This report concerns the energy of a zero-temperature many-body system of spin 1 2 fermions interacting via a two-body potential with a free space infinite scattering length and zero effective range; the Unitary limit. Given the corresponding phase-shift δ(k) = π/2 a one-term separable potential is obtained by inverse scattering assuming a momentum cutoff Λ such that δ(k) = 0 for k > Λ. The eff...

We study the nonrelativistic limit of the quantum theory of a real scalar field with quartic self-interaction. The two body scattering amplitude is written in such way as to separate the contributions of high and low energy intermediary states. From this result and the two loop computation of the self energy correction, we determine an effective nonrelativistic action.

– In order to extend the Landauer formulation of quantum transport to spinless correlated fermions, we consider a system in which charge carriers interact, connected to two reservoirs by non-interacting one-dimensional leads. We study the size of the attached leads necessary for reducing this many-body scatterer to an effective one-body scatterer with interaction-dependent parameters. To obtain...

We study the electromagnetic Casimir interaction of a compact object contained inside a closed cavity of another compact object. We express the interaction energy in terms of the objects’ scattering matrices and translation matrices that relate the coordinate systems appropriate to each object. When the enclosing object is an otherwise empty metallic spherical shell, much larger than the intern...

We study models of itinerant spinless fermions with random long-range interactions. We motivate such models from descriptions of fermionic atoms in multimode optical cavities. The solution of an infinite-range model yields a metallic phase, which has glassy charge dynamics, and a localized glass phase with suppressed density of states at low energies. We compare these phases to the conventional...

This article addresses the links and interactions between the neuroscience parallel line of theories and the parallel line of mental activity and thinking. An argument is made that the most fundamental biological entity, the human genome, provides a pathway of mind-body functional coordination via a double helix metaphor. Brief selections of neuroscience and psychological theories associated wi...