear-stress vs shear-rate. It turns out that at zero temperature the jamming transition occurs right at the isotropic coupling and anisotropic JJA behaves as an exotic fragile vortex matter : it behaves as superconductor (vortex glass) into one direction while normal conductor (vortex liquid) into the other direction even at zero temperature. Furthermore we find a variant of the theoretical model for the anisotropic JJA quantitatively reproduces universal master flow-curves of the granular systems. Our results suggest an unexpected common paradigm stretching over seemingly unrelated fields - the rheology of soft materials and superconductivity.Comment: 10 pages, 5 figures. To appear in New Journal of Physic

Domain structure and polarization reversal in ferroelectrics studied by atomic force microscopy

The ferroelectric domain structure and its dynamics under applied electric field have been studied with nanoscale resolution by atomic force microscopy (AFM). Two mechanisms responsible for the contrast between opposite domains are proposed: large built-in domains are delineated in friction mode due to the tip–sample electrostatic interaction, and small domains created by an external field are imaged in topography mode due to piezoelectric deformation of the crystal. The ability of effective control of ferroelectric domains by applying a voltage between the AFM tip and the bottom electrode is demonstrated. It is experimentally confirmed that the sidewise growth of domain proceeds through the nucleation process on the domain wall

Domain structure and polarization reversal in ferroelectrics studied by atomic force microscopy

The ferroelectric domain structure and its dynamics under applied electric field have been studied with nanoscale resolution by atomic force microscopy (AFM). Two mechanisms responsible for the contrast between opposite domains are proposed: large built-in domains are delineated in friction mode due to the tip–sample electrostatic interaction, and small domains created by an external field are imaged in topography mode due to piezoelectric deformation of the crystal. The ability of effective control of ferroelectric domains by applying a voltage between the AFM tip and the bottom electrode is demonstrated. It is experimentally confirmed that the sidewise growth of domain proceeds through the nucleation process on the domain wall

The origin of flux-flow resistance oscillations in BiSrCaCuO: Fiske steps in a single junction?

We propose an alternative explanation to the oscillations of the flux-flow resistance found in several previously published experiments with BiSrCaCuO stacks. It has been argued by the previous authors that the period of the oscillations corresponding to the field needed to add one vortex per two intrinsic Josephson junctions is associated with a moving triangular lattice of vortices (out-of-phase mode), while the period corresponding to one vortex per one junction is due to the square lattice (in-phase mode). In contrast, we show that both type of oscillations may occur in a single-layer Josephson junction and thus the above interpretation is inconsistent

On the eigenproblems of PT-symmetric oscillators

We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\prime and we find some other interesting properties of eigenfunctions.Comment: 21pages, 9 figure

A simple one-dimensional model of heat conduction which obeys Fourier's law

We present the computer simulation results of a chain of hard point particles with alternating masses interacting on its extremes with two thermal baths at different temperatures. We found that the system obeys Fourier's law at the thermodynamic limit. This result is against the actual belief that one dimensional systems with momentum conservative dynamics and nonzero pressure have infinite thermal conductivity. It seems that thermal resistivity occurs in our system due to a cooperative behavior in which light particles tend to absorb much more energy than the heavier ones.Comment: 5 pages, 4 figures, to be published in PR

Population Dynamics and Non-Hermitian Localization

We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads to a constant imaginary vector potential in the Schroedinger-like operator which appears in linearized growth models. We illustrate the basic ideas by reviewing how convection affects the evolution of a population influenced by a simple square well growth profile. Results from discrete lattice growth models in both one and two dimensions are presented. A set of similarity transformations which lead to exact results for the spectrum and winding numbers of eigenfunctions for random growth rates in one dimension is described in detail. We discuss the influence of boundary conditions, and argue that periodic boundary conditions lead to results which are in fact typical of a broad class of growth problems with convection.Comment: 19 pages, 11 figure