Optical phase estimation in the presence of phase diffusion

The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address the estimation of phase in the presence of phase diffusion and evaluate the ultimate quantum limits to precision for phase-shifted Gaussian states. We look for the optimal detection scheme and derive approximate scaling laws for the quantum Fisher information and the optimal squeezing fraction in terms of the total energy and the amount of noise. We also find that homodyne detection is a nearly optimal detection scheme in the limit of very small and large noise.     

Investigating the vortex melting phenomenon in BSCCO crystals using magneto-optical imaging technique

Using a novel differential magneto-optical imaging technique we investigate the phenomenon of vortex lattice melting in crystals of Bi₂Sr₂CaCu₂O₈ (BSCCO). The images of melting reveal complex patterns in the formation and evolution of the vortex solid-liquid interface with varying field (H)/temperature (T). We believe that the complex melting patterns are due to a random distribution of material disorder/inhomogeneities across the sample, which create fluctuations in the local melting temperature or field value. To study the fluctuations in the local melting temperature/field, we have constructed maps of the melting landscape T _m(H, r), viz., the melting temperature (T _m) at a given location (r) in the sample at a given field (H). A study of these melting landscapes reveals an unexpected feature: the melting landscape is not fixed, but changes rather dramatically with varying field and temperature along the melting line. It is concluded that the changes in both the scale and shape of the landscape result from the competing contributions of different types of quenched disorder which have opposite effects on the local melting transition.     

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR _em = 〈n _s〉/〈n _ch〉, where 〈n _ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R _em = 1·71 implies an effectiveA-dependence ofR _A =A ^0.18,i.e., a very weak dependence. Predictions ofR _em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.     

Non-divisibility and non-Markovianity in a Gaussian dissipative dynamics

We study a stochastic Schrödinger equation that generates a family of Gaussian dynamical maps in one dimension permitting a detailed exam of two different definitions of non-Markovianity: one related to the explicit dependence of the generator on the starting time, the other to the non-divisibility of the time-evolution maps. The model shows instances where one has non-Markovianity in both senses and cases when one has Markovianity in the second sense but not in the first one.     

Limit cycles in a Gause‐type predator–prey model with sigmoid functional response and weak Allee effect on prey

The goal of this work is to examine the global behavior of a Gause‐type predator–prey model in which two aspects have been taken into account: (i) the functional response is Holling type III; and (ii) the prey growth is affected by a weak Allee effect. Here, it is proved that the origin of the system is a saddle point and the existence of two limit cycles surround a stable positive equilibrium point: the innermost unstable and the outermost stable, just like with the strong Allee effect. Then, for determined parameter constraints, the trajectories can have different ω ? limit sets. The coexistence of a stable limit cycle and a stable positive equilibrium point is an important fact for ecologists to be aware of the kind of bistability shown here. So, these models are undoubtedly rather sensitive to disturbances and require careful management in applied contexts of conservation and fisheries. Copyright © 2012 John Wiley & Sons, Ltd.     

Hexacoordinated spirocyclic germanium(IV) complex: Synthesis and structural characterization

The spiro‐dibenzogermocine [O(o‐C₆H₄S)₂]₂Ge ( 1 ) was prepared in a reaction between O(o‐C₆H₄SH)₂ and Ge(OⁱPr)₄, and its molecular structure was determined by X‐ray diffraction studies. In the solid state, 1 shows the existence of two weak O → Ge transannular interactions, resulting in a hexacoordinated germanium atom that displays the geometry of a distorted bicapped tetrahedron. © 2009 Wiley Periodicals, Inc. Heteroatom Chem 20:45–49, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20510     

The golden ratio in Schwarzschild–Kottler black holes

In this paper we show that the golden ratio is present in the Schwarzschild–Kottler metric. For null geodesics with maximal radial acceleration, the turning points of the orbits are in the golden ratio \(\varPhi =(\sqrt{5}-1)/2\). This is a general result which is independent of the value and sign of the cosmological constant \(\varLambda \).     

Hydrogen in lithium niobate

This article reviews the current knowledge on the main properties and applications of hydrogen in LiNbO₃. The review is divided into three parts. The first is devoted to general properties such as methods of defect production and control, techniques used for their detection and characterization, as well as interactions with other lattice defects. The second part considers the central role played by OH^- defects in the fabrication of optical waveguides by the protonexchange method. Conditions for the exchange process, the structure of exchanged layers, optical properties of exchanged waveguides and connection with relevant practical devices are examined. Finally, the third part discusses the production of permanent volume photorefractive gratings by the fixing process, where OH^- ions are also considered to be the main responsible defects. In particular, the physics of the fixing process, current mathematical models and two major applications are discussed.