1,721,000 research outputs found
Wave dispersion in non-linear pantographic beams
No full textIn this paper, amplitude-dependent dispersion relations for flexural and axial waves travelling along a pantographic beam in non-linear deformation regime are computed. The kinetic energy of the pantographic beam, including a gradient micro-inertia contribution, is derived by homogenization. In the limit of travelling waves with infinitesimal amplitude, well-known amplitude-independent wave dispersion relations for linear deformation regime are recovered. Our analysis concludes that exotic wave propagation is observed in pantographic beams and deserves further studies. </p
Topology and quantum states: The electron-monopole system
Full text linkThis paper starts by describing the dynamics of the electronmonopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are classically described on topologically non-trivial configuration spaces, to consider Hilbert spaces of exterior differential forms. Among the advantages of this
formulation, we present—in the case of the group SU(2), how it is possible to obtain all unitary irreducible representations on such a Hilbert space, and how it is possible to write scalar Dirac-type operators, following an idea by K¨ahler
A Review of Some Selected Examples of Mechanical and Acoustic Metamaterials
No full textThe scope of this volume is limited to metamaterials based on microstructural phenomena involving purely mechanical interactions. In general the exotic behavior of metamaterials is obtained by using multiscale architectured internal structures: it is assumed here that at the lowest considered scale a mechanical description is sufficient. The literature in the field being enormous, only a targeted selection of mechanical metamaterials has been considered, aiming to give an analysis of the literature relevant to the specific application developed in Chapter 3
A quantum route to the classical Lagrangian formalism
No full textUsing the recently developed groupoidal description of Schwinger's picture of Quantum Mechanics, a new approach to Dirac's fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function on the groupoid of configurations (or kinematical groupoid) of a quantum system determines a state on the von Neumann algebra of the histories of the system. This function, which we call q-Lagrangian, can be described in terms of a new function on the Lie algebroid of the theory. When the kinematical groupoid is the pair groupoid of a smooth manifold M, the quadratic expansion of will reproduce the standard Lagrangians on TM used to describe the classical dynamics of particles
Feynman's propagator in Schwinger's picture of Quantum Mechanics
No full textA novel derivation of Feynman's sum-over-histories construction of the quantum propagator using the groupoidal description of Schwinger picture of Quantum Mechanics is presented. It is shown that such construction corresponds to the GNS representation of a natural family of states called Dirac-Feynman-Schwinger (DFS) states. Such states are obtained from a q-Lagrangian function l on the groupoid of configurations of the system. The groupoid of histories of the system is constructed and the q-Lagrangian l allows us to define a DFS state on the algebra of the groupoid. The particular instance of the groupoid of pairs of a Riemannian manifold serves to illustrate Feynman's original derivation of the propagator for a point particle described by a classical Lagrangian L
Lagrangian description of Heisenberg and Landau-von Neumann equations of motion
No full textAn explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau-von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed reference quantum state
Causality in Schwinger’s Picture of Quantum Mechanics
No full textThis paper begins the study of the relation between causality and quantum mechanics, tak-ing advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger’s picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin’s incidence theorem will be proved and some illustrative examples will be discussed
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