## Inadequacy of von Neumann entropy for characterizing extractable work

Oscar C O Dahlsten, Renato Renner, Elisabeth Rieper and Vlatko Vedral

The lack of knowledge that an observer has about a system limits the amount of work it can extract. This lack of knowledge is normally quantified using the Gibbs/von Neumann entropy. We show that this standard approach is, surprisingly, only correct in very specific circumstances. In general, one should use the recently developed smooth entropy approach. For many common physical situations, including large but internally correlated systems, the resulting values for the extractable work can deviate arbitrarily from those suggested by the standard approach.

## Equilibration of quantum systems and subsystems

Anthony J Short

We unify two recent results concerning equilibration in quantum theory. We first generalize a proof of Reimann (2008

Phys. Rev. Lett.101190403), that the expectation value of ‘realistic’ quantum observables will equilibrate under very general conditions, and discuss its implications for the equilibration of quantum systems. We then use this to re-derive an independent result of Lindenet al(2009Phys. Rev.E79061103), showing that small subsystems generically evolve to an approximately static equilibrium state. Finally, we consider subspaces in which all initial states effectively equilibrate to the same state.

## Sheet plasmons in modulated graphene on Ir(111)

T Langer, D F Förster, C Busse, T Michely, H Pfnür and C Tegenkamp

The sheet plasmon of graphene on Ir(111) was investigated in this paper by means of high-resolution electron energy loss spectroscopy. The perfect lateral coordination of sp

^{2}-hybridized C atoms on a large scale is manifested by brilliant moiré diffraction images. However, the modulation of the graphene films caused by hybridization at the interface limits the lifetimes of the collective excitation modes. This modulation within the films can be lowered owing to intercalation of Na. Linear dispersion was found, but surprisingly the overall slope of the dispersion is not dependent on the chemical potential within the graphene films. The dispersion measured for graphene on Ir(111) is almost identical to that measured on SiC(0001), although the carrier densities differ by two orders of magnitude. This contradicts the model that the relevant carrier density for a two-dimensional plasmon is given by (2π)^{− 1}k_{F}^{2}.

## Tailoring the photon emission patterns in nanostructures

Shi-Fang Guo, Su-Qing Duan, Yan Xie, Wei-Dong Chu and Wei Zhang

We investigate photon emission in coupled quantum dots on the basis of symmetry considerations. With the help of a new theorem that we have proved, we reveal the origin of various emission patterns, which is the combinative symmetry in the time domain and the spectrum domain. We are able to tailor the emission patterns to obtain emission spectra with odd harmonics alone, even harmonics alone or both odd and even harmonic components, and even with the quenching of all harmonic components. These interesting emission patterns can be obtained in experiments by a careful design of nanostructures, which have many applications in optical–electric nanodevices.

## The electronic structure of a weakly correlated antiferromagnetic metal, SrCrO_{3}: first-principles calculations

Yumin Qian, Guangtao Wang, Zhi Li, C Q Jin and Zhong Fang

On the basis of our idea of degree modulation, by using systematic first-principles calculations, we study the electronic structure and magnetic properties of SrCrO

_{3}. Our results suggest that SrCrO_{3}is a weakly correlated antiferromagnetic (AF) metal, a very rare situation in transition-metal oxides. Among various possible AF states, C-type spin ordering with a small amount of orbital polarization (the d_{xy}orbital is more occupied than the d_{yz/zx}orbital) is favored. The detailed understanding of the mechanism that stabilizes the C-type AF state is analyzed on the basis of the competition between itinerant Stoner instability and superexchange, and our results suggest that magnetic instability rather than lattice or charge instabilities plays an important role in this system. The experimentally observedc-axis compressed tetragonal distortion can be naturally explained with the C-type AF state. By using the LDA+Umethod to study this system, we show that the wrong ground state will be obtained ifUis large.

## Turbulence in collisionless plasmas: statistical analysis from numerical simulations with pressure anisotropy

G Kowal, D A Falceta-Gonçalves and A Lazarian

In recent years, we have experienced increasing interest in the understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments (e.g. the intracluster medium (ICM)) containing magnetic fields that are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions, a new class of kinetic instabilities arises, such as firehose and mirror instabilities, which have been studied extensively in the literature. Their role in the turbulence evolution and cascade process in the presence of pressure anisotropy, however, is still unclear. In this work, we present the first statistical analysis of turbulence in collisionless plasmas using three-dimensional numerical simulations and solving double-isothermal magnetohydrodynamic equations with the Chew–Goldberger–Low laws closure (CGL-MHD). We study models with different initial conditions to account for the firehose and mirror instabilities and to obtain different turbulent regimes. We found that the CGL-MHD subsonic and supersonic turbulences show small differences compared to the MHD models in most cases. However, in the regimes of strong kinetic instabilities, the statistics, i.e. the probability distribution functions (PDFs) of density and velocity, are very different. In subsonic models, the instabilities cause an increase in the dispersion of density, while the dispersion of velocity is increased by a large factor in some cases. Moreover, the spectra of density and velocity show increased power at small scales explained by the high growth rate of the instabilities. Finally, we calculated the structure functions of velocity and density fluctuations in the local reference frame defined by the direction of magnetic lines. The results indicate that in some cases the instabilities significantly increase the anisotropy of fluctuations. These results, even though preliminary and restricted to very specific conditions, show that the physical properties of turbulence in collisionless plasmas, as those found in the ICM, may be very different from what has been largely believed. Implications can range from interchange of energies to cosmic ray acceleration.

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