4,985 research outputs found
Quantum affine Toda solitons
We review some of the progress in affine Toda field theories in recent years,
explain why known dualities cannot easily be extended, and make some
suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision
Quantum Walks driven by many coins
Quantum random walks have been much studied recently, largely due to their
highly nonclassical behavior. In this paper, we study one possible route to
classical behavior for the discrete quantum random walk on the line: the use of
multiple quantum ``coins'' in order to diminish the effects of interference
between paths. We find solutions to this system in terms of the single coin
random walk, and compare the asymptotic limit of these solutions to numerical
simulations. We find exact analytical expressions for the time-dependence of
the first two moments, and show that in the long time limit the ``quantum
mechanical'' behavior of the one-coin walk persists. We further show that this
is generic for a very broad class of possible walks, and that this behavior
disappears only in the limit of a new coin for every step of the walk.Comment: 36 pages RevTeX 4.0 + 5 figures (encapsulated Postscript). Submitted
to Physical Review
The LuckyCam Survey for Very Low Mass Binaries II: 13 new M4.5-M6.0 Binaries
We present results from a high-angular-resolution survey of 78 very low mass
(VLM) binary systems with 6.0 = 0.15
arcsec/yr. 21 VLM binaries were detected, 13 of them new discoveries. The new
binary systems range in separation between 0.18 arcsec and 1.3 arcsec. The
distance-corrected binary fraction is 13.5% (+6.5%/-4%), in agreement with
previous results. 9 of the new binary systems have orbital radii > 10 AU,
including a new wide VLM binary with 27 AU projected orbital separation. One of
the new systems forms two components of a 2300 AU separation triple system. We
find that the orbital radius distribution of the binaries with V-K < 6.5 in
this survey appears to be different from that of redder (lower-mass) objects,
suggesting a possible rapid change in the orbital radius distribution at around
the M5 spectral type. The target sample was also selected to investigate X-ray
activity among VLM binaries. There is no detectable correlation between excess
X-Ray emission and the frequency and binary properties of the VLM systems.Comment: 11 pages, 8 figures. Submitted to MNRA
Secret Symmetries in AdS/CFT
We discuss special quantum group (secret) symmetries of the integrable system
associated to the AdS/CFT correspondence. These symmetries have by now been
observed in a variety of forms, including the spectral problem, the boundary
scattering problem, n-point amplitudes, the pure-spinor formulation and quantum
affine deformations.Comment: 20 pages, pdfLaTeX; Submitted to the Proceedings of the Nordita
program `Exact Results in Gauge-String Dualities'; Based on the talk
presented by A.T., Nordita, 15 February 201
Absorption problems for quantum walks in one dimension
This paper treats absorption problems for the one-dimensional quantum walk
determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N
is finite or infinite by using a new path integral approach based on an
orthonormal basis P, Q, R and S of the vector space of complex 2 times 2
matrices. Our method studied here is a natural extension of the approach in the
classical random walk.Comment: 15 pages, small corrections, journal reference adde
Scaling of the Critical Function for the Standard Map: Some Numerical Results
The behavior of the critical function for the breakdown of the homotopically
non-trivial invariant (KAM) curves for the standard map, as the rotation number
tends to a rational number, is investigated using a version of Greene's residue
criterion. The results are compared to the analogous ones for the radius of
convergence of the Lindstedt series, in which case rigorous theorems have been
proved. The conjectured interpolation of the critical function in terms of the
Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table
Excitation Thresholds for Nonlinear Localized Modes on Lattices
Breathers are spatially localized and time periodic solutions of extended
Hamiltonian dynamical systems. In this paper we study excitation thresholds for
(nonlinearly dynamically stable) ground state breather or standing wave
solutions for networks of coupled nonlinear oscillators and wave equations of
nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously
characterized by variational methods. The excitation threshold is related to
the optimal (best) constant in a class of discr ete interpolation inequalities
related to the Hamiltonian energy. We establish a precise connection among ,
the dimensionality of the lattice, , the degree of the nonlinearity
and the existence of an excitation threshold for discrete nonlinear
Schr\"odinger systems (DNLS).
We prove that if , then ground state standing waves exist if
and only if the total power is larger than some strictly positive threshold,
. This proves a conjecture of Flach, Kaldko& MacKay in
the context of DNLS. We also discuss upper and lower bounds for excitation
thresholds for ground states of coupled systems of NLS equations, which arise
in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
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