Relative Entropy of Coherent States on General CCR Algebras

For a subalgebra of a generic CCR algebra, we consider the relative entropy between a general (not necessarily pure) quasifree state and a coherent excitationthereof. We give a unified formula for this entropy in terms of single-particle modular data. Further, we investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces; here convexity of the entropy (as usually considered for the Quantum Null Energy Condition) is replaced with lower estimates for the second derivative, composed of “bulk terms” and “boundary terms”. Our main assumption is that the subspaces are in differential modular position, a regularity condition that generalizes the usual notion of half-sided modular inclusions. We illustrate our results in relevant examples, including thermal states for the conformal U(1)-current.

Entanglement distillation from quasifree fermions

We develop a scheme to distill entanglement from bipartite Fermionic systems in an arbitrary quasifree state. It can be applied if either one system containing infinite one-copy entanglement is available or if an arbitrary amount of equally prepared systems can be used. We show that the efficiency of the proposed scheme is in general very good and in some cases even optimal. Furthermore we apply it to Fermions hopping on an infinite lattice and demonstrate in this context that an efficient numerical analysis is possible for more than $10^6$ lattice sites.

Electron reactivity in liquid hydrocarbon mixtures

The electron current in neopentane–n-hexane mixtures, produced by a few nanoseconds X-ray pulse in the presence of external electric field, has been observed in the nanosecond–microsecond range. The form of the time dependence of the electron current has been shown to vary with dose per pulse and is analysed accordingly. The electron mobilities μe are thereby determined in the mixtures. The rate constant of electron–ion recombination, kr, is proportional to the mobility over the wide range of μe The rate constant for electron scavenging, ks by CC14 varies with √μe; ks for C2H5Br shows a maximum for a mixture with the mole fraction of n-hexane, xh = 0.48. The results for ks obtained for the mixtures agree with those by Allen and co-workers for various neat hydrocarbons. Further, the mechanism of electron transport in non-polar liquids is discussed. Using experimental results for V0 and Ea for the mixtures (the energy of the electron in its quasifree state and the activation energy of μe, respectively) V0 is expressed by a linear function of Ea: V0 = −0.42 + 2.6Ea at room temperature and μe is correlated with V0 as an empirical formula μe = 125/[1 + 360 exp (15V0)] based on a trapping model.