اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Spacetime Geometry picture of Forest Fire Spreading and of Quantum Navigation
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G.W. Gibbons
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The problem of finding null geodesics in a stationary Lorentzian spacetime is known to to be equivalent to finding the geodsics of a Randers-Finlser structure. This latter problem is equivalent to finding the motion of charged particles moving on a Riemannian manifold in a background magnetic field or equivalently, by a generalization of Fermats principle, to Zermelos problem of extremizing travel time of an aeroplane in the presence of a wind. In this paper this triad of equivalences is extended to include recent model of the spread of a forest fire which uses form of Huyghens principle. The construction may also be used to solve a problem in quantum control theory in which one seeks a control Hamiltonia taking an initial state of a quantum mechanical system with its own Hamiltonian to a desired final state in least time. The associated stationary spacetime may be thought of as defined on an extended quantum phase space (Souriaus evolution space), the space of quantum stares being complex projective space equipped with its Fubini-Study Kahler metric. It is possible that this spacetime view point may provide insights relevant for our understanding of quantum gravity.
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