Kinetic energy functional for Fermi vapors in spherical harmonic confinement

Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure

The chemical potential for the inhomogeneous electron liquid in terms of its kinetic and potential parts with special consideration of the surface pote ntial step and BCS-BEC crossover

The chemical potential $\mu$ of a many-body system is valuable since it carries fingerprints of phase changes. Here, we summarize results for $\mu$ for a thre e-dimensional electron liquid in terms of average kinetic and potential energie s per particle. The difference between $\mu$ and the energy per particle is fou nd to be exactly the electrostatic potential step at the surface. We also prese nt calculations for an integrable one-dimensional many-body system with delta f unction interactions, exhibiting a BCS-BEC crossover. It is shown that in the B CS regime the chemical potential can be expressed solely in terms of the ground -state energy per particle. A brief discussion is also included of the strong c oupling BEC limit.Comment: 4 pages 3 figure

When the shoe doesn’t fit: supporting students who are challenged by online educational technologies

Taking an action research approach, this paper explores the experiences of graduate level students who found a technology enabled classroom challenging. After taking part in an online orientation activity, the students began their studies in a three week face-to-face residency, followed by two distance learning sessions. At the end of the second session, 15% of the students had either taken a leave of absence, or left the program permanently. Current literature focuses on several issues that have a negative influence on students’ ability to achieve their educational goals in an online environment. These issues include isolation, lack of preparedness, and feeling overwhelmed. Building on this, we explored the following question: How can educational technology be used to increase retention for students enrolled in an online course? Aimed at identifying approaches to overcoming some of the problems associated with studying online, we sought to examine the perceptions of MBA students by asking the participants to take part in a focus group discussion. This paper will discuss the challenges found by the graduate level students who worked in a computer-mediated educational environment, as well as highlight some of the solutions aimed at increasing student retention by enhancing the online classroom. Findings revealed that technologies aimed at encouraging student presence in the online classroom, as well as those that allow them to interact socially online could positively increase student retention. In addition, employing tools that support the students’ desire to repeat and reflect on material serves to improve the experience for those studying online. Finally, instructors who display comfort with the use of technology also have a positive impact on student learning. By providing a heightened awareness of the issues faced by graduate students working online, as well as spotlighting some key solutions, this study underscores the importance of targeting appropriate technologies when designing the online classroom. Further studies in this area could explore undergraduate engagement, generational differences, as well as learning preferences in the context of online learning

Adaptive social learning

This paper investigates the learning foundations of economic models of social learning. We pursue the prevalent idea in economics that rational play is the outcome of a dynamic process of adaptation. Our learning approach offers us the possibility to clarify when and why the prevalent rational (equilibrium) view of social learning is likely to capture observed regularities in the field. In particular it enables us to address the issue of individual and interactive knowledge. We argue that knowledge about the private belief distribution is unlikely to be shared in most social learning contexts. Absent this mutual knowledge, we show that the long-run outcome of the adaptive process favors non-Bayesian rational play.social Learning ; informational herding ; adaptation ; analogies ; non-Bayesian updating