## Graphene Mini-Lab (Vol. 44 No. 1)

A mini-laboratory is proposed to study fast moving electrons in the carbon-based material called graphene as a model for massless particles moving in a noisy environment with velocities close to the speed of light, in analogy to relativistic Brownian particles such as cosmic rays.

In graphene (one atom-thick carbon layer forming a honeycomb lattice) the interaction of electrons with atoms changes the effective mass of the electrons. As a result, the energy of these electrons becomes similar to the photon energy. Therefore, electrons in graphene can be regarded as ultra-relativistic particles even though their actual velocity is 100 times lower than the speed of light.

The authors used the classical Brownian motion formalism to study the dynamics of electrons within the confines of the graphene mini-laboratory. They considered different chip geometries AND subjected them to changing conditions affecting the way these electrons diffuse through the material such as temperature and electric field strength.

Going one step further, the authors were able to rectify electron fluctuations and to control the electron motion itself from an unusual chaotic to a periodic motion by varying the electric field. Future work would experimentally demonstrate how variation of the temperature could be used positively to enhance the performance of graphene chips by gaining a greater control over electron transport. Such graphene mini-labs could also ultimately help understand the dynamics of matter and anti-matter in cosmic rays.

**A. Pototsky, F. Marchesoni, F. V. Kusmartsev, P. Hanggi and S. E. Savel'ev**, ‘Relativistic Brownian motion on a graphene chip’, *Eur. Phys. J.* B (2012) **85**: 356
**[Abstract]**

## Photocurrent simulation in TH photoconductive detectors (Vol. 44 No. 1)

Nowadays the most widely used spectroscopic technique in the terahertz band (0.1 to 10 THz) is called terahertz time-domain spectroscopy, which generates and detects pulses of terahertz light by triggering photoconductive antennae using infrared pulses from an ultrafast laser.

The influence of geometrical structure and semiconductor properties on the performance of photoconductive antennae has been studied extensively from the experimental point of view. However, theoretical studies on the semiconductor carrier dynamics of these devices have only emerged recently and have mostly focused on simulating the performance of emitters.

The present work develops a semi-classical Monte-Carlo model that can simulate ultrafast carrier dynamics in photoconductive detectors. The simulation tracks the motion of millions of charges under the electric field of a terahertz pulse at various times after their photo-generation taking into account the quantum mechanical scattering of each particle. By utilising a sequence of simulations the transient photocurrent was modelled precisely. In photoconductive detectors the rate at which electrons become trapped is an important parameter that determines how the measured current transient differs from the actual terahertz pulse's shape. By examining the role of carrier trapping at various illumination levels the authors demonstrated that high powers can distort the measured photocurrent. This model will set the path for further development of detectors of pulsed terahertz radiation by providing insights into semiconductor material design for that application.

**E. Castro-Camus, M.B. Johnston and J. Lloyd-Hughes**, ‘Simulation of fluence-dependent photocurrent in terahertz photoconductive receivers’, *Semicond. Sci. Technol.* **27**, 115011 (2012)
**[Abstract]**

## Enigmatic Nematics (Vol. 44 No. 1)

The law of hydrodynamics governing the way internally driven systems such as biological cells and bacteria behave could explain their complex structure and their inherent properties. Hydrodynamics is used here to understand the physical mechanism responsible for changes in the long-range order of groups of particles. The present work concerns ordered groups of elongated self-propelled particles, studying the breakdown of long-range order due to fluctuations that render them unstable and give rise to complex structures.

The authors coined the term self-propelled nematics to refer to internally driven elongated particles that spontaneously align head to tail, like tinned sardines. These are characterised by an ordered state that is stationary on average. This means that there is a long-range order, whereas the locally preferred direction may vary throughout the medium due to local strains or disturbances.

It is found here that a uniform nematic state can be disturbed by density fluctuations associated with an upward current of active particles. Since the density in turn controls the onset of nematic order, this phenomenon is self-regulating and universal.

It is also found that instability could be triggered by a local distortion of particles’ orientation. Such a distortion results in local currents that in turn amplify the distortion, leading to instability deep inside the nematic state.

Ultimately, this work may help us gain a deeper understanding of pattern formation and dynamics in a variety of internally driven systems, from epithelial cells and soil bacteria such as Myxococcus xanthus, to colloidal self-propelled nanorods.

**A. Baskaran and M. C. Marchetti**, ‘Self-regulation in self-propelled nematic fluids’, *Eur. Phys. J.* E **35**, 95 (2012)
**[Abstract]**

## A possible source of ultra-high-energy cosmic rays (Vol. 44 No. 1)

The origin of ultra-high-energy cosmic rays, with energies around the GZK (Greisen-Zatsepin-Kuzmin) cut-off, remains an unsolved mystery. According to this cut-off, the mean free path of very energetic particles in the Universe does not exceed 50 megaparsec, due to their scattering on the cosmic microwave background radiation. However, there are no conventional sources of ultra-high-energy cosmic rays inside this radius. Hence some new sources seem to be necessary.

In the present letter a novel and intriguing explanation is suggested that links far-reaching fundamental aspects of F(R) modified theories to an efficient production of highly energetic cosmic rays during the recent history of the Universe (let us recall that F(R) theories present a modification of the usual General Relativity by an addition of a non-linear function F(R) of the scalar curvature R. This function is chosen in such a way that it leads to accelerated cosmological expansion indicated by the recent astronomical data).

At the core of this work lies the proof that in cosmological and astrophysical systems with rising energy densities, the F(R) modified theories of gravity exhibit powerful oscillations of the curvature scalar R, with an amplitude much larger than the standard value of curvature predicted by the General Relativity. These oscillations are strongly anharmonic, with frequencies that can be as large as billions of GeV. This striking and rather unexpected oscillatory behaviour of R lends support to the idea that ultra-high energy cosmic rays can be generated by such curvature oscillations at the appropriate cosmological redshifts.

**E.V. Arbuzova, A.D. Dolgov and L. Reverberi**, ‘Curvature oscillations in modified gravity theories as possible source of ultra-high-energy cosmic rays’, *Eur. Phys. J.* C, **72**, 2247 (2012)
**[Abstract]**

## LARES: a nearly ideal satellite to test fundamental physics (Vol. 44 No. 1)

The discovery of the accelerating expansion of the Universe, thought to be driven by a ‘dark energy’ constituting most of the Universe, has further revived the interest in testing Einstein’s theory of General Relativity (GR). Frame-dragging in the gravitational field generated by a rotating body or by a current of mass-energy is one of the most fascinating phenomena predicted by GR. The recently launched LARES (LAser RElativity Satellite) space mission is aimed at improving of about one order of magnitude the accuracy of the previous frame-dragging measurements by the LAGEOS and LAGEOS 2 satellites, using GRACE-derived Earth gravity determinations. After some years of orbital analysis of LARES, LAGEOS and LAGEOS 2 satellite laser-ranging data, frame-dragging should be tested within a few percents.

However, at the very foundation of Einstein’s theory is the geodesic motion of a small, structureless ‘test-particle’. Depending on the physical context, a star, planet or satellite can behave nearly like a test-particle, so geodesic motion is used to calculate the advance of the perihelion of a planet’s orbit and the dynamics of a binary pulsar system and of an Earth-orbiting satellite. Verifying geodesic motion is thus a test of paramount importance to GR and other theories of fundamental physics. On the basis of the first few months of satellite laser-ranging observations of the LARES satellite, its orbit shows the best agreement of any satellite with the test-particle motion predicted by GR. That is, after modelling its known non-gravitational perturbations, the orbit of LARES shows the smallest deviations from geodesic motion of any artificial satellite: its residual mean acceleration away from geodesic motion is less than 0.5 x 10^{-12} m/s^{2x}. LARES-type satellites and accurate satellite laser ranging measurements can thus be used for further tests of gravitational and fundamental physics.

**I. Ciufolini, A. Paolozzi, E. Pavlis, J. Ries, V. Gurzadyan, R. Koenig, R. Matzner, R. Penrose, and G. Sindoni**, ‘Testing General Relativity and gravitational physics using the LARES satellite’, *Eur. Phys. J.* Plus **, 133 (2012)
[Abstract]
**

## Charge transfer measurements in low-energy ion-atom collisions (Vol. 44 No. 1)

We have used a radio frequency ion trap to study two charge transfer reactions:

(1) Resonant charge transfer: ^{3}He^{2+} + ^{4}He (1s^{2}) → ^{3}He + ^{4}He^{2+},

(2) Single electron charge transfer: ^{3}He^{2+} + ^{4}He (1s^{2}) → ^{3}He^{+} + ^{4}He^{+}.

We have determined the resonant charge transfer (RCT) rate coefficient of ^{3}He^{2+} with para -^{4}He (1s^{2}) at energies below 1 eV (reaction (1)). The rate coefficient is measured to be 5.9±0.6×10^{-10} cm^{3}s^{-1} at an equivalent temperature of 1200K and is in reasonable agreement with recent calculations. This measurement extends our knowledge to a lower energy region thus adding to our understanding of the charge transfer process of ^{3}He^{2+}, α-particles, with He encountered in astrophysics and fusion research.

While this measurement extends the experimental results below eV energies for the first time, it however provides an interesting observation. The rate coefficient for resonant two electrons transfer (reaction (1)) is orders of magnitude larger than the rate coefficient for single electron transfer (reaction (2)) at comparable temperature reported in the literature. This may lead to the following fundamental questions. The electron spin in para-He is anti-parallel. The spatial wave function that represents the two electrons is symmetric. The probability density for the two electrons close together is finite. Can the proximity of the two electrons account for this relatively large two electrons resonant charge transfer rate coefficient? Is it possible that the two anti-parallel electrons couple to form a loosely bound electron pair that is responsible for this relatively fast two-electron transfer? Can we gain some physical insight by measuring the rate coefficient of the resonant charge transfer of ^{3}He^{2+} with ortho-^{4}He (1s2s) (metastable helium (2^{3}S_{1})) where the two electron spins are parallel?

**C. Kyriakides, B.S. Clarke, W. M. O'Donnell, B. Zygelman and V.H.S. Kwong**, ‘Resonant charge transfer of ^{3}He^{2+} with ^{4}He(1s^{2}) at energies below 1 eV’, *J. Phys. B: At. Mol. Opt. Phys.* **45** 235701 (2012)
**[Abstract]**

## Physics of Squeezed Helices (Vol. 44 No. 1)

Helically coiled filaments are everywhere in living nature. In experimental situations, filaments are often squeezed flat (or nearly flat) onto two-dimensional surfaces. Under such 2D confinement filament-helices form what we call "squeelices" - peculiar squeezed conformations often resembling looped waves, spirals or circles. Many such shapes have been observed and reported for a variety of biological and man-made filaments.

With filament-helices being such a ubiquitous structure, we asked the question: what happens when filament helices become confined? We found that the confinement produces some dramatic changes in filaments shape, giving rise to several notable and surprising effects. In particular “squeelices” can display an enhanced cyclisation probability, unusually strong end-to-end fluctuations and a conformational multistability. The conformational dynamics of confined helices is most naturally described in terms of discrete particle-like entities – which we call the "twist-kinks". These "twist-kinks" turn out to be analogous and are physically related to crystal dislocations in solids and Sine-Gordon-kinks from soliton physics. Twist-kinks move thermally along the confined helix and interact much like quasi-particles. Confined helices can further thermally switch between discrete twist-quantized states comprising different numbers of twist-kinks.

Doing simple things (confining) to simple objects (helical filaments) can give rise to complex physics.

**G-M. Nam, N-K. Lee, H. Mohrbach, A. Johner and I. M. Kulíc**, ‘Helices at interfaces’, *EPL*, **100**, 28001 (2012)
**[Abstract]**

## Heat flux anomaly at nanoscale (Vol. 44 No. 1)

Nanomaterials are promising platforms for testing fundamental heat transport theories. The present review article outlines anomalous heat transport in nanometric scale materials from the latest developments in experimental, theoretical and numerical studies of heat conduction. It shows that the standard laws governing conduction at macroscopic scale no longer apply in nanostructures, which has implications in electronic, optoelectronic, and thermal devices.

Nanostructures are low-dimensional materials such as single carbon atom layers of graphene, nanowires or nanotubes. Laws governing heat transport through what are known as phonons, representing the vibrational modes of lattices, are different in such materials compared to the macroscopic scale. This is because the phonon characteristic lengths are comparable to the characteristic lengths of these nanostructures. Particularly, heat carriers diffuse faster than in a random walk but slower than in a straight trajectory motion.

This paper outlines the recent experiments on quasi-one-dimensional nanostructures and two-dimensional graphene that display a thermal conductivity with this anomalous behaviour, linked to heat diffusion’s size dependency. Such studies present a dual challenge in that the technique associated with measuring heat ﬂux in nanosystems is combined with the complexity of accurately controlling object at nanoscale.

Due to these measurement challenges, experimental results need to be complemented by theoretical studies. Hence, this paper also accounts for numerical studies on heat conduction of nanotubes, nanowires and graphene, concentrating particularly on atomic-level simulations.

In addition, the latest theories explaining the mechanisms of such anomalous heat conduction are presented. But these are by no means complete. Further systematic investigations are needed for better thermal energy management and control in nanoscale devices.

**S. Liu, X. F. Xu, R. G. Xie, G. Zhang and B. W. Li**, ‘Anomalous heat conduction and anomalous diffusion in low dimensional nanoscale systems’, *Eur. Phys. J.* B, **85**, 337 (2012)
**[Abstract]**

## Conjugate Fermi hole and the first Hund rule (Vol. 44 No. 1)

_{n}of 20, 5, and 2, respectively. (a’) – (c’) represent the electron repulsion potential for the corresponding Z

_{n}.

Empirically derived Hund's rules of the pre-quantum-mechanics era predict the ordering of the energy levels possessing different spin and orbital angular momentum quantum numbers. They have proved to be almost universally valid for atoms, molecules, and quantum dots. Yet, despite of a long-standing debate, the search for their origin persists primarily due to the lack of the precise knowledge of the electronic structure in different spin states. We explore the origin of the first Hund rule for a two-dimensional model of He-like systems and that of two-electron quantum dots. They represent ideal systems providing a direct fundamental insight into the structure of the internal part of the fully correlated wave functions, allowing an unambiguous argument.

An examination of their probability density distributions reveals indeed the existence of a region in the internal space, which we refer to as a *conjugate Fermi hole*. In this region the singlet wave function has a smaller probability density than the corresponding triplet one, in contrast to the genuine Fermi hole where the triplet has a smaller density than the singlet. Due to the presence of this conjugate Fermi hole the singlet probability density has to migrate far away from the centre of the one-electron potential. This rationalizes the well-known broader electron density distribution of the singlet state relative to the corresponding triplet. This key observation explains the singlet-triplet energy gap.

**T. Sako, J.Paldus, A. Ichimura and G. H. F. Diercksen,** ‘Origin of the first Hund rule and the structure of Fermi holes in two-dimensional He-like atoms and two-electron quantum dots’, *J. Phys. B: At. Mol. Opt. Phys.* **45**, 235001 (2012)
**[Abstract]**

## Replica techniques can predict learning curves (Vol. 44 No. 1)

^{2}(triangles), agree very well with numerical simulations (circles, graphs with 500 vertices) and improve significantly on existing approximations (dashed line).

We show that statistical physics approaches, in particular the replica method, can be used to accurately predict the learning curve of a Gaussian process (GP) inferring a function from noisy data, for a wide range of discrete input spaces. The learning curve quantifies performance as average mean square error versus number of training examples.

GPs are a popular Bayesian inference technique. A GP prior is placed over a function space, and combined with the likelihood of the observed data given a function. Bayes’ theorem then gives a posterior distribution over functions. For a likelihood describing Gaussian noise corrupting the observed function values, this is again a GP, which can be used to make predictions about the function. GPs are “non-parametric”: they effectively represent functions with infinitely many parameters. This makes analysis of their learning curves non-trivial, and much has been achieved for GPs learning functions whose inputs are real-valued. However, predictions are generally only qualitatively correct, with exact solutions only for special cases. We show for the case where inputs are discrete, specifically vertices on a random graph, that replica techniques can be used to predict learning curves exactly in the limit of large graphs.

The starting point is to represent the average error as the derivative of a partition function. We rewrite this so that only neighbouring vertices are directly coupled. From here one can apply the replica method to find the required quenched average over the randomness in the data set. The results apply to random graph ensembles constrained by any fixed degree distribution, and can be generalised to more complicated ensembles.

**M. J. Urry and P. Sollich**, ‘Replica theory for learning curves for Gaussian processes on random graphs’, *J. Phys. A: Math. Theor.* **45**, 425005 (2012)
**[Abstract]**

## Droplet production for electrolyte solutions (Vol. 44 No. 1)

_{j}and nanoaerosol plume angle θ

_{plume}are observed to be strong functions of the ionic strength C

_{∞}and interfacial tension γ

_{f}.

Proteomic mass spectrometry and chemical imaging require the generation of nanometer-sized charged water drops that are emitted in a precise direction. This is done with the remarkable ability of an electric field to sharpen a mm-sized spherical drop into a sharp cone with a universal half angle of 49 degrees, to emit a micro-jet at the cone tip and to breakup the charged micro-jet explosively into a plume of nanodrops, whose plume angle and charge per drop sensitively affect the measurement accuracy of the instrument. This paper captures the underlying nanoscale physics of DC electrospray with a combination of strong electrolyte theory, electrostatics, interfacial phenomena and potential spectral theory for geometric singularities. The electric field of the most singular harmonic near a cone that sharpens the drop is also shown to charge a nanoscale capacitor at the interface of the micro-jet, with a dimension of the Debye length. The interfacial charging increases downstream of the cone tip until the space charge separation is below the Bjerrum length, when the repulsive Coulombic energy between two charges exceeds the thermal energy. The resulting Coulombic fission accounts for the explosive breakup of the micro-jet into the nanodrop plume. The micro-jet length, the charge per nanodrop and the nanodrop plume angle as functions of ion strength are accurately captured by the theory as functions of the ionic strength and surface tension. Strong ionic strength and low surface tension produce the longest micro-jet, the smallest plume and the most precisely directed nanodrops.

**Y. Wang, M. K. Tan, D. B. Go and H-C. Chang**, ‘Electrospray cone-jet breakup and droplet production for electrolyte solutions’, *EPL*, **99**, 64003 (2012)
**[Abstract]**

## Plasmas as gaseous electrodes for aqueous electrochemistry (Vol. 44 No. 1)

Plasmas are ionized gases made-up of electrons and gaseous ions. In theory, plasmas are a source of charge that can be coupled with liquids to initiate electrochemical reactions in solution. This has been known for some time, at least since 1887 when Gubkin first reported the use of plasmas for electroplating silver from silver nitrate. Unfortunately, plasmas are inherently difficult to stabilize at atmospheric pressure, and vacuum operation has limited prior experiments to solvents with low vapour pressures such as ionic liquids.

The present work shows how to get stable atmospheric-pressure plasmas allowing *aqueous* electrochemical reactions. The approach is based on *pd* scaling (gas pressure *p* and dimension *d* of the plasma) which imposes to reduce the dimension of the plasma to go to higher pressure. Atmospheric operation is achieved by forming a µm-scale plasma, or microplasma.

Upon operating the microplasma as the cathode at the surface of an aqueous solution, the electrons from the plasma reduce the protons to produce hydrogen gas. At the platinum counter-electrode, oxidation reactions lead to the formation of oxygen gas. The electrolysis of water is well known in electrochemistry, but this is the first time it has been demonstrated with a plasma electrode. As plasmas are increasingly in use with wet electrodes for medical and materials applications, it is crucial to understand the high complexity of plasma-liquid interactions. The role of electrons has thus far been largely overlooked, and this work brings a crucial piece of the puzzle.

**M. Witzke, P. Rumbach, D. B. Go and R. M. Sankaran**, ’Evidence for the electrolysis of water by atmospheric-pressure plasmas formed at the surface of aqueous solutions’, *J. Phys.* D **45**, 442001 (2012)
**[Abstract]**