Molecular Physics

X -ray radiographic absorption imaging is an invaluable tool in medical diagnostics and materials science. For biological tissue samples, polymers or fibre composites, however, the use of conventional X-ray radiography is limited due to their weak absorption. This is resolved at highly brilliant X-ray synchrotron or micro-focus sources by using phase-sensitive imaging methods to improve the contrast 1,2 . However, the requirements of the illuminating radiation mean that hard-X-ray phase-sensitive imaging has until now been impractical with more readily available X-ray sources, such as X-ray tubes. In this letter, we report how a setup consisting of three transmission gratings can efficiently yield quantitative differential phase-contrast images with conventional X-ray tubes. In contrast with existing techniques, the method requires no spatial or temporal coherence, is mechanically robust, and can be scaled up to large fields of view. Our method provides all the benefits of contrast-enhanced phase-sensitive imaging, but is also fully compatible with conventional absorption radiography. It is applicable to X-ray medical imaging, industrial non-destructive testing, and to other low-brilliance radiation, such as neutrons or atoms.

Explicit reversible integrators, suitable for use in large-scale computer simulations, are derived for extended systems generating the canonical and isothermal± isobaric ensem bles. The new methods are compared with the standard implicit (iterative) integrators on some illustrative example problem s. In addition, modi® cation of the proposed algorithms for multiple time step integration is outlined.

We present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz$^{1/2}$.

In this paper we write down equations of motion (following the approach pioneered by Hoover) for an exact isothermal-isobaric molecular dynamics simulation, and we extend them to multiple thermostating rates, to a shape-varying cell and to molecular systems, coherently with the previous 'extended system method'. An integration scheme is proposed together with a numerical illustration of the method.

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties 1,2,3,4,5 . The "rich-club" phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences 4,5,6,7,8 . Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.

There is growing interest to investigate states of matter with topological order, which support excitations in the form of anyons, and which underly topological quantum computing. Examples of such systems include lattice spin models in two dimensions. Here we show that relevant Hamiltonians can be systematically engineered with polar molecules stored in optical lattices, where the spin is represented by a single electron outside a closed shell of a heteronuclear molecule in its rotational ground state. Combining microwave excitation with the dipole-dipole interactions and spin-rotation couplings allows us to build a complete toolbox for effective twospin interactions with designable range and spatial anisotropy, and with coupling strengths significantly larger than relevant decoherence rates. As an illustration we discuss two models: a 2D square lattice with an energy gap providing for protected quantum memory, and another on stacked triangular lattices leading to topological quantum computing.

A computationally efficient molecular dynamics method for estimating the rates of rare events that occur by activated processes is described. The system is constrained at "bottleneck" regions on a general many-body reaction coordinate in order to generate a biased configurational distribution. Suitable reweighting of this biased distribution, along with correct momentum distribution sampling, provides a new ensemble, the constrained-reaction-coordinate-dynamics ensemble, with which to study rare events of this type. Applications to chemical reaction rates are made.

A recurrent idea in the study of complex systems is that optimal information processing is to be found near bifurcation points or phase transitions. However, this heuristic hypothesis has few (if any) concrete realizations where a standard and biologically relevant quantity is optimized at criticality. Here we give a clear example of such a phenomenon: a network of excitable elements has its sensitivity and dynamic range maximized at the critical point of a non-equilibrium phase transition. Our results are compatible with the essential role of gap junctions in olfactory glomeruli and retinal ganglionar cell output. Synchronization and global oscillations also appear in the network dynamics. We propose that the main functional role of electrical coupling is to provide an enhancement of dynamic range, therefore allowing the coding of information spanning several orders of magnitude. The mechanism could provide a microscopic neural basis for psychophysical laws.

In 1929, Leó Szilárd invented a feedback protocol in which a hypothetical intelligence-dubbed Maxwell's demon-pumps heat from an isothermal environment and transforms it into work. After a long-lasting and intense controversy it was finally clarified that the demon's role does not contradict the second law of thermodynamics, implying that we can, in principle, convert information to free energy. An experimental

Dynamical reaction-diffusion processes and metapopulation models are standard modelling approaches for a wide array of phenomena in which local quantities-such as density, potentials and particles-diffuse and interact according to the physical laws. Here, we study the behaviour of the basic reaction-diffusion process (given by the reaction steps B → A and B + A → 2B) defined on networks with heterogeneous topology and no limit on the nodes' occupation number. We investigate the effect of network topology on the basic properties of the system's phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density-driven phase transitions, whereas phase transition and critical points independent of the particle density are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic metapopulation and agent-based models that include the complex features of real-world networks.

Matter-wave interference experiments enable us to study matter at its most basic, quantum level and form the basis of high-precision sensors for applications such as inertial and gravitational field sensing. Success in both of these pursuits requires the development of atom-optical elements that can manipulate matter waves at the same time as preserving their coherence and phase. Here, we present an integrated interferometer based on a simple, coherent matter-wave beam splitter constructed on an atom chip. Through the use of radio-frequency-induced adiabatic double-well potentials, we demonstrate the splitting of Bose-Einstein condensates into two clouds separated by distances ranging from 3 to 80 μm, enabling access to both tunnelling and isolated regimes.

A formulation of the n-electron valence state perturbation theory ͑NEVPT͒ at the third order of perturbation is presented. The present implementation concerns the so-called strongly contracted variant of NEVPT, where only a subspace of the first-order interacting space is taken into account. The resulting strongly contracted NEVPT3 approach is discussed in three test cases: ͑a͒ the energy difference between the 3 B 1 and 1 A 1 states of the methylene molecule, ͑b͒ the potential-energy curve of the N 2 molecule ground state, and ͑c͒ the chromium dimer ͑Cr 2 ͒ ground-state potential-energy profile. Particular attention is devoted to the last case where large basis sets comprising also h orbitals are adopted and where remarkable differences between the second-and third-order results show up.

A mong the variety of roles for nanopores in biology, an important one is enabling polymer transport, for example in gene transfer between bacteria 1 and transport of RNA through the nuclear membrane 2 . Recently, this has inspired the use of protein 3-5 and solid-state 6-10 nanopores as single-molecule sensors for the detection and structural analysis of DNA and RNA by voltage-driven translocation. The magnitude of the force involved is of fundamental importance in understanding and exploiting this translocation mechanism, yet so far it has remained unknown. Here, we demonstrate the first measurements of the force on a single DNA molecule in a solid-state nanopore by combining optical tweezers 11 with ionic-current detection. The opposing force exerted by the optical tweezers can be used to slow down and even arrest the translocation of the DNA molecules. We obtain a value of 0.24 ± 0.02 pN mV −1 for the force on a single DNA molecule, independent of salt concentration from 0.02 to 1 M KCl. This force corresponds to an effective charge of 0.50 ± 0.05 electrons per base pair equivalent to a 75% reduction of the bare DNA charge.

Quantum entanglement [1, 2] plays a vital role in many quantum information and communication tasks . Entangled states of higher dimensional systems are of great interest due to the extended possibilities they provide. For example, they allow the realisation of new types of quantum information schemes that can offer higher information-density coding and greater resilience to errors than can be achieved with entangled two-dimensional systems (see and references therein). Closing the detection loophole in Bell test experiments is also more experimentally feasible when higher dimensional entangled systems are used . We have measured previously untested correlations between two entangled photons to experimentally demonstrate high-dimensional entangled states. We show violations of Bell-type inequalities for two d-dimensional particles (qudits) [6] with d reaching up to 11. Our experiments use photons entangled in orbital angular momentum (OAM) [7], generated through spontaneous parametric downconversion (SPDC) , and manipulated using computer controlled holograms.

The transfer of spin angular momentum from a spin-polarized current to a ferromagnet can generate sufficient torque to reorient the magnet’s moment. This torque could enable the development of efficient electrically actuated magnetic memories and nanoscale microwave oscillators. Yet difficulties in making quantitative measurements of the spin-torque vector have hampered understanding. Here we present direct measurements of both the magnitude

Recently, condensed matter and atomic experiments have reached a length-scale and temperature regime where new quantum collective phenomena emerge. Finding such physics in systems of photons, however, is problematic, as photons typically do not interact with each other and can be created or destroyed at will. Here, we introduce a physical system of photons that exhibits strongly correlated dynamics on a meso-scale. By adding photons to a two-dimensional array of coupled optical cavities each containing a single two-level atom in the photon-blockade regime, we form dressed states, or polaritons, that are both long-lived and strongly interacting. Our zero temperature results predict that this photonic system will undergo a characteristic Mott insulator (excitations localised on each site) to superfluid (excitations delocalised across the lattice) quantum phase transition. Each cavity's impressive photon out-coupling potential may lead to actual devices based on these quantum manybody effects, as well as observable, tunable quantum simulators.

A description of the ab initio quantum chemistry package GAMESS-UK is presented. The package offers a wide range of quantum mechanical wavefunctions, capable of treating systems ranging from closed-shell molecules through to the species involved in complex reaction mechanisms. The availability of a wide variety of correlation methods provides the necessary functionality to tackle a number of chemically important tasks, ranging from geometry optimization and transition-state location to the treatment of solvation effects and the prediction of excited state spectra. With the availability of relativistic ECPs and the development of ZORA, such calculations may be performed on the entire Periodic including the lanthanides. Emphasis is given to the DFT module, which has been extensively developed in recent years, and a number of other, novel features of the program. The parallelization strategy used in the program is outlined, and detailed speedup results are given. Applications of the code in the areas of enzyme and zeolite catalysis and in spectroscopy are described.

We report the observation of nonclassical light generated via photon blockade in a photonic crystal cavity with a strongly coupled quantum dot. By tuning the frequency of the probe laser with respect to the cavity and quantum dot resonance we can probe the system in either photon blockade or photon-induced tunneling regime. The transition from one regime to the other is confirmed by the measurement of the second order correlation that changes from anti-bunching to bunching.

Fermionic alkaline-earth atoms have unique properties that make them attractive candidates for the realization of novel atomic clocks and degenerate quantum gases. At the same time, they are attracting considerable theoretical attention in the context of quantum information processing. Here we demonstrate that when such atoms are loaded in optical lattices, they can be used as quantum simulators of unique many-body phenomena. In particular, we show that the decoupling of the nuclear spin from the electronic angular momentum can be used to implement many-body systems with an unprecedented degree of symmetry, characterized by the SU(N) group with N as large as 10. Moreover, the interplay of the nuclear spin with the electronic degree of freedom provided by a stable optically excited state allows for the study of spin-orbital physics. Such systems may provide valuable insights into strongly correlated physics of transition metal oxides, heavy fermion materials, and spin liquid phases.

We present a new relativistic formulation for the calculation of nuclear magnetic resonance ͑NMR͒ shielding tensors. The formulation makes use of gauge-including atomic orbitals and is based on density functional theory. The relativistic effects are included by making use of the zeroth-order regular approximation. This formulation has been implemented and the 199 Hg NMR shifts of HgMe 2 , HgMeCN, Hg͑CN͒ 2 , HgMeCl, HgMeBr, HgMeI, HgCl 2 , HgBr 2 , and HgI 2 have been calculated using both experimental and optimized geometries. For experimental geometries, good qualitative agreement with experiment is obtained. Quantitatively, the calculated results deviate from experiment on average by 163 ppm, which is approximately 3% of the range of 199 Hg NMR. The experimental effects of an electron donating solvent on the mercury shifts have been reproduced with calculations on HgCl 2 ͑NH 3 ͒ 2 , HgBr 2 ͑NH 3 ͒ 2 , and HgI 2 ͑NH 3 ͒ 2 . In addition, it is shown that the mercury NMR shieldings are sensitive to geometry with changes for HgCl 2 of approximately 50 ppm for each 0.01 Å change in bond length, and 100 ppm for each 10°change in bond angle.

The y-expansion as introduced by Barboy and Gelbart is applied to a system of hard ellipsoids-of-revolution. The expansion is truncated after the third order term yielding an approximate theory requiring the second-and third-virial coefficients as inputs. As the third virial coefficient is not known analytically, numerical results are obtained for this quantity. The equation of state is obtained from a free-energy variational calculation. The results are compared with Monte Carlo data taken from the preceding paper in this series. The application of scaled particle theory to the same system is discussed, and shown to have serious shortcomings.

A striking feature of bilayer graphene is the induction of a significant band gap in the electronic states by the application of a perpendicular electric field 1-6. Thicker graphene layers are also highly attractive materials. The ability to produce a band gap in these systems is of great fundamental and practical interest 7-23. Both experimental 10 and theoretical 14,21,22 investigations of graphene trilayers with the typical ABA layer stacking have, however, revealed the lack of any appreciable induced gap. Here we contrast this behavior with that exhibited by graphene trilayers with ABC crystallographic stacking. The symmetry of this structure is similar to that of AB stacked graphene bilayers and, as shown by infrared conductivity measurements, permits a large band gap to be formed by an applied electric field. Our results demonstrate the critical and hitherto neglected role of the crystallographic stacking sequence on the induction of a band gap in fewlayer graphene.

The conventional cold, particle interpretation of dark matter (CDM) still lacks laboratory support and struggles with the basic properties of common dwarf galaxies, which have surprisingly uniform central masses and shallow density profiles 1-4 . In contrast, galaxies predicted by CDM extend to much lower masses, with steeper, singular profiles 5-7 . This tension motivates cold, wavelike dark matter (ψDM) composed of a non-relativistic Bose-Einstein condensate, so the uncertainty principle counters gravity below a Jeans scale 8, 9 . Here we achieve the first cosmological simulations of this quantum state at unprecedentedly high resolution capable of resolving dwarf galaxies, with only one free parameter, m B , the boson mass. We demonstrate the large scale structure of this ψDM simulation is indistinguishable from CDM, as desired, but differs radically inside galaxies. Connected filaments and collapsed haloes form a large interference network, with gravitationally selfbound solitonic cores inside every galaxy surrounded by extended haloes of fluctuating density granules. These results allow us to determine m B = (8.1 +1.6 −1.7 ) × 10 −23 eV using stellar phase-space distributions in dwarf spheroidal galaxies. Denser, more massive solitons are predicted for Milky Way sized galaxies, providing a substantial seed to help explain early spheroid formation. Suppression of small structures means the onset of galaxy formation for ψDM is substantially delayed relative to CDM, appearing at z 13 in our simulations.

Qubits, the quantum mechanical bits required for quantum computing, must retain their quantum states for times long enough to allow the information contained in them to be processed. In many types of electron-spin qubits, the primary source of information loss is decoherence due to the interaction with nuclear spins of the host lattice. For electrons in gate-defined GaAs quantum dots, spin-echo measurements have revealed coherence times of about 1 µs at magnetic fields below 100 mT (refs 1,2). Here, we show that coherence in such devices can survive much longer, and provide a detailed understanding of the measured nuclearspin-induced decoherence. At fields above a few hundred millitesla, the coherence time measured using a singlepulse spin echo is 30 µs. At lower fields, the echo first collapses, but then revives at times determined by the relative Larmor precession of different nuclear species. This behaviour was recently predicted 3,4 , and can, as we show, be quantitatively accounted for by a semiclassical model for the dynamics of electron and nuclear spins. Using a multiple-pulse Carr-Purcell-Meiboom-Gill echo sequence, the decoherence time can be extended to more than 200 µs, an improvement by two orders of magnitude compared with previous measurements 1,2,5 .

Magnetic reconnection releases energy explosively as field lines break and reconnect in plasmas ranging from the Earth's magnetosphere to solar eruptions and astrophysical applications. Collisionless kinetic simulations have shown that this process involves both ion and electron kinetic-scale features, with electron current layers forming nonlinearly during the onset phase and playing an important role in enabling field lines to break 1-4 . In larger two-dimensional studies, these electron current layers become highly extended, which can trigger the formation of secondary magnetic islands 5-10 , but the influence of realistic three-dimensional dynamics remains poorly understood. Here we show that, for the most common type of reconnection layer with a finite guide field, the three-dimensional evolution is dominated by the formation and interaction of helical magnetic structures known as flux ropes. In contrast to previous theories 11 , the majority of flux ropes are produced by secondary instabilities within the electron layers. New flux ropes spontaneously appear within these layers, leading to a turbulent evolution where electron physics plays a central role.

Molecular Physics, 1992. Vol. 76, No. 6, 1319-1333 Vapour liquid equilibria of the Lennard-Jones fluid from the NpT plus test particle method By AMAL LOTFI, JADRAN VRABKC and JOHANN FISCHER Institut für Thermo-und Fluiddynamik, Ruhr-Univcrsitäl, DW-4630 Bochum I, ...

Devices that harness the laws of quantum physics hold the promise for information processing that outperforms their classical counterparts, and for unconditionally secure communication 1 . However, in particular, implementations based on condensed-matter systems face the challenge of short coherence times. Carbon materials 2,3 , particularly diamond 4-6 , however, are suitable for hosting robust solid-state quantum registers, owing to their spin-free lattice and weak spin-orbit coupling. Here we show that quantum logic elements can be realized by exploring long-range magnetic dipolar coupling between individually addressable single electron spins associated with separate colour centres in diamond. The strong distance dependence of this coupling was used to characterize the separation of single qubits (98±3 Å) with an accuracy close to the value of the crystal-lattice spacing. Our demonstration of coherent control over both electron spins, conditional dynamics, selective readout as well as switchable interaction should open the way towards a viable room-temperature solid-state quantum register. As both electron spins are optically addressable, this solid-state quantum device operating at ambient conditions provides a degree of control that is at present available only for a few systems at low temperature.

Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation. However, in many real networks nodes communicate efficiently even without such global intelligence. Here we show that the peculiar structural characteristics of many complex networks support efficient communication without global knowledge. We also describe a general mechanism that explains this connection between network structure and function. This mechanism relies on the presence of a metric space hidden behind an observable network. Our findings suggest that real networks in nature have underlying metric spaces that remain undiscovered. Their discovery would have practical applications ranging from routing in the Internet and searching social networks, to studying information flows in neural, gene regulatory networks, or signaling pathways.

In this article we review state-of-the-art methods for computing vibrational energies of polyatomic molecules using quantum mechanical, variationally-based approaches. We illustrate the power of those methods by presenting applications to molecules with more than four atoms. This demonstrates the great progress that has been made in this field in the last decade in dealing with the exponential scaling with the number of vibrational degrees of freedom. In this review we present three methods that effectively obviate this bottleneck. The first important idea is the n-mode representation of the Hamiltonian and notably the potential. The potential (and other functions) are represented as a sum of terms that depend on a subset of the coordinates. This makes it possible to compute matrix elements, form a Hamiltonian matrix, and compute its eigenvalues and eigenfunctions. Another approach takes advantage of this multimode representation and represents the terms as sum of products. It then exploits the powerful multiconfiguration Hartree time dependent method to solve the time-dependent Schrödinger equation and extract the eigenvalue spectrum. The third approach we present uses contracted basis functions in conjunction with a Lanczos eigensolver. Matrix vector products are done without transforming to a direct-product grid. The usefulness of these methods is demonstrated for several example molecules, e.g., methane, methanol and the Zundel cation.

Experiments on single nitrogen-vacancy (N-V) centres in diamond, which include electron spin resonance, Rabi oscillations, single-shot spin readout and two-qubit operations with a nearby13C nuclear spin, show the potential of this spin system for solid-state quantum information processing. Moreover, N-V centre ensembles can have spin-coherence times exceeding 50 μs at room temperature. We have developed an angle-resolved magneto-photoluminescence microscope apparatus to investigate the anisotropic electron-spin interactions of single N-V centres at room temperature. We observe negative peaks in the photoluminescence as a function of both magnetic-field magnitude and angle that are explained by coherent spin precession and anisotropic relaxation at spin-level anti-crossings. In addition, precise field alignment unmasks the resonant coupling to neighbouring `dark' nitrogen spins, otherwise undetected by photoluminescence. These results demonstrate the capability of our spectroscopic technique for measuring small numbers of dark spins by means of a single bright spin under ambient conditions.

We review the current status of quantum chemistry as a predictive tool of chemistry and molecular physics, capable of providing highly accurate, quantitative data about molecular systems. We begin by reviewing wave-function based electronic-structure theory, emphasizing the N-electron hierarchy of coupled-cluster theory and the one-electron hierarchy of correlation-consistent basis sets. Following a discussion of the slow basis-set convergence of dynamical correlation and basis-set extrapolations, we consider the methods of explicit correlation, from the early work of Hylleraas in the 1920s to the latest developments in such methods, capable of yielding high-accuracy results in medium-sized basis sets. Next, we consider the small corrections to the electronic energy (high-order virtual excitations, vibrational, relativistic, and diagonal Born-Oppenheimer corrections) needed for high accuracy and conclude with a review of the composite methods and computational protocols of electronic-structure theory.

At timescales once deemed immeasurably small by Einstein, the random movement of Brownian particles in a liquid is expected to be replaced by ballistic motion. So far, an experimental verification of this prediction has been out of reach due to a lack of instrumentation fast and precise enough to capture this motion. Here we report the observation of the Brownian motion of a single particle in an optical trap with 75MHz bandwidth and sub-ångström spatial precision and the determination of the particle's velocity autocorrelation function. Our observation is the first measurement of ballistic Brownian motion of a particle in a liquid. The data are in excellent agreement with theoretical predictions taking into account the inertia of the particle and hydrodynamic memory effects.

interfaces occurs in a wide variety of atmospheric, oceanic, geophysical and astrophysical flows. The Rayleigh-Taylor instability, a process by which fluids seek to reduce their combined potential energy, plays a key role in all types of fusion. Despite decades of investigation, fundamental questions regarding turbulent Rayleigh-Taylor flow persist, namely: does the flow forget its initial conditions, is the flow self-similar, what is the scaling constant, and how does mixing influence the growth rate? Here, we show results from a large direct numerical simulation addressing such questions. The simulated flow reaches a Reynolds number of 32,000, far exceeding that of all previous Rayleigh-Taylor simulations.

Magnetic monopoles have been predicted to occur as emergent fractional quasiparticles inside pyrochlore spin ice, a frustrated magnetic insulator. Experimental signatures of such emergent monopoles accompanied by Dirac strings have been detected by means of neutron scattering in reciprocal space in pyrochlore spin ice at sub-Kelvin temperatures, but their real-space observation has remained elusive. Here we report on direct, real-space observations of emergent monopoles and their associated Dirac strings in two-dimensional (2D) artificial kagome spin ice at room temperature using synchrotron X-ray photoemission electron microscopy. Magnetization reversal proceeds through the nucleation and avalanche-type dissociation of monopole-antimonopole pairs along 1D Dirac strings. This is in sharp contrast to conventional domain growth in 2D systems, providing a striking example of dimensional reduction due to frustration. The observed hysteresis, monopole densities and 1D Dirac-string avalanches are quantitatively explained by Monte Carlo simulations.

Einstein's general theory of relativity establishes equality between matter-energy density and the curvature of spacetime. As a result, light and matter follow natural paths in the inherent spacetime and may experience bending and trapping in a specific region of space. So far, the interaction of light and matter with curved spacetime has been predominantly studied theoretically and through astronomical observations. Here, we propose to link the newly emerged field of artificial optical materials to that of celestial mechanics, thus opening the way to investigate light phenomena reminiscent of orbital motion, strange attractors and chaos, in a controlled laboratory environment. The optical-mechanical analogy enables direct studies of critical light/matter behaviour around massive celestial bodies and, on the other hand, points towards the design of novel optical cavities and photon traps for application in microscopic devices and lasers systems.

In this article we demonstrate that the Gibbs ensemble and the canonical ensemble are equivalent in the thermodynamic limit. Furthermore, we discuss some interesting aspects of the method when applied close to the critical point. We show that for a finite number of particles the Gibbs ensemble leads to a lower value of the critical temperature of the finite system than that obtained by standard N,V,T simulations with the same number of particlesl This is due to entropic considerations. Simulations in the Gibbs ensemble, because it allows for fluctuations in the number of particles and in the volume of the sub-systems, may lead to a better estimate of the critical temperature of the infinite system.

Magnetic insulators have proved to be fertile ground for studying new types of quantum many body states, and I survey recent experimental and theoretical examples. The insights and methods transfer also to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle-or wave-like interpretation, and control a significant portion of the finite temperature phase diagram. Remarkably, their theory is connected to holographic descriptions of Hawking radiation from black holes.

A splash is usually heard when a solid body enters water at large velocity. This phenomenon originates from the formation of an air cavity during the impact. The classical view of impacts on free surfaces relies solely on fluid inertia; therefore, surface properties and viscous ...

Dissociative recombination is a cornerstone reaction in the synthesis of interstellar molecules and plays an important role in the ionised layers of the atmospheres of the Earth, other planets, and their satellites. The studies of dissociative recombination reactions was for a long time dominated by afterglow techniques, and these techniques are used in improved versions also today, but the bulk of the relevant data have in recent years been produced at ion storage rings. We review briefly these different experimental techniques. As examples of recent developments in the field, we discuss in particular the dissociative recombination of H 3 + , the role of dissociative recombination in the chemistry of hydrocarbons and sulphur compounds in the interstellar medium and planetary ionospheres, and the synthesis of interstellar methanol.

The Similarity Transformed Equation of Motion Coupled Cluster (STEOM-CC) method is benchmarked against CC3 and EOM-CCSDT-3 for a large test set of valence excited states of organic molecules studied by Schreiber et al. [M. Schreiber, M.R. Silva-Junior, S.P. Sauer, and W. Thiel, J. Chem. Phys. 128, 134110 ]. STEOM-CC is found to behave quite satisfactorily and provides significant improvement over EOM-CCSD, CASPT2, and NEVPT2 for singlet excited states; lowering standard deviations of these methods by almost a factor of two. Triplet excited states are found to be described less accurately, however. Besides the parent version of STEOM-CC additional variations are considered. STEOM-D includes a perturbative correction from doubly excited determinants. The novel STEOM-H ( ) approach presents a sophisticated technique to render the STEOM-CC transformed Hamiltonian hermitian. In STEOM-PT the expensive CCSD step is replaced by MBPT(2), while Extended STEOM (EXT-STEOM) provides access to doubly excited states. To study orbital invariance in STEOM, we investigate orbital rotation in the STEOM-ORB approach. Comparison of theses variations of STEOM for the large test set provides a comprehensive statistical basis to gauge the usefulness of these approaches. ω