On finite-size effects in computer simulations using the Ewald potential

We discuss the origin and relevance for computer simulations of a strong finite-size effect that appears when using the Ewald summation formula. It can be understood as arising from a volume-dependent shift of the potential in a finite, periodic box relative to the infinite volume limit. This shift is due to the fact that the ``zero of energy'' for a periodic system cannot be defined by letting the interacting particles be separated by an infinite distance; the correct definition corresponds to setting its \bbox k=\bbox 0 Fourier mode to zero. The implications of this effect for computer simulations are discussed.Comment: Submitted to Journal of Chemical Physic

Analysis of high load dampers

High load damping requirements for modern jet engines are discussed. The design of damping systems which could satisfy these requirements is also discusseed. In order to evaluate high load damping requirements, engines in three major classes were studied; large transport engines, small general aviation engines, and military engines. Four damper concepts applicable to these engines were evaluated; multi-ring, cartridge, curved beam, and viscous/friction. The most promising damper concept was selected for each engine and performance was assessed relative to conventional dampers and in light of projected damping requirements for advanced jet engines

Tunable non-Gaussian resources for continuous-variable quantum technologies

We introduce and discuss a set of tunable two-mode states of continuous-variable systems, as well as an efficient scheme for their experimental generation. This novel class of tunable entangled resources is defined by a general ansatz depending on two experimentally adjustable parameters. It is very ample and flexible as it encompasses Gaussian as well as non-Gaussian states. The latter include, among others, known states such as squeezed number states and de-Gaussified photon-added and photon-subtracted squeezed states, the latter being the most efficient non-Gaussian resources currently available in the laboratory. Moreover, it contains the classes of squeezed Bell states and even more general non-Gaussian resources that can be optimized according to the specific quantum technological task that needs to be realized. The proposed experimental scheme exploits linear optical operations and photon detections performed on a pair of uncorrelated two--mode Gaussian squeezed states. The desired non-Gaussian state is then realized via ancillary squeezing and conditioning. Two independent, freely tunable experimental parameters can be exploited to generate different states and to optimize the performance in implementing a given quantum protocol. As a concrete instance, we analyze in detail the performance of different states considered as resources for the realization of quantum teleportation in realistic conditions. For the fidelity of teleportation of an unknown coherent state, we show that the resources associated to the optimized parameters outperform, in a significant range of experimental values, both Gaussian twin beams and photon-subtracted squeezed states.Comment: 13 pages, 7 figure

Experimental pre-assessing entanglement in Gaussian states mixing

We suggest and demonstrate a method to assess entanglement generation schemes based on mixing of Gaussian states at a beam splitter (BS). Our method is based on the fidelity criterion and represents a tool to analyze the effect of losses and noise before the BS in both symmetric and asymmetric channels with and without thermal effects. More generally, our scheme allows one to pre-assess entanglement resources and to optimize the design of BS-based schemes for the generation of continuous variable entanglement.Comment: 10 pages, 15 figure

On the zero set of G-equivariant maps

Let $G$ be a finite group acting on vector spaces $V$ and $W$ and consider a smooth $G$-equivariant mapping $f:V\to W$. This paper addresses the question of the zero set near a zero $x$ of $f$ with isotropy subgroup $G$. It is known from results of Bierstone and Field on $G$-transversality theory that the zero set in a neighborhood of $x$ is a stratified set. The purpose of this paper is to partially determine the structure of the stratified set near $x$ using only information from the representations $V$ and $W$. We define an index $s(\Sigma)$ for isotropy subgroups $\Sigma$ of $G$ which is the difference of the dimension of the fixed point subspace of $\Sigma$ in $V$ and $W$. Our main result states that if $V$ contains a subspace $G$-isomorphic to $W$, then for every maximal isotropy subgroup $\Sigma$ satisfying $s(\Sigma)>s(G)$, the zero set of $f$ near $x$ contains a smooth manifold of zeros with isotropy subgroup $\Sigma$ of dimension $s(\Sigma)$. We also present a systematic method to study the zero sets for group representations $V$ and $W$ which do not satisfy the conditions of our main theorem. The paper contains many examples and raises several questions concerning the computation of zero sets of equivariant maps. These results have application to the bifurcation theory of $G$-reversible equivariant vector fields

H, not O or pressure, causes eutectic T depression in the Fe-FeS System to 8 GPa

The Fe-FeS system maintains a eutectic temperature of 990 ± 10 °C to at least 8 GPa if starting materials and pressure media are rigorously dehydrated. Literature reports of pressure-induced freezing point depression of the eutectic for the Fe-FeS system are not confirmed. Modest addition of oxygen alone is confirmed to cause negligible freezing point depression at 6 GPa. Addition of H alone causes a progressive decrease in the eutectic temperature with P in the Fe-FeS-H system to below 965 °C at 6 GPa to below 950 °C at 8 GPa. It is our hypothesis that moisture contamination in unrigorously dried experiments may be an H source for freezing point depression. O released from H₂O disproportionation reacts with Fe and is sequestered as ferropericlase along the sample capsules walls, leaving the H to escape the system and/or enter the Fe-FeS mixture. The observed occurrence of ferropericlase on undried MgO capsule margins is otherwise difficult to explain, because an alternate source for the oxygen in the ferropericlase layer is difficult to identify. This study questions the use of pressure-depressed Fe-S eutectic temperatures and suggests that the lower eutectic temperatures sometimes reported are achieved by moving into the ternary Fe-S-H system. These results adjust slightly the constraints on eutectic temperatures allowed for partly solidified cores on small planets. H substantially diminishes the temperature extent of the melting interval in Fe-S by reducing the melting points of the crystalline phases more than it depresses the eutectic