A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations

We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter which extend those proposed by Kohn and Serfaty (2010). These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution of the PDE as the parameter tends to zero. Moreover, our construction allows us to treat both the oblique and the mixed type Dirichlet-Neumann boundary conditions.Comment: 58 pages, 2 figure

Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses

We show how to construct loss-tolerant linear steering inequalities using a generic set of von Neumann measurements that are violated by $d$-dimensional states, and that rely only upon a simple property of the set of measurements used (the maximal overlap between measurement directions). Using these inequalities we show that the critical detection efficiency above which $n$ von Neumann measurements can demonstrate steering is $1/n$. We show furthermore that using our construction and high dimensional states allows for steering demonstrations which are also highly robust to depolarising noise and produce unbounded violations in the presence of loss. Finally, our results provide an explicit means to certify the non-joint measurability of any set of inefficient von Neuman measurements.Comment: 4+3 pages. v2: title changed. Results on unbounded violation of steering inequalities added. Accepted by PR

Uniform Semiclassical Wavepacket Propagation and Eigenstate Extraction in a Smooth Chaotic System

A uniform semiclassical propagator is used to time evolve a wavepacket in a smooth Hamiltonian system at energies for which the underlying classical motion is chaotic. The propagated wavepacket is Fourier transformed to yield a scarred eigenstate.Comment: Postscript file is tar-compressed and uuencoded (342K); postscript file produced is 1216

On the collision of two shock waves in AdS5

We consider two ultrarelativistic shock waves propagating and colliding in five-dimensional Anti-de-Sitter spacetime. By transforming to Rosen coordinates, we are able to find the form of the metric shortly after the collision. Using holographic renormalization, we calculate the energy-momentum tensor on the boundary of AdS space for early times after the collision. Via the gauge-gravity duality, this gives some insights on bulk dynamics of systems created by high energy scattering in strongly coupled gauge theories. We find that Bjorken boost-invariance is explicitely violated at early times and we obtain an estimate for the thermalization time in this simple system.Comment: 15 pages, 1 figure; v2: clarifications on boost-invariance and appendix added; v3: minor modifications, references added, matches published versio

Elastic waves in a soft electrically conducting solid in a strong magnetic field

Shear wave motion of a soft, electrically-conducting solid in the presence of a strong magnetic field excites eddy currents in the solid. These, in turn, give rise to Lorentz forces that resist the wave motion. We derive a mathematical model for linear elastic wave propagation in a soft electrically conducting solid in the presence of a strong magnetic field. The model reduces to an effective anisotropic dissipation term resembling an anisotropic viscous foundation. The application to magnetic resonance elastography, which uses strong magnetic fields to measure shear wave speed in soft tissues for diagnostic purposes, is considered