Quantum zigzag transition in ion chains

A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one-dimensional optical lattice.     

Demuškin fields with valuations

We study the arithmetic structure of fields F of characteristic containing a primitive pth root of unity for which the maximal pro-p Galois group of F is a (finitely generated) Demuškin group. Received: 3 July 2001 / Published online: 2 December 2002 The research has been supported by the Israel Science Foundation grant 8007/99     

Formation of a resistive region at the anode end in DNA capillary electrophoresis.

We have studied the formation of a resistive region in the capillary during DNA separation. This effect is caused by an unequal change in the mobilities of cations and anions at the interface between the running buffer solution and the capillary. We studied the motion of the resistive region boundary by sequential removal of portions of the affected capillary end. We found that in the process of developing the resistive region the distribution of the electric fields in the capillary changes from uniform to extremely nonuniform, with a very high field (above 1 MV/cm) in the resistive region and a reduced field (80 V/cm) in the rest of the capillary. Though theoretically a resistive region may appear either at the anode (detection) or the cathode (injection) end of the capillary, all previous publications report the formation of the resistive region at the cathode side. In our experiments, however, the anomalous region is formed at the anode. Thus, the separated DNA peaks move towards the slowly progressing resistive region. Our results indicate that the DNA is stopped at the boundary and does not enter the region. When the resistive region is clipped off the peak motion resumes. This suggests that there exists a potential barrier at the resistive layer boundary that prevents the drift of the peaks towards the anode. The formation of the resistive region interferes with a normal separation process causing a gradual decrease of the capillary current and the deceleration and eventual quenching of the peak motion. For the ABI chemistry, we experimented with adding polymers to the electrode buffer to equate the transference numbers for anions and cations, and found the conditions at which this effect is completely eliminated.     

On the Complexity of the Union of Fat Convex Objects in the Plane

We prove a near-linear bound on the combinatorial complexity of the union of n fat convex objects in the plane, each pair of whose boundaries cross at most a constant number of times. Received April 7, 1998, and in revised form August 24, 1999.     

Quasicrystals: A Matter of Definition

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.     

A direct measurement of g-factors in II–VI and III–V core–shell nanocrystals

This study describes a direct measurement of spectroscopic g-factors of photo-generated carriers in InP/ZnS and HgTe/Hg_xCd_1−xTe(S) core–shell nanocrystals. The g-factor of trapped electrons and their spin-lattice versus radiative relaxation ratio (T₁/τ) were measured by the use of continuous-wave and time-resolved optically detected magnetic resonance (ODMR) spectroscopy. The g-factors of excitons and donor–hole pairs were derived by the use of field-induced circular-polarized photoluminescence (CP-PL) spectroscopy. The combined information enabled to determine the g-factors of the individual band-edge electrons and holes. The results suggested an increase of the g-factor of the exciton and conduction electron with a decrease of the nanocrystal size.     

The temporal evolution of the city size distribution

We present an application of a growth model for a system of cities. This computer model simulates the evolution of systems with measurable entities (e.g. city size), and takes into account the growth of the entities in terms of size and number. It includes a random multiplicative process for the growth of individual entities and for the creation of new ones. We use a new mathematical expression with a positive exponent α (which we call the ‘shape exponent’) and additional three parameters, to describe the dynamics of the systems’ size distributions through time. We compare the changes of a real system of cities and the model’s results quantitatively and qualitatively. Our findings suggest that there is a good agreement at the macro level between the model and the real data.     

Ultraviolet photoelectron spectroscopy investigation of interface formation in an indium-tin oxide/fluorocarbon/organic semiconductor contact

It has been demonstrated that hole-injection in organic light-emitting devices (OLEDs) can be enhanced by inserting a UV-illuminated fluorocarbon (CF_x) layer between indium-tin oxide (ITO) and organic hole-transporting layer (HTL). In this work, the process of interface formation and electronic properties of the ITO/CF_x/HTL interface were investigated with ultraviolet photoelectron spectroscopy. It was found that UV-illuminated fluorocarbon layer decreases the hole-injection barrier from ITO to α-napthylphenylbiphenyl diamine (NPB). Energy level diagrams deduced from the ultraviolet photoelectron spectroscopy (UPS) spectra show that the hole-injection barrier in ITO/UV-treated CF_x/NPB is the smallest (0.46 eV), compared to that in the ITO/untreated CF_x/NPB (0.60 eV) and the standard ITO/NPB interface (0.68 eV). The improved current density-voltage (I-V) characteristics in the UV-treated CF_x-coated ITO contact are consistent with its smallest barrier height.     

New Similarity Measures between Polylines with Applications to Morphing and Polygon Sweeping

Abstract. We introduce two new related metrics, the geodesic width and the link width , for measuring the ``distance' between two nonintersecting polylines in the plane. If the two polylines have n vertices in total, we present algorithms to compute the geodesic width of the two polylines in O(n <sup>2</sup> log n) time using O(n <sup>2</sup> ) space and the link width in O(n <sup>3</sup> log n) time using O(n <sup>2</sup> ) working space where n is the total number of edges of the polylines. Our computation of these metrics relies on two closely related combinatorial strutures: the shortest-path diagram and the link diagram of a simple polygon. The shortest-path (resp., link) diagram encodes the Euclidean (resp., link) shortest path distance between all pairs of points on the boundary of the polygon. We use these algorithms to solve two problems: • Compute a continuous transformation that ``morphs' one polyline into another polyline. Our morphing strategies ensure that each point on a polyline moves as little as necessary during the morphing, that every intermediate polyline is also simple and disjoint to any other intermediate polyline, and that no portion of the polylines to be morphed is stretched or compressed by more than a user-defined parameter during the entire morphing. We present an algorithm that computes the geodesic width of the two polylines and utilizes it to construct a corresponding morphing strategy in O(n ² log ² n) time using O(n ² ) space. We also give an O(nlog n) time algorithm to compute a 2-approximation of the geodesic width and a corresponding morphing scheme. • Locate a continuously moving target using a group of guards moving inside a simple polygon. The guards always determine a simple polygonal chain within the polygon, with consecutive guards along the chain being mutually visible. We compute a strategy that sweeps such a chain of guards through the polygon in order to locate a target. We compute in O(n ³ ) time and O(n ² ) working space the minimum number r ^* of guards needed to sweep an n -vertex polygon. We also give an approximation algorithm, using O(n log n) time and O(n) space, to compute an integer r such that max(r - 16, 2)≤ r ^* ≤ r and P can be swept with a chain of r guards.