98,135 research outputs found

    Hybrid Mechanical Systems

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    We discuss hybrid systems in which a mechanical oscillator is coupled to another (microscopic) quantum system, such as trapped atoms or ions, solid-state spin qubits, or superconducting devices. We summarize and compare different coupling schemes and describe first experimental implementations. Hybrid mechanical systems enable new approaches to quantum control of mechanical objects, precision sensing, and quantum information processing.Comment: To cite this review, please refer to the published book chapter (see Journal-ref and DOI). This v2 corresponds to the published versio

    General Volume-Preserving Mechanical Systems

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    In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, \omega). It is shown that every volume-preserving flow has some 2-forms acting the role of the Hamiltonian functions in the Hamiltonian mechanics and the ordinary Hamilton equations are included as a special case with a 2-form \frac{1}{n-1} H \omega where H is the corresponding Hamiltonian.Comment: Plain LaTeX, 13 pages, no figure

    Mechanical Systems: Symmetry and Reduction

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    Reduction theory is concerned with mechanical systems with symmetries. It constructs a lower dimensional reduced space in which associated conservation laws are taken out and symmetries are \factored out" and studies the relation between the dynamics of the given system with the dynamics on the reduced space. This subject is important in many areas, such as stability of relative equilibria, geometric phases and integrable systems

    Control of interconnected mechanical systems

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    In this paper control systems design approach, based on siding mode methods, that allows maintain some functional relation – like bilateral or multilateral systems, establishment of virtual relation among mobile robots or control of haptic systems - is presented. It is shown that all basic motion control problems - trajectory tracking, force control, hybrid position/force control scheme and the impedance control for the interacting systems- can be treated in the same way while avoiding the structural change of the controller and guarantying stable behavior of the system In order to show applicability of the proposed techniques simulation and experimental results for high precision systems in microsystems assembly tasks are presented.

    Temporal behavior of quantum mechanical systems

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    The temporal behavior of quantum mechanical systems is reviewed. We study the so-called quantum Zeno effect, that arises from the quadratic short-time behavior, and the analytic properties of the ``survival" amplitude. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system. Some attempts at extracting the exponential decay law from quantum theory, aiming at the master equation, are briefly reviewed, including van Hove's pioneering work and his well-known ``λ2T\lambda^2T" limit. We clarify these general arguments by introducing and studying a solvable dynamical model. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.Comment: 48 pages, LaTeX, uuencoded file with 7 figures include

    Structural identifiability of viscoelastic mechanical systems

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    We solve the local and global structural identifiability problems for viscoelastic mechanical models represented by networks of springs and dashpots. We propose a very simple characterization of both local and global structural identifiability based on identifiability tables, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks. We illustrate how to use our results in a number of examples and point to some applications in cardiovascular modeling.Comment: 3 figure

    BRST analysis of general mechanical systems

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    We study the groups of local BRST cohomology associated to the general systems of ordinary differential equations, not necessarily Lagrangian or Hamiltonian. Starting with the involutive normal form of the equations, we explicitly compute certain cohomology groups having clear physical meaning. These include the groups of global symmetries, conservation laws and Lagrange structures. It is shown that the space of integrable Lagrange structures is naturally isomorphic to the space of weak Poisson brackets. The last fact allows one to establish a direct link between the path-integral quantization of general not necessarily variational dynamics by means of Lagrange structures and the deformation quantization of weak Poisson brackets.Comment: 38 pages, misprints corrected, references and the Conclusion adde
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