Probing molecular dynamics at the nanoscale via an individual paramagnetic center

Understanding the dynamics of molecules adsorbed to surfaces or confined to small volumes is a matter of increasing scientific and technological importance. Here, we demonstrate a pulse protocol using individual paramagnetic nitrogen vacancy (NV) centers in diamond to observe the time evolution of 1H spins from organic molecules located a few nanometers from the diamond surface. The protocol records temporal correlations among the interacting 1H spins, and thus is sensitive to the local system dynamics via its impact on the nuclear spin relaxation and interaction with the NV. We are able to gather information on the nanoscale rotational and translational diffusion dynamics by carefully analyzing the time dependence of the NMR signal. Applying this technique to various liquid and solid samples, we find evidence that liquid samples form a semi-solid layer of 1.5 nm thickness on the surface of diamond, where translational diffusion is suppressed while rotational diffusion remains present. Extensions of the present technique could be adapted to highlight the chemical composition of molecules tethered to the diamond surface or to investigate thermally or chemically activated dynamical processes such as molecular folding

Exact solution of discrete two-dimensional R2^{2} gravity

We exactly solve a special matrix model of dually weighted planar graphs describing pure two-dimensional quantum gravity with a R^2 interaction in order to study the intermediate regimes between the gravitating and flat metric. The flat space is modeled by a regular square lattice, while localized curvature is being introduced through defects of the lattice. No ``flattening'' phase transition is found with respect to the R^2 coupling: the infrared behaviour of the system is that of pure gravity for any finite R^2 coupling. In the limit of infinite coupling, we are able to extract a scaling function interpolating between pure gravity and a phase of a dilute gas of curvature defects on a flat background. We introduce and explain some novel techniques concerning our method of large N character expansions and the calculation of Schur characters on big Young tableaux

Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to generic finite-dimensional representations in quantum space. The results equally apply to non-compact representations of highest or lowest weight type. We furthermore fill an apparent gap in the literature, and provide the nearest-neighbor Hamiltonians of the spin chains in question for all cases where the gl(n) representations are described by rectangular Young diagrams, as well as for their infinite-dimensional generalizations. They take the form of digamma functions depending on operator-valued shifted weights

Oscillator construction of su(n|m) Q-operators

We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded Yang-Baxter equation, leading to an amalgam of bosonic and fermionic oscillator algebras. Our approach is fully algebraic, and leads to the exact solution of the associated compact spin chains while avoiding Bethe ansatz techniques. It furthermore elucidates the algebraic and combinatorial structures underlying the system of nested Bethe equations. Finally, our construction naturally reproduces the representation, due to Z. Tsuboi, of the hierarchy of Baxter Q-operators in terms of hypercubic Hasse diagrams. © 2011 Elsevier B.V

Non-Integrability of Two-Dimensional QCD

In this paper we numerically demonstrate that massless two-dimensional QCD is not integrable. To this aim, we explicitly solve the 't Hooft integral equation for bound states by an adaptive spline procedure, and compute the decay amplitudes. These amplitudes significantly differ from zero except in all cases in which the decay also produces a pion.Comment: 9 pages, 6 encapsulated Postscript figures, uses epsfi

A shortcut to the Q-operator

Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare our approach to and differentiate it from earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT. © 2010 IOP Publishing Ltd and SISSA

Harmonic R matrices for scattering amplitudes and spectral regularization

Planar N=4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of nonintegrable four-dimensional field theories. © 2013 American Physical Society

Strong coupling from the Hubbard model

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter \lambda becomes large. We show that the full dimension \Delta of the Konishi superpartner is the solution of a sixth order polynomial while \Delta for a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large \lambda and the equations can be inverted to express \lambda as an explicit function of \Delta. We then consider more general operators and show how \Delta depends on \lambda in the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of \lambda. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.Comment: 14 pages; v2: 17 pages, 2 figures, appendix and references added; typos fixed, minor changes; v3 fixed figures; v4 more references added, minor correctio

Spectral parameters for scattering amplitudes in N=4 super Yang-Mills theory

Planar N= 4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N= 4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions. © 2014 The Author(s)

Generalized Two-Dimensional QCD

We study two-dimensional gauge theories with fundamental fermions and a general first order gauge-field Lagrangian. For the case of U(1) we show how standard bosonization of the Schwinger model generalizes to give mesons interacting through a general Landau-Ginzburg potential. We then show how for a subclass of SU(N) theories, 't Hooft's solution of large N two-dimensional QCD can be generalized in a consistent and natural manner. We finally point out the possible relevance of studying these theories to the string formulation of two-dimensional QCD as well as to understanding QCD in higher dimensions.Comment: LPTENS-94/2, IASSNS-HEP-94/3, and RU-94-8. (harvmac with 4 figures, 23 pp.