## Shape analysis of strongly interacting systems: the heavy ion case

Collisions between nuclei at ultrarelativistic energies produce a colour-deconfined plasma that expands explosively and rapidly reverts to the colour-confined (hadronic) state. In non-central collisions, the zone of hot matter is transversely anisotropic and may be 'tilted' relative to the direction of the incoming beams. As the matter cools and expands into the vacuum, the evolution of the system shape depends sensitively on the dynamical response of the plasma under extreme conditions. Two-pion intensity interferometry performed relative to the impact parameter can be used to measure the approximate final shape of the system when pions decouple from the system. We use several transport models to illustrate the dependence of the final shape on the QCD equation of state and late-stage hadronic rescattering. The dependence of the final shape on collision energy may reveal non-trivial structures in the QCD phase diagram. Indeed, the few measurements published to date show an intriguing behaviour in an energy region under intense experimental and theoretical scrutiny, as signatures of a first-order phase transition may appear there. We discuss strong parallels between shape studies in heavy-ion collisions and those in two other strongly coupled systems.

## Topologically non-trivial superconductivity in spin–orbit-coupled systems: bulk phases and quantum phase transitions

Topologically non-trivial superconductivity has been predicted to occur in superconductors with a sizable spin–orbit (SO) coupling in the presence of an external Zeeman splitting. Two such systems have been proposed: (a) s-wave superconductor pair potential is proximity induced on a semiconductor and (b) pair potential naturally arises from an intrinsic s-wave pairing interaction. As it is now well known, such systems in the form of a two-dimensional (2D) film or 1D nano-wires in a wire network can be used in topological quantum computation. When the external Zeeman splitting Γ crosses a critical value Γ

_{c}, the system passes from a regular superconducting phase to a non-Abelian topological superconducting phase. In both cases (a) and (b) that we consider in this paper, the pair potential Δ is strictly s-wave in both the ordinary and the topological superconducting phases, which are separated by a topological quantum critical point at , where μ (Δ) is the chemical potential. On the other hand, since Γ_{c}Δ, the Zeeman splitting required for the topological phase (Γ>Γ_{c}) far exceeds the value (Γ~Δ) above which an s-wave pair potential is expected to vanish (and the system to become non-superconducting) in the absence of SO coupling. We are thus led to the situation that the topological superconducting phase appears to set in a parameter regime at which the system is actually non-superconducting in the absence of SO coupling. In this paper, we address the question of how a pure s-wave pair potential can survive a strong Zeeman field to give rise to a topological superconducting phase. We show that the SO coupling is the crucial parameter for the quantum transition into and the robustness of the topologically non-trivial superconducting phase realized for ΓΔ.

## Formation of dust in low-pressure magnetized hydrocarbon plasmas

The rapid formation of large molecules and the subsequent production of solid-state dust particles in a low-pressure discharge is unlikely, because of the low rates of the polymerization reactions and short lifetimes of the species. Here, we suggest that C dust particles can form in atypically low (10

^{− 3}mbar)-pressure hydrocarbon plasmas if the dust charging time is much shorter than the gas residence time in the device; we present supporting experimental evidence for this. Such a condition can be obtained by the production of high-density plasmas. The results show that dust formation from the gaseous phase can occur in a much wider parameter range than is commonly assumed.

## Solitons as probes of the structure of holographic superfluids

The detailed features of solitons in holographic superfluids are discussed. Using solitons as probes, we study the behavior of holographic superfluids by varying the scaling dimension of the condensing operator and make a comparison to the Bose–Einstein condensate–Bardeen–Cooper–Schrieffer comparison phenomena. Further evidence of this analogy is provided by the behavior of the solitons' length scales as well as by the superfluid critical velocity.

## Enhanced photoluminescence extraction efficiency from a diamond photonic crystal via leaky modes

Two-dimensional photonic crystal can be exploited as the top part of a light source in order to increase its extraction efficiency. Here, we report on the room-temperature intrinsic photoluminescence (PL) behavior of a nanocrystalline diamond (NCD) layer with diamond columns prepared on the top and periodically ordered into the lattice with square symmetry. Angle-resolved far-field measurements in the Γ–X crystal direction of broadband visible PL revealed up to six-fold enhancement of extraction efficiency as compared to a smooth NCD layer. A photonic band diagram above the lightcone derived from these measurements is in agreement with the diagram obtained from transmission measurements and simulation, suggesting that the enhancement is primarily due to light's coupling to leaky modes.

## Global neutrino data and recent reactor fluxes: the status of three-flavour oscillation parameters

Thomas Schwetz, Mariam Tórtola and J W F Valle

We present the results of a global neutrino oscillation data analysis within the three-flavour framework. We include the latest results from the MINOS long-baseline experiment (including electron neutrino appearance and anti-neutrino data), updating all relevant solar (Super-Kamiokande (SK) II+III), atmospheric (SK I+II+III) and reactor (KamLAND) data. Furthermore, we include a recent re-calculation of the anti-neutrino fluxes emitted from nuclear reactors. These results have important consequences for the analysis of reactor experiments and in particular for the status of the mixing angle θ_{13}. In our recommended default analysis, we find from the global fit that the hint for nonzero θ_{13} remains weak, at 1.8σ for both neutrino mass hierarchy schemes. However, we discuss in detail the dependence of these results on assumptions regarding the reactor neutrino analysis.

## A derivation of quantum theory from physical requirements

Lluís Masanes and Markus P Müller

Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements—the principles of relativity and light speed invariance—are used to derive the mathematical structure of Minkowski space–time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.

## Quantum Fourier transform, Heisenberg groups and quasi-probability distributions

Manas K Patra and Samuel L Braunstein

This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl–Gabor–Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.