Quantum control and the Strocchi map

Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite real inner product which provides a geometrical interpretation of the measurement process. Together they endow the quantum Hilbert space with the structure of a K\"{a}ller manifold. Quantum control is discussed in this setting. Quantum time-evolution corresponds to smooth Hamiltonian dynamics and measurements to jumps in the phase space. This adds additional power to quantum control, non unitarily controllable systems becoming controllable by ``measurement plus evolution''. A picture of quantum evolution as Hamiltonian dynamics in a classical-like phase-space is the appropriate setting to carry over techniques from classical to quantum control. This is illustrated by a discussion of optimal control and sliding mode techniques.Comment: 16 pages Late

Geometry-dependent scattering through quantum billiards: Experiment and theory

We present experimental studies of the geometry-specific quantum scattering in microwave billiards of a given shape. We perform full quantum mechanical scattering calculations and find an excellent agreement with the experimental results. We also carry out the semiclassical calculations where the conductance is given as a sum of all classical trajectories between the leads, each of them carrying the quantum-mechanical phase. We unambiguously demonstrate that the characteristic frequencies of the oscillations in the transmission and reflection amplitudes are related to the length distribution of the classical trajectories between the leads, whereas the frequencies of the probabilities can be understood in terms of the length difference distribution in the pairs of classical trajectories. We also discuss the effect of non-classical "ghost" trajectories that include classically forbidden reflection off the lead mouths.Comment: 4 pages, 4 figure

BetaMDGP: Protein Structure Determination Algorithm Based on the Beta-complex

International audienceThe molecular distance geometry problem (MDGP) is a fundamental problem in determining molecular structures from the NMR data. We present a heuristic algorithm, the BetaMDGP, which outperforms existing algorithms for solving the MDGP. The BetaMDGP algorithm is based on the beta-complex, which is a geometric construct extracted from the quasi-triangulation derived from the Voronoi diagram of atoms. Starting with an initial tetrahedron defined by the centers of four closely located atoms, the BetaMDGP determines a molecular structure by adding one shell of atoms around the currently determined substructure using the beta-complex. The proposed algorithm has been entirely implemented and tested with atomic arrangements stored in an NMR format created from PDB files. Experimental results are also provided to show the powerful capability of the proposed algorithm

Solution structure of the second PDZ domain of the neuronal adaptor X11alpha and its interaction with the C-terminal peptide of the human copper chaperone for superoxide dismutase

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