1,721,160 research outputs found
Abstract dynamical systems: Remarks on symmetries and reduction
No full textIn this paper, we review how an algebraic formulation for the dynamics of a physical system allows to describe a reduction procedure for both classical and quantum evolutions
A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture
No full textTopology 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
Topological Order, Mixed States and Open Systems
No full textThe role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states have received attention in the literature only quite recently. In particular, it is still unclear whether the generalisation of the Aharonov-Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse, from a general viewpoint, topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries
Symmetries and reduction Part II-Lagrangian and Hamilton-Jacobi picture
No full textFollowing the analysis we have presented in a previous paper (that we refer to as [I]), we describe a Noether theorem related to symmetries, with the associated reduction procedures, for classical dynamics within the Lagrangian and the Hamilton-Jacobi formalism
Symmetries and reduction Part i - Poisson and symplectic picture
No full textCoherently with the principle of analogy suggested by Dirac, we describe a general setting for reducing a classical dynamics, and the role of the Noether theorem - connecting symmetries with constants of the motion - within a reduction. This is the first of two papers, and it focuses on the reduction within the Poisson and the symplectic formalism
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