Analytic Controllability of Time-Dependent Quantum Control Systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page

Capturing, sharing and analysing biophysical data from protein engineering and protein characterization studies

Large amounts of data are being generated annually on the connection between the sequence, structure and function of proteins using site-directed mutagenesis, protein design and directed evolution techniques. These data provide the fundamental building blocks for our understanding of protein function, molecular biology and living organisms in general. However, much experimental data are never deposited in databases and is thus ‘lost’ in journal publications or in PhD theses. At the same time theoretical scientists are in need of large amounts of experimental data for benchmarking and calibrating novel predictive algorithms, and theoretical progress is therefore often hampered by the lack of suitable data to validate or disprove a theoretical assumption. We present PEAT (Protein Engineering Analysis Tool), an application that integrates data deposition, storage and analysis for researchers carrying out protein engineering projects or biophysical characterization of proteins. PEAT contains modules for DNA sequence manipulation, primer design, fitting of biophysical characterization data (enzyme kinetics, circular dichroism spectroscopy, NMR titration data, etc.), and facilitates sharing of experimental data and analyses for a typical university-based research group. PEAT is freely available to academic researchers at http://enzyme.ucd.ie/PEAT