Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions

The vortex-boson (or Abelian-Higgs, XY) duality in 2+1 dimensions demonstrates that the quantum disordered superfluid is equivalent to an ordered superconductor and the other way around. Such a duality structure should be ubiquitous but in 3+1 (and higher) dimensions a precise formulation of the duality is lacking. The problem is that the topological defects become extended objects, strings in 3+1D. We argue how the condensate of such vortex strings must behave from the known physics of the disordered superfluid, namely the Bose-Mott insulator. A flaw in earlier proposals is repaired, and a more direct viewpoint, avoiding gauge fields, in terms of the physical supercurrent is laid out, that also easily generalizes to higher-dimensional and more complicated systems. Furthermore topological defects are readily identified; we demonstrate that the Bose-Mott insulator supports line defects, which may be seen in cold atom experiments.Comment: LaTeX, 25 pages, 5 figures; several revisions and addition

Pacifying the Fermi-liquid: battling the devious fermion signs

The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated into a geometrical constraint structure (the {\em nodal hypersurface}) acting on an effective bosonic dynamics. As an illustrative example we use this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some possible connections between mixed Bose/Fermi systems and supersymmetry.Comment: 28 pages, 5 figure

Efficient Enumeration of Non-Equivalent Squares in Partial Words with Few Holes

International audienceA partial word is a word with holes (also called don't cares: special symbols which match any symbol). A p-square is a partial word matching at least one standard square without holes (called a full square). Two p-squares are called equivalent if they match the same sets of full squares. Denote by psquares(T) the number of non-equivalent p-squares which are subwords of a partial word T. Let PSQUARES k (n) be the maximum value of psquares(T) over all partial words of length n with k holes. We show asympthotically tight bounds: c1 · min(nk 2 , n 2) ≤ PSQUARES k (n) ≤ c2 · min(nk 2 , n 2) for some constants c1, c2 > 0. We also present an algorithm that computes psquares(T) in O(nk 3) time for a partial word T of length n with k holes. In particular, our algorithm runs in linear time for k = O(1) and its time complexity near-matches the maximum number of non-equivalent p-squares

The Berry phase of dislocations in graphene and valley conserving decoherence

We demonstrate that dislocations in the graphene lattice give rise to electron Berry phases equivalent to quantized values {0,1/3,-1/3} in units of the flux quantum, but with an opposite sign for the two valleys. An elementary scale consideration of a graphene Aharonov-Bohm ring equipped with valley filters on both terminals, encircling a dislocation, says that in the regime where the intervalley mean free path is large compared to the intravalley phase coherence length, such that the valley quantum numbers can be regarded as conserved on the relevant scale, the coherent valley-polarized currents sensitive to the topological phases have to traverse the device many times before both valleys contribute, and this is not possible at intermediate temperatures where the latter length becomes of order of the device size, thus leading to an apparent violation of the basic law of linear transport that magnetoconductance is even in the applied flux. We discuss this discrepancy in the Feynman path picture of dephasing, when addressing the transition from quantum to classical dissipative transport. We also investigate this device in the scattering matrix formalism, accounting for the effects of decoherence by the Buttiker dephasing voltage probe type model which conserves the valleys, where the magnetoconductance remains even in the flux, also when different decoherence times are allowed for the individual, time reversal connected, valleys.Comment: 14 pages, 7 figures; revised text, added figure, accepted for publication by PR

Electronic States of Graphene Grain Boundaries

We introduce a model for amorphous grain boundaries in graphene, and find that stable structures can exist along the boundary that are responsible for local density of states enhancements both at zero and finite (~0.5 eV) energies. Such zero energy peaks in particular were identified in STS measurements [J. \v{C}ervenka, M. I. Katsnelson, and C. F. J. Flipse, Nature Physics 5, 840 (2009)], but are not present in the simplest pentagon-heptagon dislocation array model [O. V. Yazyev and S. G. Louie, Physical Review B 81, 195420 (2010)]. We consider the low energy continuum theory of arrays of dislocations in graphene and show that it predicts localized zero energy states. Since the continuum theory is based on an idealized lattice scale physics it is a priori not literally applicable. However, we identify stable dislocation cores, different from the pentagon-heptagon pairs, that do carry zero energy states. These might be responsible for the enhanced magnetism seen experimentally at graphite grain boundaries.Comment: 10 pages, 4 figures, submitted to Physical Review

Abelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1

We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds applications in several fields such as combinatorics on words; for example, in pattern avoidance it is often used to construct infinite words avoiding given patterns. It has been shown that the factor complexity of vtm, i.e., the number of factors of length n, is Θ(n); in fact, it is bounded by ¹⁰⁄₃n for all n, and it reaches that bound precisely when n can be written as 3 times a power of 2. In this paper, we show that the abelian complexity of vtm, i.e., the number of Parikh vectors of length n, is O(log n) with constant approaching ¾ (assuming base 2 logarithm), and it is Ω(1) with constant 3 (and these are the best possible bounds). We also prove some results regarding factor indices in vtm."F. Blanchet-Sadri and Nathan Fox’s research was supported by the National Science Foundation under Grant No. DMS–1060775." "James D. Currie and Narad Rampersad’s research was supported by NSERC Discovery grants.

Bethe Ansatz Equations for General Orbifolds of N=4 SYM

We consider the Bethe Ansatz Equations for orbifolds of N =4 SYM w.r.t. an arbitrary discrete group. Techniques used for the Abelian orbifolds can be extended to the generic non-Abelian case with minor modifications. We show how to make a transition between the different notations in the quiver gauge theory.Comment: LaTeX, 66 pages, 9 eps figures, minor corrections, references adde

What Will You Do for the Rest of the Day?

Understanding and predicting human mobility is vital to a large number of applications, ranging from recommendations to safety and urban service planning. In some travel applications, the ability to accurately predict the user's future trajectory is vital for delivering high quality of service. The accurate prediction of detailed trajectories would empower location-based service providers with the ability to deliver more precise recommendations to users. Existing work on human mobility prediction has mainly focused on the prediction of the next location (or the set of locations) visited by the user, rather than on the prediction of the continuous trajectory (sequences of further locations and the corresponding arrival and departure times). Furthermore, existing approaches often return predicted locations as regions with coarse granularity rather than geographical coordinates, which limits the practicality of the prediction. In this paper, we introduce a novel trajectory prediction problem: given historical data and a user's initial trajectory in the morning, can we predict the user's full trajectory later in the day (e.g. the afternoon trajectory)? The predicted continuous trajectory includes the sequence of future locations, the stay times, and the departure times. We first conduct a comprehensive analysis about the relationship between morning trajectories and the corresponding afternoon trajectories, and found there is a positive correlation between them. Our proposed method combines similarity metrics over the extracted temporal sequences of locations to estimate similar informative segments across user trajectories. Our evaluation shows results on both labeled and geographical trajectories with a prediction error reduced by 10-35% in comparison to the baselines. This improvement has the potential to enable precise location services, raising usefulness to users to unprecedented levels. We also present empirical evaluations with Markov model and Long Short Term Memory (LSTM), a state-of-the-art Recurrent Neural Network model. Our proposed method is shown to be more effective when smaller number of samples are used and is exponentially more efficient than LSTM.</jats:p