English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The problem of finding null geodesics in a stationary Lorentzian spacetime isknown to to be equivalent to finding the geodsics of a Randers-Finlserstructure. This latter problem is equivalent to finding the motion of chargedparticles moving on a Riemannian manifold in a background magnetic field orequivalently, by a generalization of Fermat's principle, to Zermelo's problemof extremizing travel time of an aeroplane in the presence of a wind. In thispaper this triad of equivalences is extended to include recent model of thespread of a forest fire which uses form of Huyghen's principle. Theconstruction may also be used to solve a problem in quantum control theory inwhich one seeks a control Hamiltonia taking an initial state of a quantummechanical system with its own Hamiltonian to a desired final state in leasttime.  The associated stationary spacetime may be thought of as defined on anextended quantum phase space (Souriau's evolution space), the space of quantumstares being complex projective space equipped with its Fubini-Study K\"ahlermetric. It is possible that this spacetime view point may provide insightsrelevant for our understanding of quantum gravity.

A Spacetime Geometry picture of Forest Fire Spreading and of Quantum Navigation