Imaging Anyons with Scanning Tunneling Microscopy

Anyons are exotic quasiparticles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-Abelian statistics—a property that would help realize fault-tolerant quantum computation. Non-Abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases in the presence of a large magnetic field, such as the ν=5/2 FQH state. However, direct experimental evidence of anyons and tests that can distinguish between Abelian and non-Abelian quantum ground states with such excitations have remained elusive. Here, we propose a new experimental approach to directly visualize the structure of interacting electronic states of FQH states with the STM. Our theoretical calculations show how spectroscopy mapping with the STM near individual impurity defects can be used to image fractional statistics in FQH states, identifying unique signatures in such measurements that can distinguish different proposed ground states. The presence of locally trapped anyons should leave distinct signatures in STM spectroscopic maps, and enables a new approach to directly detect—and perhaps ultimately manipulate—these exotic quasiparticles

Exact Matrix Product States for Quantum Hall Wave Functions

We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite cylinders, which provides an efficient way of calculating arbitrary observables. We extend this approach to the charged excitations and numerically compute their Berry phases. Finally, we present an algorithm for numerically computing the real-space entanglement spectrum starting from an arbitrary orbital basis MPS, which allows us to study the scaling properties of the real-space entanglement spectra on infinite cylinders. The real-space entanglement spectrum obeys a scaling form dictated by the edge conformal field theory, allowing us to accurately extract the two entanglement velocities of the Moore-Read state. In contrast, the orbital space spectrum is observed to scale according to a complex set of power laws that rule out a similar collapse.Comment: 10 pages and Appendix, v3 published versio

Stabilization of Multiple Robots on Stable Orbits via Local Sensing

We develop decentralized controllers for a team of disk-shaped robots to converge to and circulate along the boundary of a desired two-dimensional geometric pattern specified by a smooth function with collision avoidance. The proposed feedback controllers rely solely on each robot\u27s range and bearing sensors which allow them to obtain information about positions of neighbors within a given range. This is relevant for applications such as perimeter surveillance or containing hazardous regions where limited bandwidth must be preserved for situational awareness. The computational complexity of the decentralized controller for each agent is linear in the number of neighboring agents, making it scalable to robot swarms. We establish stability and convergence properties of the controllers and verify the feasibility of the method through computer simulations

Sleep and the Endocrine Brain

Univ Maryland, Dept Pharmacol & Expt Therapeut, Sch Med, Baltimore, MD 21201 USAUniv Maryland, Sch Med, Program Neurosci, Baltimore, MD 21201 USAUniversidade Federal de São Paulo, Dept Psychobiol, BR-04024002 São Paulo, BrazilDalhousie Univ, Dept Anat & Neurobiol, Halifax, NS B3H 4R2, CanadaUniv Calif San Diego, Dept Psychiat, San Diego, CA 92037 USAUniversidade Federal de São Paulo, Dept Psychobiol, BR-04024002 São Paulo, BrazilWeb of Scienc

Constructing Radio Signal Strength Maps with Multiple Robots

Communication is essential for coordination in most cooperative control and sensing paradigms. In this paper, we investigate the construction of a map of radio signal strength that can be used to plan multirobot tasks and also serve as useful perceptual information. We show how nominal models of an urban environment, such as those obtained by aerial surveillance, can be used to generate strategies for exploration and present preliminary experimental results with our multi-robot testbed

Rapid Total Synthesis of DARPin pE59 and Barnase

We report the convergent total synthesis of two proteins: DARPin pE59 and Bacillus amyloliquefaciens RNase (Barnase). Leveraging our recently developed fast-flow peptide-synthesis platform, we rapidly explored numerous conditions for the assembly of long polypeptides, and were able to mitigate common side reactions, including deletion and aspartimide products. We report general strategies for improving the synthetic quality of difficult peptide sequences with our system. High-quality protein fragments produced under optimal synthetic conditions were subjected to convergent native chemical ligation, which afforded native full-length proteins after a final desulfurization step. Both DARPin and Barnase were folded and found to be as active as their recombinant analogues.MIT Faculty Start-up FundMassachusetts Institute of Technology (Charles E. Reed Faculty Initiative Fund)Deshpande Center for Technological InnovationDamon Runyon-Rachleff (Innovation Award)Sontag Foundation (Distinguished Scientist Award)AstraZeneca (Firm) (Distinguished Graduate Student Fellowship)Daniel S. Kemp Summer FellowshipNational Institutes of Health (U.S.). Biotechnology Training Program (5T32GM008334-25

A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Quantized Response and Topology of Insulators with Inversion Symmetry

We study three dimensional insulators with inversion symmetry, in which other point group symmetries, such as time reversal, are generically absent. Their band topology is found to be classified by the parities of occupied states at time reversal invariant momenta (TRIM parities), and by three Chern numbers. The TRIM parities of any insulator must satisfy a constraint: their product must be +1. The TRIM parities also constrain the Chern numbers modulo two. When the Chern numbers vanish, a magneto-electric response parameterized by "theta" is defined and is quantized to theta= 0, 2pi. Its value is entirely determined by the TRIM parities. These results may be useful in the search for magnetic topological insulators with large theta. A classification of inversion symmetric insulators is also given for general dimensions. An alternate geometrical derivation of our results is obtained by using the entanglement spectrum of the ground state wave-function.Comment: 12 pages main text; 12 pages appendices; 11 figures. Added new refs. in 2nd versio