Observation of PT phase transition in a simple mechanical system

If a Hamiltonian is PT symmetric, there are two possibilities: Either the eigenvalues are entirely real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else the eigenvalues are partly real and partly complex, in which case the Hamiltonian is said to be in a broken-PT-symmetric phase. As one varies the parameters of the Hamiltonian, one can pass through the phase transition that separates the unbroken and broken phases. This transition has recently been observed in a variety of laboratory experiments. This paper explains the phase transition in a simple and intuitive fashion and then describes an extremely elementary experiment in which the phase transition is easily observed.Comment: 9 pages, 9 figure

A comparison of Piagetian and psychometric measures of intelligence

The ideas of Jean Piaget have sooner or later been applied to practically every aspect of education. These ideas are based on Piaget\u27s theory that every individual progresses through four cognitive developmental stages: the sensorimotor stage, the preoperational stage, the concrete operational stage, and the formal operational stage. According to Piaget, during these stages an individual progresses from reflex reactions to the environment to the point, if and when he reaches the level of formal operations, he can think abstractly and test hypotheses

Consistency of the B\"acklund transformation for the spin Calogero-Moser system

We prove the consistency of the B\"{a}cklund transformation (BT) for the spin Calogero-Moser (sCM) system in the rational, trigonometric, and hyperbolic cases. The BT for the sCM system consists of an overdetermined system of ODEs; to establish our result, we construct and analyze certain functions that measure the departure of this overdetermined system from consistency and show, under mild assumptions, that these functions are identically zero and that this allows for a unique solution to the initial value problem for the overdetermined system.Comment: 14 page