The Gorenstein defect category

We consider the homotopy category of complexes of projective modules over a Noetherian ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic complexes to the stable derived category. We show that if the ring is either Artin or commutative Noetherian local, then the functor is dense if and only if the ring is Gorenstein. Motivated by this, we define the Gorenstein defect category of the ring, a category which in some sense measures how far the ring is from being Gorenstein.Comment: 11 pages, updated versio

Circuit theory of crossed Andreev reflection

We consider transport in a three terminal device attached to one superconducting and two normal metal terminals, using the circuit theory of mesoscopic superconductivity. We compute the nonlocal conductance of the current out of the first normal metal terminal in response to a bias voltage between the second normal metal terminal and the superconducting terminal. The nonlocal conductance is given by competing contributions from crossed Andreev reflection and electron cotunneling, and we determine the contribution from each process. The nonlocal conductance vanishes when there is no resistance between the superconducting terminal and the device, in agreement with previous theoretical work. Electron cotunneling dominates when there is a finite resistance between the device and the superconducting reservoir. Decoherence is taken into account, and the characteristic timescale is the particle dwell time. This gives rise to an effective Thouless energy. Both the conductance due to crossed Andreev reflection and electron cotunneling depend strongly on the Thouless energy. We suggest to experimentally determine independently the conductance due to crossed Andreev reflection and electron cotunneling in measurement of both energy and charge flow into one normal metal terminal in response to a bias voltage between the other normal metal terminal and the superconductor.Comment: v2: Published version with minor changes, 12 pages and 9 figure

Higher order corrections to the Newtonian potential in the Randall-Sundrum model

The general formalism for calculating the Newtonian potential in fine-tuned or critical Randall-Sundrum braneworlds is outlined. It is based on using the full tensor structure of the graviton propagator. This approach avoids the brane-bending effect arising from calculating the potential for a point source. For a single brane, this gives a clear understanding of the disputed overall factor 4/3 entering the correction. The result can be written on a compact form which is evaluated to high accuracy for both short and large distances.Comment: 12 pages, LaTeX2e with RevTeX4, 3 postscript figures; Minor corrections, references update