Properties of Squeezed-State Excitations

The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented in closed form through the Hermite polynomials and their limiting cases. Expectation values of photon numbers and their dispersion are calculated. Some three-dimensional plots of photon distributions for different squeezing parameters demonstrating oscillatory behaviour are given.Comment: Latex,35 pages,submitted to Quant.Semiclassical Op

Effect of the Microstructure of Copper Films on the Damping of Oscillating Quartz Resonators*

An electrochemical procedure is described which allows the preparation of copper films of various crystallinity. Impedance spectra recorded for copper loaded quartz resonators were analysed in terms oft he lumped-element circuit of the Butterworth-Van Dyke type to obtain their electrical and mechanical properties. Plots of the damping resistance versus film thickness indicate that the film's dissipation factor is significantly smaller in the case of disordered films with a finer crystallinity (10—100nm) than in the case of more ordered structures having a grain size between 600—1500nm. This observations states, that the finely structured copper phase behaves more rigid than the coarse material. The suggested explanation relates this effect to energy losses which occur during oscillation at the phase boundary of the grains by wearless internal friction. No contributions to the damping from surface roughness were observed for films thicker 0.5pm. Thus, the damping of the quartz oscillator caused by different degrees of surface roughness of the generated copper films was of secondary importance, compared with the effect of the crystallinity

Effect of soil fertilization on the incidence of berry shrivel and the quality of resulting wine

Berry shrivel is becoming an increasing concern for winegrowers all over the world. Until today, no single factor causing this physiological disorder has been determined. Studies concerning berry shrivel conducted in Austria have shown that an unbalanced ratio of K and Mg in the soil is a likely factor contributing to the disorder. The aims of the present study were to establish a better understanding of the causes and consequences of berry shrivel and observe the effects of K and Mg fertilization via the soil on the incidence of berry shrivel, the mineral composition of affected berries and the resulting wine quality. A two-year fertilization trial was conducted on two sites located within southern Germany with the varieties 'Zweigelt' and 'Pinot Blanc'. Different amounts of K and Mg were applied each year at both locations in order to generate different ratios of K and Mg in the soil. Before harvest, the incidences of berry shrivel of the different treatments were determined. In addition, macronutrients including K, Mg and Ca that were translocated in healthy berries and berries affected by berry shrivel were determined at harvest. To compare the quality of wine influenced by berry shrivel, different wines were produced consisting of shrivelled berries, berries affected by bunch stem necrosis and healthy berries. In the soil fertilization trials, no significant differences in the incidences of berry shrivel were observed in relation to the soil fertilization. Major differences were found in the wine qualities of the different wines. Wines produced from healthy berries were always rated as the best wines, whereas wines produced from shrivelled berries were always rated as the lowest quality. The low quality parameters found in the must did not improve in the wine making process. Wines produced from berries affected by bunch stem necrosis were rated better than berry-shrivel-wines, however, rated less than the wine produced from healthy berries. The determinations of macronutrients’ level in the berries showed significant differences regarding the concentration of Ca. In the variety 'Zweigelt' in 2009, an average of 36 mg∙L-1 of Ca were found in healthy berries and 107 mg∙L-1 in berries affected by berry shrivel. In 'Pinot Blanc' in 2010, the average of Ca in healthy berries was 46 mg∙L-1 and 70 mg∙L-1 in berries affected by berry shrivel. No significant differences were found for K and Mg in the berries.

Energy-Sensitive and "Classical-like" Distances Between Quantum States

We introduce the concept of the ``polarized'' distance, which distinguishes the orthogonal states with different energies. We also give new inequalities for the known Hilbert-Schmidt distance between neighbouring states and express this distance in terms of the quasiprobability distributions and the normally ordered moments. Besides, we discuss the distance problem in the framework of the recently proposed ``classical-like'' formulation of quantum mechanics, based on the symplectic tomography scheme. The examples of the Fock, coherent, ``Schroedinger cats,'' squeezed, phase, and thermal states are considered.Comment: 23 pages, LaTex, 2 eps figures, to appear in Physica Script

Characterization of estrogenicity of phytoestrogens in an endometrial-derived experimental model.

Severe developmental and reproductive disorders in wild animals have been linked to high exposure to persistent environmental chemicals with hormonal activity. These adverse effects of environmental estrogens have raised considerable concern and have received increasing attention. Although numerous chemicals with the capacity to interfere with the estrogen receptor (ER) have been identified, information on their molecular mechanism of action and their relative potency is rather limited. For the endometrium, the lack of information is due to the lack of a suitable experimental model. We investigated the functions of phytoestrogens in an endometrial-derived model, RUCA-I rat endometrial adenocarcinoma cells. The cells were cultured on a reconstituted basement membrane to preserve their functional differentiation and estrogen responsiveness. We assessed the relative binding affinity to the estrogen receptor of the selected phytoestrogens coumestrol, genistein, daidzein, and the putative phytoestrogen mangostin compared to estradiol by a competitive Scatchard analysis. The following affinity ranking was measured: 17beta-estradiol >>> coumestrol > genistein > daidzein >>> mangostin. In addition, we investigated the capacity of these compounds to promote the increased production of complement C3, a well-known estradiol-regulated protein of the rat endometrium. All substances tested increased the production of complement C3, although different concentrations were necessary to achieve equivalent levels of induction compared to estradiol. Mechanistically we were able to demonstrate that the increase of complement C3 production was mediated by primarily increasing its steady-state mRNA level. These findings indicate that RUCA-I cells represent a sensitive model system to elucidate relative potencies and functions of environmental estrogens in an endometrium-derived model

Husimi Transform of an Operator Product

It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing the time evolution of the Husimi function, is absolutely convergent for a large class of Hamiltonians. By contrast, the series derived by Groenewold, giving the Weyl transform of an operator product, is often only asymptotic, or even undefined. The result is used to derive an alternative way of expressing expectation values in terms of the Husimi function. The advantage of this formula is that it applies in many of the cases where the anti-Husimi transform (or contravariant symbol) is so highly singular that it fails to exist as a tempered distribution.Comment: AMS-Latex, 13 page

Analytic representations based on SU(1,1) coherent states and their applications

We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disk based on the SU(1,1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A ``weak'' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index $k$ is smaller than one half. Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.Comment: LaTeX, 15 pages, no figures, to appear in J. Phys. A. More information on http://www.technion.ac.il/~brif/science.htm

On the squeezed states for n observables

Three basic properties (eigenstate, orbit and intelligence) of the canonical squeezed states (SS) are extended to the case of arbitrary n observables. The SS for n observables X_i can be constructed as eigenstates of their linear complex combinations or as states which minimize the Robertson uncertainty relation. When X_i close a Lie algebra L the generalized SS could also be introduced as orbit of Aut(L^C). It is shown that for the nilpotent algebra h_N the three generalizations are equivalent. For the simple su(1,1) the family of eigenstates of uK_- + vK_+ (K_\pm being lowering and raising operators) is a family of ideal K_1-K_2 SS, but it cannot be represented as an Aut(su^C(1,1)) orbit although the SU(1,1) group related coherent states (CS) with symmetry are contained in it. Eigenstates |z,u,v,w;k> of general combination uK_- + vK_+ + wK_3 of the three generators K_j of SU(1,1) in the representations with Bargman index k = 1/2,1, ..., and k = 1/4,3/4 are constructed and discussed in greater detail. These are ideal SS for K_{1,2,3}. In the case of the one mode realization of su(1,1) the nonclassical properties (sub-Poissonian statistics, quadrature squeezing) of the generalized even CS |z,u,v;+> are demonstrated. The states |z,u,v,w;k=1/4,3/4> can exhibit strong both linear and quadratic squeezing.Comment: 25 pages, LaTex, 4 .pic and .ps figures. Improvements in text, discussion on generation scheme added. To appear in Phys. Script

Characterization of the K2-18 multi-planetary system with HARPS: A habitable zone super-Earth and discovery of a second, warm super-Earth on a non-coplanar orbit

The bright M dwarf K2-18 at 34 pc is known to host a transiting super-Earth-sized planet orbiting within the star's habitable zone; K2-18b. Given the superlative nature of this system for studying an exoplanetary atmosphere receiving similar levels of insolation as the Earth, we aim to characterize the planet's mass which is required to interpret atmospheric properties and infer the planet's bulk composition. We obtain precision radial velocity measurements with the HARPS spectrograph and couple those measurements with the K2 photometry to jointly model the observed radial velocity variation with planetary signals and a radial velocity jitter model based on Gaussian process regression. We measure the mass of K2-18b to be $8.0 \pm 1.9$ M$_{\oplus}$ with a bulk density of $3.7 \pm 0.9$ g/cm$^3$ which may correspond to a predominantly rocky planet with a significant gaseous envelope or an ocean planet with a water mass fraction $\gtrsim 50$%. We also find strong evidence for a second, warm super-Earth K2-18c at $\sim 9$ days with a semi-major axis 2.4 times smaller than the transiting K2-18b. After re-analyzing the available light curves of K2-18 we conclude that K2-18c is not detected in transit and therefore likely has an orbit that is non-coplanar with K2-18b. A suite of dynamical integrations with varying simulated orbital eccentricities of the two planets are used to further constrain each planet's eccentricity posterior from which we measure $e_b < 0.43$ and $e_c < 0.47$ at 99% confidence. The discovery of the inner planet K2-18c further emphasizes the prevalence of multi-planet systems around M dwarfs. The characterization of the density of K2-18b reveals that the planet likely has a thick gaseous envelope which along with its proximity to the Solar system makes the K2-18 planetary system an interesting target for the atmospheric study of an exoplanet receiving Earth-like insolation.Comment: 13 pages, 8 figures including 4 interactive figures best viewed in Adobe Acrobat. Submitted to Astronomy & Astrophysics. Comments welcom

Retrodictively Optimal Localisations in Phase Space

In a previous paper it was shown that the distribution of measured values for a retrodictively optimal simultaneous measurement of position and momentum is always given by the initial state Husimi function. This result is now generalised to retrodictively optimal simultaneous measurements of an arbitrary pair of rotated quadratures x_theta1 and x_theta2. It is shown, that given any such measurement, it is possible to find another such measurement, informationally equivalent to the first, for which the axes defined by the two quadratures are perpendicular. It is further shown that the distribution of measured values for such a meaurement belongs to the class of generalised Husimi functions most recently discussed by Wuensche and Buzek. The class consists of the subset of Wodkiewicz's operational probability distributions for which the filter reference state is a squeezed vaccuum state.Comment: 11 pages, 2 figures. AMS Latex. Replaced with published versio