Relative entropy of entanglement for certain multipartite mixed states

We prove conjectures on the relative entropy of entanglement (REE) for two families of multipartite qubit states. Thus, analytic expressions of REE for these families of states can be given. The first family of states are composed of mixture of some permutation-invariant multi-qubit states. The results generalized to multi-qudit states are also shown to hold. The second family of states contain D\"ur's bound entangled states. Along the way, we have discussed the relation of REE to two other measures: robustness of entanglement and geometric measure of entanglement, slightly extending previous results.Comment: Single column, 22 pages, 9 figures, comments welcom

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction rates (p,q,r,s) satisfy 1<p<()+, q>0, r>0, s0, 1<<+, the diffusion constant is chosen such that 1, and the time relaxation constant is such that 0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 1<p<1+4/N or if r=p+1 and 1<p<, then for aA>1 and sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 1<p3 or if r=p+1 and 1<p<, then for 0<aA<1 the near-boundary spike is stable. (iii) For N=1 if 3<p<5 and r=2, then there exist a0(0,1) and µ0>1 such that for a(a0,1) and µ=2q/(s+1)(p−1)(1,µ0) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as 0. ©2007 American Institute of Physic

A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters

Superconductivity in Inhomogeneous Hubbard Models

We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, $t'$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters ({\it e.g.} the effective mass) which are smooth functions of the Hubbard interaction, $U$. By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, $d$-BEC) for $0 < U < U_c$, which smoothly crosses over to an intermediate BCS-like superconducting phase ($d$-BCS), also with no nodal quasi-particles, for $|U - U_c| < {\cal O}(t^\prime)$, which gives way to a Fermi liquid phase at large $U > U_c = 4.58$.Comment: 7 pages, a sign error in Eq.(3) has been corrected and its consequence has been discussed with updated figure

Evidence for "Propeller" Effects In X-ray Pulsars GX 1+4 And GROJ1744-28

We present observational evidence for "propeller" effects in two X-ray pulsars, GX 1+4 and GROJ1744-28. Both sources were monitored regularly by the Rossi X-ray Timing Explorer (RXTE) throughout a decaying period in the X-ray brightness. Quite remarkably, strong X-ray pulsation became unmeasurable when total X-ray flux had dropped below a certain threshold. Such a phenomenon is a clear indication of the propeller effects which take place when pulsar magnetosphere grows beyond the co-rotation radius as a result of the decrease in mass accretion rate and centrifugal force prevents accreting matter from reaching the magnetic poles. The entire process should simply reverse as the accretion rate increases. Indeed, steady X-ray pulsation was reestablished as the sources emerged from the non-pulsating faint state. These data allow us to directly derive the surface polar magnetic field strength for both pulsars: 3.1E+13 G for GX 1+4 and 2.4E+11 G for GROJ1744-28. The results are likely to be accurate to within a factor of 2, with the total uncertainty dominated by the uncertainty in estimating the distances to the sources. Possible mechanisms for the persistent emission observed in the faint state are discussed in light of the extreme magnetic properties of the sources.Comment: 12 pages including 3 ps figures. To appear in ApJ Letters Vol. 48

Semiconductor-metal nanoparticle molecules: hybrid excitons and non-linear Fano effect

Modern nanotechnology opens the possibility of combining nanocrystals of various materials with very different characteristics in one superstructure. The resultant superstructure may provide new physical properties not encountered in homogeneous systems. Here we study theoretically the optical properties of hybrid molecules composed of semiconductor and metal nanoparticles. Excitons and plasmons in such a hybrid molecule become strongly coupled and demonstrate novel properties. At low incident light intensity, the exciton peak in the absorption spectrum is broadened and shifted due to incoherent and coherent interactions between metal and semiconductor nanoparticles. At high light intensity, the absorption spectrum demonstrates a surprising, strongly asymmetric shape. This shape originates from the coherent inter-nanoparticle Coulomb interaction and can be viewed as a non-linear Fano effect which is quite different from the usual linear Fano resonance.Comment: 5 pages, 5 figures, submitted to Phys. Rev. Let