Single-beam, ponderomotive-optical trap for free electrons and neutral atoms

A ponderomotive-optical trap for energetic free electrons has been generated with a single, high-peak-power laser beam. The focal region consists of an intensity minimum at the center of the focus, with increasing intensities in all directions. The focus can be generated with a two-zone binary phase plate, or with a novel, coaxially segmented wave plate. This scheme can also be used to trap neutral atoms.     

Microcanonical density functionals for critical systems: An exact one-dimensional example

Free-energy functionals suitable for describing realistic, nonuniform systems near criticality are discussed with emphasis on the advantages of a local formalism. It is proposed to investigatemicro canonical functionals in which both the usual order-parameter (or magnetization) density m(r)and the local energy density (r), which has independent critical fluctuations, are employed. This approach is tested by an exact calculation of the microcanonical functional [{m}, {}] in the continuum limit for a one-dimensional Ising model. Remarkably, the microcanonical functional is found to be local irrespective of the proximity to the critical point (located at zero temperature and zero field). Furthermore, its form relates closely to the scaling postulate advanced earlier by de Gennes and Fisher and displays features of conformal covariance.