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

The Quantum Dynamics of Two Coupled Qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as non positive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. We conclude that the dynamics is a quantum element of NMR quantum information processing. There are two limits where our quantum evolution coincide with the classical one: the short time limit before spin-spin interaction sets in and the long time limit when phase diffusion is incorporated

"‘We just want to be treated with respect!’: Using restorative approaches and the dramatic arts to build positive relationships between the police and young people"

This article explores the application of an ambitious arts-based restorative intervention that has been applied in a direct response to perceived issues with procedural justice, legitimacy and community relations between police and young people. The research focuses on a series of Youth Forums that took place in the West of England, employed as an attempt to improve strained relationships between both parties. It reports on detailed ethnographic research of the Forum processes and procedures presenting this primary evidence in light of the existing literature on police legitimacy and procedural justice in police-youth encounters. The findings suggest that community-based arts programmes can be a powerful and effective tool for challenging entrenched views with the potential to improve future encounters between police and young people; and that the relevance and effectiveness of arts-based interventions can be increased by combining with restorative justice principles