High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.Comment: ITP.SB-93-22,17 page

Relatedness, Complexity and Local Growth

We derive a measure of the relatedness between economic activities based on weighted correlations of local employment shares, and use this measure to estimate city and activity complexity. Our approach extends discrete measures used in previous studies by recognising the extent of activities' local over-representation and by adjusting for differences in signal quality between geographic areas with different sizes. We examine the contribution of relatedness and complexity to urban employment growth, using 1981–2013 census data from New Zealand. Complex activities experienced faster employment growth during our period of study, especially in complex cities. However, this growth was not significantly stronger in cities more dense with related activities. Relatedness and complexity appear to be most relevant for analysing how large, complex cities grow, and are less informative for understanding employment dynamics in small, less complex cities

Development and Use of a Screening Procedure for Production of (alpha)-Acetolactate by Lactococcus lactis subsp. lactis biovar diacetylactis Strains

A method was developed to screen and isolate mutagenized Lactococcus lactis subsp. lactis biovar diacetylactis strains accumulating (alpha)-acetolactate. This compound is accumulated by (alpha)-acetolactate decarboxylase-deficient strains and undergoes spontaneous degradation into diacetyl on agar plates. The diacetyl produced is detected by a colorimetric reaction yielding a red halo around the colonies

Diacetyl production in milk by an α-acetolactic acid accumulating strain of Lactococcus lactis ssp. lactis biovar. diacetylactis

When grown in skim milk, Lactococcus lactis ssp. lactis biovar. diacetylactis D1 accumulated alpha-acetolactic acid at 1.7 mM because of the absence of alpha-acetolactate decarboxylase. The alpha-acetolactic acid produced was unstable and underwent a chemical decarboxylation. At the beginning of the culture, the redox potential was high, and the decarboxylation of alpha-acetolactic acid produced diacetyl and acetoin. At the end of the culture, the redox potential was low, and alpha-acetolactic acid was converted into acetoin only. When synthetic alpha-acetolactic acid was added to skim milk or fermented milk, the chemical decarboxylation of alpha-acetolactic acid into diacetyl occurred only at high redox potential. The strain D1 has been cultivated under constant agitation, permitting high redox potential to be maintained. In these conditions, diacetyl production was threefold higher than in an unagitated culture. When the strain D1 was cultivated in association with an acidifying Lactococcus lactis ssp. lactis strain, the amount of diacetyl was <.02 mM because of the rapid drop of the redox potential at the beginning of the fermentation, which prevented the formation of diacetyl from the chemical oxidative decarboxylation of alpha-acetolactic acid

Method for assaying volatile compounds by headspace gas chromatography and application to growing starter cultures

Automatic headspace gas chromatography was used to assay volatile compounds in fermented milks, including diacetyl, which is of particular interest because of its aromatic properties. Alpha-acetolactic acid, produced by lactic acid bacteria, is an unstable compound that is chemically transformed to acetoin and diacetyl during incubation at 85-degrees-C in the headspace sampler, leading to an over-estimation of diacetyl concentrations in fermented milks. The oxidative decarboxylation of synthetic alpha-acetolactic acid to diacetyl during the assay decreased as the pH increased: at pH 4.0, 40% of the ce-acetolactic acid present was transformed to diacetyl, but this reaction was limited to 6% at pH 7.0. When the assay mixture was degassed and heated to 100-degrees-C before analysis, the reaction was limited to 2%, leading to a more precise assay of diacetyl in the presence of alpha-acetolactic acid. The method for assaying diacetyl was applied to a mixed culture of Leuconostoc mesenteroides ssp. cremoris and Lactococcus lactis ssp. lactis in milk. Acetoin (1.07 mM) and alpha-acetolactic acid (.18 mM) were produced, but not diacetyl. In our culture conditions, the redox potential dropped rapidly at the beginning of fermentation, which prevented diacetyl production by the oxidative decarboxylation of alpha-acetolactic acid. When the same fermentation was carried out with agitation, the redox potential remained high, and diacetyl production was significant, reaching .032 mM (2.8 mg/L)

Polyacrylamide-Entrapped Rhizobium as an Inoculant for Legumes

Pot experiments showed that Rhizobium japonicum cells entrapped in a polyacrylamide gel could be used as an inoculant for soybeans and compared favorably to laboratory-made peat base inoculant containing the same bacterial strain