Non-Linear Sigma Models on a Half Plane

In the context of integrable field theory with boundary, the integrable non-linear sigma models in two dimensions, for example, the $O(N)$, the principal chiral, the ${\rm CP}^{N-1}$ and the complex Grassmannian sigma models are discussed on a half plane. In contrast to the well known cases of sine-Gordon, non-linear Schr\"odinger and affine Toda field theories, these non-linear sigma models in two dimensions are not classically integrable if restricted on a half plane. It is shown that the infinite set of non-local charges characterising the integrability on the whole plane is not conserved for the free (Neumann) boundary condition. If we require that these non-local charges to be conserved, then the solutions become trivial.Comment: 25 pages, latex, no figure

A note on the equivalence of a barotropic perfect fluid with a K-essence scalar field

In this short note, we obtain the necessary and sufficient condition for a class of non-canonical single scalar field models to be exactly equivalent to barotropic perfect fluids, under the assumption of an irrotational fluid flow. An immediate consequence of this result is that the non-adiabatic pressure perturbation in this class of scalar field systems vanishes exactly at all orders in perturbation theory and on all scales. The Lagrangian for this general class of scalar field models depends on both the kinetic term and the value of the field. However, after a field redefinition, it can be effectively cast in the form of a purely kinetic K-essence model.Comment: 4 pages, 1 figure; v2: References and footnotes 3 and 4 added. Replaced to match published versio

Demonstration of an optical quantum controlled-NOT gate without path interference

We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals (Phys. Rev. A {\bf 66}, 024308 (2001), Phys. Rev. A {\bf 65}, 012314 (2002)) have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittances and reflectances. The performance of the device is evaluated using a recently proposed method (Phys. Rev. Lett. {\bf 94}, 160504 (2005)), by which the quantum process fidelity and the entanglement capability can be estimated from the 32 measurement results of two classical truth tables, significantly less than the 256 measurement results required for full quantum tomography.Comment: 4 pages, 3 figure

Temperature Chaos, Rejuvenation and Memory in Migdal-Kadanoff Spin Glasses

We use simulations within the Migdal-Kadanoff real space renormalization approach to probe the scales relevant for rejuvenation and memory in spin glasses. One of the central questions concerns the role of temperature chaos. First we investigate scaling laws of equilibrium temperature chaos, finding super-exponential decay of correlations but no chaos for the total free energy. Then we perform out of equilibrium simulations that follow experimental protocols. We find that: (1) rejuvenation arises at a length scale smaller than the ``overlap length'' l(T,T'); (2) memory survives even if equilibration goes out to length scales much larger than l(T,T').Comment: 4 pages, 4 figures, added references, slightly changed content, modified Fig.