Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).

The policy dilemma of the unitary patent. Bruegel Working Paper 2014/13, 27 November 2014

This paper provides new evidence about the budgetary consequences – for patent offices – of the coexistence of the forthcoming Unitary Patent (UP) with the current European Patent (EP). Simulation results illustrate a dilemma between (1) high UP renewal fees to ensure enough financial income for all national patent offices (NPOs) and (2) low UP renewal fees to make the UP system affordable, with very few NPOs losing on financial revenues. The simulations help to understand the positions of several patent offices, and underline an alternative way to proceed with the negotiations while reducing financial risks for the whole system.

Maize Stress DIESI-MS Data and R Script

Climatic change is an increasing challenge for agriculture that is driving the development of suitable crops in order to ensure supply for both human nutrition and animal feed. In this context, it is increasingly important to understand the biochemical responses of cells to environmental cues at the whole system level, an aim that is being brought closer by advances in high throughput, cost-efficient plant metabolomics. To support molecular breeding activities, we have assessed the economic, technical and statistical feasibility of using direct mass spectrometry methods to evaluate the physiological state of maize (Zea mays L.) plants grown under different stress conditions.

Upgrade Volvo production restraint systems. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Highway travel: 1970-2000. Final report.

Federal Highway Administration, Washington, D.C.

Identification of approaches for the control of health, environmental, and safety hazards associated with air bag use and disposal. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Development of the DEPLOY computer math model for the investigation of various airbag and crash parameters on the out-of-position occupant. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Development of specifications for passive belt systems. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Comfort and convenience specifications for safety belts: shoulder belt fit, pressure and pullout forces. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Passive restraint development of light trucks and vans. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Liquid-metals handbook : sodium-NaK supplement.

Sponsored by the Atomic Energy Commission and the Bureau of Ships, Dept. of the Navy.

Information processing relevant to military command: survey, recommendations and bibliography (final report)

Vol. 2: Bibliography appendix.

Designing defense systems /

Cover title: Designing defense systems, the trade-off process.

Report to the Los Angeles Metropolitan Transit Authority on a monorail rapid transit line for Los Angeles, January 15, 1954.

Part of the illustrative material is fold., part col.