We study caustics in classical and quantum mechanics for systems with quadratic Lagrangians of the form L = 1 2 ẋ − 1 2 λ(t)x − μ(t)x. We derive a closed form of the transition amplitude on caustics and discuss their physical implications in the Gaussian slit (gedanken-)experiment. Application to the quantum mechanical rotor casts doubt on the validity of Jevicki’s correspondence hypothesis whi...

We simulate the growth of isolated dark matter haloes from self-similar and spherically symmetric initial conditions. Our N-body code integrates the geodesic deviation equation in order to track the streams and caustics associated with individual simulation particles. The radial orbit instability causes our haloes to develop major-to-minor axis ratios approaching 10 to 1 in their inner regions....

We study semiclassical sequences of distributions \(u_h\) associated with a Lagrangian submanifold phase space \(\mathcal {L}\subset T^*X\). If is distribution, which concentrates at maximal rate on {L},\) then the asymptotics are well understood by work Arnol’d, provided {L}\) projects to X stable simple singularity. establish sup-norm estimates under much more general hypotheses it concentrat...

introduction domestic and industrial swallowing of caustic substances can cause acute and chronic injuries. in the acute phase of care, focus is on the immediate control of tissue damage and perforation, and in the chronic phase, the focus is on the treatment of pharyngeal narrowing and impaired swallowing. conclusions treatment of esophageal burn lesions is by immediate and delayed removing of...

We discuss the nonparaxial focusing of laser light into a three-dimensional (3D) spiral distribution. For calculating tangential and normal components electromagnetic field on preset curved surface we propose an asymptotic method, using which derive equations for stationary points relations in form one-dimensional (1D) integrals over radial component. The results obtained through approach direc...