First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

Gaussian quantum operator representation for bosons

We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods.

Nonclassicality Criteria from Phase-Space Representations and Information-Theoretical Constraints Are Maximally Inequivalent

We consider two celebrated criteria for defining the nonclassicality of bipartite bosonic quantum systems, the first stemming from information theoretic concepts and the second from physical constraints on the quantum phase space. Consequently, two sets of allegedly classical states are singled out: (i) the set C composed of the so-called classical-classical (CC) states—separable states that are locally distinguishable and do not possess quantum discord; (ii) the set P of states endowed with a positive P representation (P-classical states)—mixtures of Glauber coherent states that, e.g., fail to show negativity of their Wigner function. By showing that C and P are almost disjoint, we prove that the two defining criteria are maximally inequivalent. Thus, the notions of classicality that they put forward are radically different. In particular, generic CC states show quantumness in their P representation, and vice versa, almost all P-classical states have positive quantum discord and, hence, are not CC. This inequivalence is further elucidated considering different applications of P-classical and CC states. Our results suggest that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

Gauge Poisson representations for birth/death master equations

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.

Phase-space analysis of bosonic spontaneous emission

We present phase-space techniques for the modelling of spontaneous emission in two-level bosonic atoms. The positive-P representation is shown to give a full and complete description within the limits of our model. The Wigner representation, even when truncated at second order, is shown to need a doubling of the phase-space to allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck equation and still fails to agree with the full quantum results of the positive-P representation. We show that quantum statistics and correlations between the ground and excited states affect the dynamics of the emission process, so that it is in general non-exponential. (c) 2005 Elsevier B.V. All rights reserved.

First-principles quantum dynamics in interacting Bose gases II: stochastic gauges

First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analysed. In a companion paper, we showed how the positive-P representation can be applied to these problems using stochastic differential equations. That method, however, is limited by increased sampling error as time evolves. Here, we show how the sampling error can be greatly reduced and the simulation time significantly extended using stochastic gauges. In particular, local stochastic gauges (a subset) are investigated. Improvements are confirmed in numerical calculations of single-, double- and multi-mode systems in the weak-mode coupling regime. Convergence issues are investigated, including the recognition of two modes by which stochastic equations produced by phase-space methods in general can diverge: movable singularities and a noise-weight relationship. The example calculated here displays wave-like behaviour in spatial correlation functions propagating in a uniform 1D gas after a sudden change in the coupling constant. This could in principle be tested experimentally using Feshbach resonance methods.

First-principles quantum simulations of dissociation of molecular condensates: Atom correlations in momentum space

We investigate the quantum many-body dynamics of dissociation of a Bose-Einstein condensate of molecular dimers into pairs of constituent bosonic atoms and analyze the resulting atom-atom correlations. The quantum fields of both the molecules and atoms are simulated from first principles in three dimensions using the positive-P representation method. This allows us to provide an exact treatment of the molecular field depletion and s-wave scattering interactions between the particles, as well as to extend the analysis to nonuniform systems. In the simplest uniform case, we find that the major source of atom-atom decorrelation is atom-atom recombination which produces molecules outside the initially occupied condensate mode. The unwanted molecules are formed from dissociated atom pairs with nonopposite momenta. The net effect of this process-which becomes increasingly significant for dissociation durations corresponding to more than about 40% conversion-is to reduce the atom-atom correlations. In addition, for nonuniform systems we find that mode mixing due to inhomogeneity can result in further degradation of the correlation signal. We characterize the correlation strength via the degree of squeezing of particle number-difference fluctuations in a certain momentum-space volume and show that the correlation strength can be increased if the signals are binned into larger counting volumes.

p Dissipative operator

In this paper the authors prove that the generalized positive p selfadjoint (GPpS) operators in Banach space satisfy the generalized Schwarz inequality, solve the maximal dissipative extension representation of p dissipative operators in Banach space by using the inequality and introducing the generalized indefinite inner product (GIIP) space, and apply the result to a certain type of Schrodinger operator.

Staphylococcus spp., Enterobacteriaceae and Pseudomonadaceae oral isolates from Brazilian HIV-positive patients. Correlation with CD4 cell counts and viral load

The aim was to evaluate the presence of Staphylococcus spp., Enterobacteriaceae and Pseudomonadaceae in the oral cavities of HIV-positive patients. Forty-five individuals diagnosed as HIV-positive by ELISA and Western-blot, and under anti-retroviral therapy for at least 1 year, were included in the study. The control group constituted 45 systemically healthy individuals matched to the HIV patients to gender, age and oral conditions. Oral rinses were collected and isolates were identified by API system. Counts of microorganisms from HIV and control groups were compared statistically by a Mann-Whitney test (alpha = 5%). The percentages of individuals positive for staphylococci were similar between the groups (p = 0.764), whereas for Gram-negative rods, a higher percentage was observed amongst HIV-positive (p = 0.001).There was no difference in Staphylococcus counts between HIV and control groups (p = 0.1008). Counts were lower in the oral cavities of patients with low viral load (p = 0.021), and no difference was observed in relation to CD4 counts (p = 0.929). Staphylococcus aureus was the most frequently isolated species in HIV group, and Staphylococcus epidermidis was the prevalent species in the control group. Significantly higher numbers of enteric bacteria and pseudomonas were detected in the oral cavities of the HIV group than in the control (p = 0.0001). Enterobacter cloacae was the most frequently isolated species in both groups. Counts of enteric bacteria and pseudomonas were significantly lower in patients with low CD4 counts (p = 0.011); however, there was no difference relating to viral load. It may be concluded that HIV group showed greater species diversity and a higher prevalence of Enterobacteriaceae/Pseudomonadaceae. (C) 2011 Elsevier Ltd. All rights reserved.

Predictors of early relapse in postmenopausal women with hormone receptor-positive breast cancer in the BIG 1-98 trial

BACKGROUND: Aromatase inhibitors are considered standard adjuvant endocrine treatment of postmenopausal women with hormone receptor-positive breast cancer, but it remains uncertain whether aromatase inhibitors should be given upfront or sequentially with tamoxifen. Awaiting results from ongoing randomized trials, we examined prognostic factors of an early relapse among patients in the BIG 1-98 trial to aid in treatment choices. PATIENTS AND METHODS: Analyses included all 7707 eligible patients treated on BIG 1-98. The median follow-up was 2 years, and the primary end point was breast cancer relapse. Cox proportional hazards regression was used to identify prognostic factors. RESULTS: Two hundred and eighty-five patients (3.7%) had an early relapse (3.1% on letrozole, 4.4% on tamoxifen). Predictive factors for early relapse were node positivity (P < 0.001), absence of both receptors being positive (P < 0.001), high tumor grade (P < 0.001), HER-2 overexpression/amplification (P < 0.001), large tumor size (P = 0.001), treatment with tamoxifen (P = 0.002), and vascular invasion (P = 0.02). There were no significant interactions between treatment and the covariates, though letrozole appeared to provide a greater than average reduction in the risk of early relapse in patients with many involved lymph nodes, large tumors, and vascular invasion present. CONCLUSION: Upfront letrozole resulted in significantly fewer early relapses than tamoxifen, even after adjusting for significant prognostic factors.

Herceptest: HER2 expression and gene amplification in non-small cell lung cancer

HER2 is an erbB/HER type I tyrosine kinase receptor that is frequently over-expressed in malignant epithelial tumours. Herceptin, a humanised mouse monoclonal antibody to HER2, is proven therapeutically in the management of metastatic breast cancer, significantly prolonging survival when combined with cytotoxic chemotherapeutic agents. Immunohistochemical studies suggest that non-small-cell lung cancer (NSCLC) tumours may over-express HER2. Our aim was to evaluate HER2 gene amplification and semi-quantitative immuno-expression in NSCLC. A total of 344 NSCLC cases were immunostained for HER2 expression in 2 centres using the HercepTest. Fluorescence in situ hybridisation (FISH) analysis for HER2 gene amplification was performed on most positive cases and a subset of negative cases. Fifteen cases (4.3%) demonstrated 2+ or 3+ membranous HER2 immuno-expression. There was no correlation between immuno-expression and tumour histology or grade. Tumours from higher-stage disease were more often HercepTest-positive (p < 0.001). All 4 HercepTest 3 + cases demonstrated gene amplification. One of the 5 2+ cases tested for gene amplification showed areas of borderline amplification and areas of polyploidy. None of the 19 HercepTest-negative cases demonstrated gene amplification or polyploidy (p < 0.001). Gene amplification was demonstrated in all HercepTest 3+ scoring NSCLC cases. Unlike breast cancer, gene amplification and HER2 protein over-expression assessed by the HercepTest appeared to be uncommon in NSCLC. Herceptin may therefore target only a small proportion of NSCLC tumours and be of limited clinical value in this disease, particularly in the adjuvant setting. © 2001 Wiley-Liss, Inc.

A large proportion of asymptomatic Plasmodium infections with low and sub-microscopic parasite densities in the low transmission setting of Temotu Province, Solomon Islands : challenges for malaria diagnostics in an elimination setting

Background Many countries are scaling up malaria interventions towards elimination. This transition changes demands on malaria diagnostics from diagnosing ill patients to detecting parasites in all carriers including asymptomatic infections and infections with low parasite densities. Detection methods suitable to local malaria epidemiology must be selected prior to transitioning a malaria control programme to elimination. A baseline malaria survey conducted in Temotu Province, Solomon Islands in late 2008, as the first step in a provincial malaria elimination programme, provided malaria epidemiology data and an opportunity to assess how well different diagnostic methods performed in this setting. Methods During the survey, 9,491 blood samples were collected and examined by microscopy for Plasmodium species and density, with a subset also examined by polymerase chain reaction (PCR) and rapid diagnostic tests (RDTs). The performances of these diagnostic methods were compared. Results A total of 256 samples were positive by microscopy, giving a point prevalence of 2.7%. The species distribution was 17.5% Plasmodium falciparum and 82.4% Plasmodium vivax. In this low transmission setting, only 17.8% of the P. falciparum and 2.9% of P. vivax infected subjects were febrile (≥38°C) at the time of the survey. A significant proportion of infections detected by microscopy, 40% and 65.6% for P. falciparum and P. vivax respectively, had parasite density below 100/μL. There was an age correlation for the proportion of parasite density below 100/μL for P. vivax infections, but not for P. falciparum infections. PCR detected substantially more infections than microscopy (point prevalence of 8.71%), indicating a large number of subjects had sub-microscopic parasitemia. The concordance between PCR and microscopy in detecting single species was greater for P. vivax (135/162) compared to P. falciparum (36/118). The malaria RDT detected the 12 microscopy and PCR positive P. falciparum, but failed to detect 12/13 microscopy and PCR positive P. vivax infections. Conclusion Asymptomatic malaria infections and infections with low and sub-microscopic parasite densities are highly prevalent in Temotu province where malaria transmission is low. This presents a challenge for elimination since the large proportion of the parasite reservoir will not be detected by standard active and passive case detection. Therefore effective mass screening and treatment campaigns will most likely need more sensitive assays such as a field deployable molecular based assay.

Phosphorus in agricultural soils of Finland - characterization of reserves and retention in mineral soil profiles

An overwhelming majority of all the research on soil phosphorus (P) has been carried out with soil samples taken from the surface soils only, and our understanding of the forms and the reactions of P at a soil profile scale is based on few observations. In Finland, the interest in studying the P in complete soil profiles has been particularly small because of the lack of tradition in studying soil genesis, morphology, or classification. In this thesis, the P reserves and the retention of orthophosphate phosphorus (PO4-P) were examined in four cultivated mineral soil profiles in Finland (three Inceptisols and one Spodosol). The soils were classified according to the U.S. Soil Taxonomy and soil samples were taken from the genetic horizons in the profiles. The samples were analyzed for total P concentration, Chang and Jackson P fractions, P sorption properties, concentrations of water-extractable P, and for concentrations of oxalate-extractable Al and Fe. Theoretical P sorption capacities and degrees of P saturation were calculated with the data from the oxalate-extractions and the P fractionations. The studied profiles can be divided into sections with clearly differing P characteristics by their master horizons Ap, B and C. The C (or transitional BC) horizons below an approximate depth of 70 cm were dominated by, assumingly apatitic, H2SO4-soluble P. The concentration of total P in the C horizons ranged from 729 to 810 mg kg-1. In the B horizons between the depths of 30 and 70 cm, a significant part of the primary acid-soluble P has been weathered and transformed to secondary P forms. A mean weathering rate of the primary P in the soils was estimated to vary between 230 and 290 g ha-1 year-1. The degrees of P saturation in the B and C horizons were smaller than 7%, and the solubility of PO4-P was negligible. The P conditions in the Ap horizons differed drastically from those in the subsurface horizons. The high concentrations of total P (689-1870 mg kg-1) in the Ap horizons are most likely attributable to long-term cultivation with positive P balances. A significant proportion of the P in the Ap horizons occurred in the NH4F- and NaOH-extractable forms and as organic P. These three P pools, together with the concentrations of oxalate-extractable Al and Fe, seem to control the dynamics of PO4-P in the soils. The degrees of P saturation in the Ap horizons were greater (8-36%) than in the subsurface horizons. This was also reflected in the sorption experiments: Only the Ap horizons were able to maintain elevated PO4-P concentrations in the solution phase − all the subsoil horizons acted as sinks for PO4-P. Most of the available sorption capacity in the soils is located in the B horizons. The results suggest that this capacity could be utilized in reducing the losses of soluble P from excessively fertilized soils by mixing highly sorptive material from the B horizons with the P-enriched surface soil. The drastic differences in the P characteristics observed between adjoining horizons have to be taken into consideration when conducting soil sampling. Sampling of subsoils has to be made according to the genetic horizons or at small depth increments. Otherwise, contrasting materials are likely to be mixed in the same sample; and the results of such samples are not representative of any material present in the studied profile. Air-drying of soil samples was found to alter the results of the sorption experiments and the water extractions. This indicates that the studies on the most labile P forms in soil should be carried out with moist samples.