Contact geometry extends the symplectic framework to odd-dimensional phase spaces, providing a natural arena for systems with dissipation or energy exchange. A contact manifold is endowed with a ...
Sub-Riemannian geometry is a branch of differential geometry in which the motion of a system is constrained to lie within a specified distribution of allowable directions on a manifold. Unlike its ...
MIT physicists and colleagues have for the first time measured the geometry, or shape, of electrons in solids at the quantum level. Scientists have long known how to measure the energies and ...
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