ar X iv : 0 90 3 . 37 11 v 4 [ qu an t - ph ] 9 A pr 2 00 9 Temperley - Lieb Algebra , Yang - Baxterization and universal Gate

ar X iv : 0 90 4 . 42 75 v 1 [ m at h . FA ] 2 7 A pr 2 00 9 INVERSION POSITIVITY AND THE SHARP HARDY – LITTLEWOOD – SOBOLEV INEQUALITY

We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.

ar X iv : c on d - m at / 9 80 72 21 v 1 1 5 Ju l 1 99 8 Applications of Temperley - Lieb algebras to Lorentz lattice gases

Motived by the study of motion in a random environment we introduce and investigate a variant of the Temperley-Lieb algebra. This algebra is very rich, providing us three classes of solutions of the Yang-Baxter equation. This allows us to establish a theoretical framework to study the diffusive behaviour of a Lorentz Lattice gas. Exact results for the geometrical scaling behaviour of closed pat...

ar X iv : 0 90 7 . 47 37 v 2 [ qu an t - ph ] 3 A ug 2 00 9 QIP = PSPACE

We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a class of semidefinite programs that captures the computational power of quantum interactive proofs. As the containment of PSPACE in QIP follows i...

ar X iv : 0 90 3 . 05 62 v 1 [ as tr o - ph . G A ] 3 M ar 2 00 9 Introduction to Millimeter / Sub - Millimeter

ar X iv : m at h - ph / 0 11 00 12 v 1 9 O ct 2 00 1 Functional Equations and Poincare Invariant Mechanical Systems

We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincaré algebra: