Entanglement between collective operators in a linear harmonic chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several noncontiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.

Hydrogen bonding and collective proton modes in clusters and periodic layers of squaric acid: A density functional study

Hydrogen bonding in clusters and extended layers of squaric acid molecules has been investigated by density functional computations. Equilibrium geometries, harmonic vibrational frequencies, and energy barriers for proton transfer along hydrogen bonds have been determined using the Car-Parrinello method. The results provide crucial parameters for a first principles modeling of the potential energy surface, and highlight the role of collective modes in the low-energy proton dynamics. The importance of quantum effects in condensed squaric acid systems has been investigated, and shown to be negligible for the lowest-energy collective proton modes. This information provides a quantitative basis for improved atomistic models of the order-disorder and displacive transitions undergone by squaric acid crystals as a function of temperature and pressure. (C) 2001 American Institute of Physics.

Chronic child abuse and domestic violence: Children and families with long-term and complex needs

It is estimated that up to one million children may have been exposed to domestic violence in the UK, with significant consequences for their social and emotional development in childhood and later life. At a time when the central and devolved administrations in the UK have developed strategies to tackle domestic violence, this paper reports the findings from a study conducted on children in the child protection system with long-term and complex needs as a result of experiencing domestic violence. The research identifies the characteristics of the children and their families and tracks their careers through the child protection system. The findings indicate that professionals have an awareness of domestic violence, and that younger children with younger parents are most likely to experience prolonged periods in the child protection system. Domestic violence in this context typically co-exists in families experiencing other difficulties such as substance misuse and socio-economic deprivation. In conclusion, the paper argues that Government policy and professional practice should primarily be concerned with assessing the risk that men present, rather than the risk that children are at. By reframing professional interventions, men are more likely to be challenged to accept responsibility for their behaviour and the consequences for their families.

Ultrafast Probing of Collective Electron Dynamics Driven by Dielectronic Repulsion

We use the time-dependent R-matrix approach to investigate an ultrashort pump-probe scheme to observe collective electron dynamics in C(+). The ionization probability of a coherent superposition of the 2s2p(2) (2)D and (2)S states shows rapid modulation due to collective dynamics of the two equivalent 2p electrons, with the modulation frequency linked to the dielectronic repulsion. The best insight into this collective dynamics is achieved by a transformation from LS symmetry to the uncoupled basis. Such dynamics may be important in high-harmonic generation using open-shell atoms and ions.