Excessive noise as a test for many-body localization

Recent experimental reports suggested the existence of a finite-temperature insulator in the vicinity of the superconductor-insulator transition. The rapid decay of conductivity over a narrow temperature range was theoretically linked to both a finite-temperature transition to a many-body-localized state, and to a charge-Berezinskii-Kosterlitz-Thouless transition. Here we report of low-frequency noise measurements of such insulators to test for many-body localization. We observed a huge enhancement of the low-temperatures noise when exceeding a threshold voltage for nonlinear conductivity and discuss our results in light of the theoretical models

Grover's Quantum Search Algorithm and Diophantine Approximation

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's basic step (and no other algorithm). Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m < (2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change

The Geometric Maximum Traveling Salesman Problem

We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(n^{f-2} log n), where f is the number of facets of the polyhedron determining the polyhedral norm. Thus for example we have O(n^2 log n) algorithms for the cases of points in the plane under the Rectilinear and Sup norms. This is in contrast to the fact that finding a minimum length tour in each case is NP-hard. Our approach can be extended to the more general case of quasi-norms with not necessarily symmetric unit ball, where we get a complexity of O(n^{2f-2} log n). For the special case of two-dimensional metrics with f=4 (which includes the Rectilinear and Sup norms), we present a simple algorithm with O(n) running time. The algorithm does not use any indirect addressing, so its running time remains valid even in comparison based models in which sorting requires Omega(n \log n) time. The basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms. Complementing the results on simplicity for polyhedral norms, we prove that for the case of Euclidean distances in R^d for d>2, the Maximum TSP is NP-hard. This sheds new light on the well-studied difficulties of Euclidean distances.Comment: 24 pages, 6 figures; revised to appear in Journal of the ACM. (clarified some minor points, fixed typos

Intrinsic tethering activity of endosomal Rab proteins.

Rab small G proteins control membrane trafficking events required for many processes including secretion, lipid metabolism, antigen presentation and growth factor signaling. Rabs recruit effectors that mediate diverse functions including vesicle tethering and fusion. However, many mechanistic questions about Rab-regulated vesicle tethering are unresolved. Using chemically defined reaction systems, we discovered that Vps21, a Saccharomyces cerevisiae ortholog of mammalian endosomal Rab5, functions in trans with itself and with at least two other endosomal Rabs to directly mediate GTP-dependent tethering. Vps21-mediated tethering was stringently and reversibly regulated by an upstream activator, Vps9, and an inhibitor, Gyp1, which were sufficient to drive dynamic cycles of tethering and detethering. These experiments reveal a previously undescribed mode of tethering by endocytic Rabs. In our working model, the intrinsic tethering capacity Vps21 operates in concert with conventional effectors and SNAREs to drive efficient docking and fusion

Sensitivity of the superconducting state in thin films

For more than two decades, there have been reports on an unexpected metallic state separating the established superconducting and insulating phases of thin-film superconductors. To date, no theoretical explanation has been able to fully capture the existence of such a state for the large variety of superconductors exhibiting it. Here, we show that for two very different thin-film superconductors, amorphous indium oxide and a single crystal of 2H-NbSe2, this metallic state can be eliminated by adequately filtering external radiation. Our results show that the appearance of temperature-independent, metallic-like transport at low temperatures is sufficiently described by the extreme sensitivity of these superconducting films to external perturbations. We relate this sensitivity to the theoretical observation that, in two dimensions, superconductivity is only marginally stable

Continuous atom laser with Bose-Einstein condensates involving three-body interactions

We demonstrate, through numerical simulations, the emission of a coherent continuous matter wave of constant amplitude from a Bose-Einstein Condensate in a shallow optical dipole trap. The process is achieved by spatial control of the variations of the scattering length along the trapping axis, including elastic three body interactions due to dipole interactions. In our approach, the outcoupling mechanism are atomic interactions and thus, the trap remains unaltered. We calculate analytically the parameters for the experimental implementation of this CW atom laser.Comment: 11 pages, 4 figure