Bohmian trajectories and the Path Integral Paradigm. Complexified Lagrangian Mechanics

David Bohm shown that the Schr{\"o}dinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions - action and probability density. The first equation is the Hamilton-Jacobi (HJ) equation, a "visiting card" of classical mechanics, to be modified by the Bohmian quantum potential. And the second is the continuity equation. The latter can be transformed to the entropy balance equation. The Bohmian quantum potential is transformed to two Bohmian quantum correctors. The first corrector modifies kinetic energy term of the HJ equation, and the second one modifies potential energy term. Unification of the quantum HJ equation and the entropy balance equation gives complexified HJ equation containing complex kinetic and potential terms. Imaginary parts of these terms have order of smallness about the Planck constant. The Bohmian quantum corrector is indispensable term modifying the Feynman's path integral by expanding coordinates and momenta to imaginary sector.Comment: 14 pages, 3 figures, 46 references, 48 equation

Experimental search for long-range forces in neutron scattering via a gravitational spectrometer

© 2014 American Physical Society, https://dx.doi.org/10.1103/physrevc.89.044002In this work we introduce a method of measuring low-energy scattering cross section with a gravitational spectrometer. In this method we add atoms (i.e., He) to the gravitational spectrometer filled with a target gas of ultracold neutrons (UCN). We search for long-range forces between atoms and UCN by measuring transfer of a small recoil energy similar to 10(-7) eV using the gravitational spectrometer. As a result of this search we set new constraints on the strength of long-range forces within the range of the effective radius of interaction of 10(-7)-10(-4) cm.Russian Foundation for Basic Research (Projects No. 08-02-01052a, No. 10-02-00217a, and No. 10-02-00224a)Ministry of Education and Science of the Russian Federation (Contracts No. 02.740.11.0532 and No. 14.740.11.0083