Non-hermitean delocalization in an array of wells with variable-range widths

Nonhermitean hamiltonians of convection-diffusion type occur in the description of vortex motion in the presence of a tilted magnetic field as well as in models of driven population dynamics. We study such hamiltonians in the case of rectangular barriers of variable size. We determine Lyapunov exponent and wavenumber of the eigenfunctions within an adiabatic approach, allowing to reduce the original d=2 phase space to a d=1 attractor. PACS numbers:05.70.Ln,72.15Rn,74.60.GeComment: 20 pages,10 figure

Vortices in a cylinder: Localization after depinning

Edge effects in the depinned phase of flux lines in hollow superconducting cylinder with columnar defects and electric current along the cylinder are investigated. Far from the ends of the cylinder vortices are distributed almost uniformly (delocalized). Nevertheless, near the edges these free vortices come closer together and form well resolved dense bunches. A semiclassical picture of this localization after depinning is described. For a large number of vortices their density $\rho(x)$ has square root singularity at the border of the bunch ($\rho(x)$ is semicircle in the simplest case). However, by tuning the strength of current, the various singular regimes for $\rho(x)$ may be reached. Remarkably, this singular behaviour reproduces the phase transitions discussed during the past decade within the random matrix regularization of 2d-Gravity.Comment: 4 pages, REVTEX, 2 eps figure

Specialized mouse embryonic stem cells for studying vascular development.

Vascular progenitor cells are desirable in a variety of therapeutic strategies; however, the lineage commitment of endothelial and smooth muscle cell from a common progenitor is not well-understood. Here, we report the generation of the first dual reporter mouse embryonic stem cell (mESC) lines designed to facilitate the study of vascular endothelial and smooth muscle development in vitro. These mESC lines express green fluorescent protein (GFP) under the endothelial promoter, Tie-2, and Discomsoma sp. red fluorescent protein (RFP) under the promoter for alpha-smooth muscle actin (α-SMA). The lines were then characterized for morphology, marker expression, and pluripotency. The mESC colonies were found to exhibit dome-shaped morphology, alkaline phosphotase activity, as well as expression of Oct 3/4 and stage-specific embryonic antigen-1. The mESC colonies were also found to display normal karyotypes and are able to generate cells from all three germ layers, verifying pluripotency. Tissue staining confirmed the coexpression of VE (vascular endothelial)-cadherin with the Tie-2 GFP+ expression on endothelial structures and smooth muscle myosin heavy chain with the α-SMA RFP+ smooth muscle cells. Lastly, it was verified that the developing mESC do express Tie-2 GFP+ and α-SMA RFP+ cells during differentiation and that the GFP+ cells colocalize with the vascular-like structures surrounded by α-SMA-RFP cells. These dual reporter vascular-specific mESC permit visualization and cell tracking of individual endothelial and smooth muscle cells over time and in multiple dimensions, a powerful new tool for studying vascular development in real time

Impurity effects in few-electron quantum dots: Incipient Wigner molecule regime

Numerically exact path-integral Monte Carlo data are presented for $N\leq 10$ strongly interacting electrons confined in a 2D parabolic quantum dot, including a defect to break rotational symmetry. Low densities are studied, where an incipient Wigner molecule forms. A single impurity is found to cause drastic effects: (1) The standard shell-filling sequence with magic numbers $N=4,6,9$, corresponding to peaks in the addition energy $\Delta(N)$, is destroyed, with a new peak at N=8, (2) spin gaps decrease, (3) for N=8, sub-Hund's rule spin S=0 is induced, and (4) spatial ordering of the electrons becomes rather sensitive to spin. We also comment on the recently observed bunching phenomenon.Comment: 7 pages, 1 table, 4 figures, accepted for publication in Europhysics Letter

Finite Size Effects in Vortex Localization

The equilibrium properties of flux lines pinned by columnar disorder are studied, using the analogy with the time evolution of a diffusing scalar density in a randomly amplifying medium. Near H_{c1}, the physical features of the vortices in the localized phase are shown to be determined by the density of states near the band edge. As a result, H_{c1} is inversely proportional to the logarithm of the sample size, and the screening length of the perpendicular magnetic field decreases with temperature. For large tilt the extended ground state turns out to wander in the plane perpendicular to the defects with exponents corresponding to a directed polymer in a random medium, and the energy difference between two competing metastable states in this case is extensive. The divergence of the effective potential associated with strong pinning centers as the tilt approaches its critical value is discussed as well.Comment: 10 pages, 2 figure

Winding Numbers, Complex Currents, and Non-Hermitian Localization

The nature of extended states in disordered tight binding models with a constant imaginary vector potential is explored. Such models, relevant to vortex physics in superconductors and to population biology, exhibit a delocalization transition and a band of extended states even for a one dimensional ring. Using an analysis of eigenvalue trajectories in the complex plane, we demonstrate that each delocalized state is characterized by an (integer) winding number, and evaluate the associated complex current. Winding numbers in higher dimensions are also discussed.Comment: 4 pages, 2 figure

On the Relevance of Disorder for Dirac Fermions with Imaginary Vector Potential

We consider the effects of disorder in a Dirac-like Hamiltonian. In order to use conformal perturbation theory, we argue that one should consider disorder in an imaginary vector potential. This affects significantly the signs of the lowest order $\beta$eta functions. We present evidence for the existence of two distinct universality classes, depending on the relative strengths of the gauge field verses impurity disorder strengths. In one class all disorder is driven irrelevant by the gauge field disorder.Comment: 4 pages, 1 figure. New version has expanded and improved discussion of why one should consider an imaginary vector potential in a physical localization problem. Factors of 2 in beta functions corrected. References adde