Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer

Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces

Perturbative Gravity in the Causal Approach

Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system (massless and massive). Then we investigate the interaction of massless gravity with matter (described by scalars and spinors) and massless Yang-Mills fields. We obtain a difference with respect to the classical field theory due to the fact that in quantum field theory one cannot enforce the divergenceless property on the vector potential and this spoils the divergenceless property of the usual energy-momentum tensor. To correct this one needs a supplementary ghost term in the interaction Lagrangian.Comment: 50 pages, no figures, some changes in the last sectio

Tube Width Fluctuations in F-Actin Solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.Comment: Final version, 5 pages, 4 figure

Dynamics in binary cluster crystals

As a result of the application of coarse-graining procedures to describe complex fluids, the study of systems consisting of particles interacting through bounded, repulsive pair potentials has become of increasing interest in the last years. A well known example is the so-called Generalized Exponential Model (GEM-$m$), for which the interaction between particles is described by the potential $v(r)=\epsilon\exp[-(r/\sigma)^m]$. Interactions with $m > 2$ lead to the formation of a novel phase of soft matter consisting of cluster crystals. Recent studies on the phase behavior of binary mixtures of GEM-$m$ particles have provided evidence for the formation of novel kinds of alloys, depending on the cross interactions between the two species. This work aims to study the dynamic behavior of such binary mixtures by means of extensive molecular dynamics simulations, and in particular to investigate the effect of the addition of non-clustering particles on the dynamic scenario of one-component cluster crystals. Analogies and differences with the one-component case are revealed and discussed by analyzing self- and collective dynamic correlators.Comment: 17 pages, 8 figures, submitted to JSTA

Quantum pattern recognition with liquid-state nuclear magnetic resonance

A novel quantum pattern recognition scheme is presented, which combines the idea of a classic Hopfield neural network with adiabatic quantum computation. Both the input and the memorized patterns are represented by means of the problem Hamiltonian. In contrast to classic neural networks, the algorithm can return a quantum superposition of multiple recognized patterns. A proof of principle for the algorithm for two qubits is provided using a liquid state NMR quantum computer.Comment: updated version, Journal-ref adde

Time Optimal Control in Spin Systems

In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem of time optimal control of the unitary propagator. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. Here, we give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. We have adopted a general mathematical formulation, and present many of our results in this setting, mindful of the fact that new structures in optimal pulse design are constantly arising. Moreover, the general proofs are no more difficult than the specific problems of current interest. From a general control theory perspective, the problems we want to study have the following character. Suppose we are given a controllable right invariant system on a compact Lie group, what is the minimum time required to steer the system from some initial point to a specified final point? In NMR spectroscopy and quantum computing, this translates to, what is the minimum time required to produce a unitary propagator? We also give an analytical characterization of maximum achievable transfer in a given time for the two spin system.Comment: 20 Pages, 3 figure

Capturing the essence of grounded theory: the importance of understanding commonalities and variants

This paper aims to capture the essence of grounded theory (GT) by setting out its commonalities and variants and, importantly, the implications of the latter for the implementation of the former, and for the truth claims and the contributions to knowledge that a GT study might make. Firstly, three ontological and epistemological variants of GT are outlined. Secondly, the commonalities of GT are set out as eight core elements of GT methodology that are individually necessary, but only sufficient collectively, to define a GT study. These elements are: an iterative process; theoretical sampling; theoretical sensitivity; codes, memos and concepts; constant comparison; theoretical saturation; fit, work, relevance and modifiability; and substantive theory. Thirdly, the implications of the ontological and epistemological variants of GT for, firstly, the implementation of the core common elements of the methodology and, secondly, the truth claims and contributions to knowledge that might be made, are discussed. Finally, the paper concludes by arguing that published GT studies in sport, exercise and health research have not always explicitly demonstrated a full understand of the commonalities and variants of GT, and that researchers publishing GT studies must take responsibility for doing this

The Glassy Wormlike Chain

We introduce a new model for the dynamics of a wormlike chain in an environment that gives rise to a rough free energy landscape, which we baptise the glassy wormlike chain. It is obtained from the common wormlike chain by an exponential stretching of the relaxation spectrum of its long-wavelength eigenmodes, controlled by a single stretching parameter. Predictions for pertinent observables such as the dynamic structure factor and the microrheological susceptibility exhibit the characteristics of soft glassy rheology and compare favourably with experimental data for reconstituted cytoskeletal networks and live cells. We speculate about the possible microscopic origin of the stretching, implications for the nonlinear rheology, and the potential physiological significance of our results.Comment: 12 pages, 8 figures. Minor correction