Energy localization in two chaotically coupled systems

We set up and analyze a random matrix model to study energy localization and its time behavior in two chaotically coupled systems. This investigation is prompted by a recent experimental and theoretical study of Weaver and Lobkis on coupled elastomechanical systems. Our random matrix model properly describes the main features of the findings by Weaver and Lobkis. Due to its general character, our model is also applicable to similar systems in other areas of physics -- for example, to chaotically coupled quantum dots.Comment: 20 pages, 15 figure

Long-Term Impact of Liming on Soil C and N in a Fertile Spruce Forest Ecosystem

Liming can counteract acidification in forest soils, but the effects on soil C and N pools and fluxes over long periods are less well understood. Replicated plots in an acidic and N-rich 40-year-old Norway spruce (Picea abies) forest in SW Sweden (Hasslov) were treated with 0, 3.45 and 8.75 Mg ha(-1)of dolomitic lime (D0, D2 and D3) in 1984. Between 1984 and 2016, soil organic C to 30 cm depth increased by 28 Mg ha(-1)(30% increase) in D0 and decreased by 9 Mg ha(-1)(9.4% decrease) in D3. The change in D2 was not significant (+ 2 Mg ha(-1)). Soil N pools changed proportionally to those in soil C pools. The C and N changes occurred almost exclusively in the top organic layer. Non-burrowing earthworms responded positively to liming and stimulated heterotrophic respiration in this layer in both D2 and D3. Burrowing earthworms in D3 further accelerated C and N turnover and loss of soil. The high soil C and N loss at our relatively N-rich site differs from studies of N-poor sites showing no C and N loss. Earthworms need both high pH and N-rich food to reach high abundance and biomass. This can explain why liming of N-rich soils often results in decreasing C and N pools, whereas liming of N-poor soils with few earthworms will not show any change in soil C and N. Extractable nitrate N was always higher in D3 than in D2 and D0. After 6 years (1990), potential nitrification was much higher in D3 (197 kg N ha(-1)) than in D0 (36 kg N ha(-1)), but this difference decreased during the following years, when also the unlimed organic layers showed high nitrification potential. Our experiment finds that high-dose liming of acidic N-rich forest soils produces an initial pulse of soil heterotrophic respiration and increases in earthworm biomass, which together cause long-term declines in soil C and N pools

The k-Point Random Matrix Kernels Obtained from One-Point Supermatrix Models

The k-point correlation functions of the Gaussian Random Matrix Ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We show that the kernels are obtained, for arbitrary level number, directly from supermatrix models for one-point functions. More precisely, the generating functions of the one-point functions are equivalent to the kernels. This is surprising, because it implies that already the one-point generating function holds essential information about the k-point correlations. This also establishes a link to the averaged ratios of spectral determinants, i.e. of characteristic polynomials

On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix

The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all Rothstein contributions known as Efetov-Wegner terms in physics was quite cumbersome. We derive the supermatrix Bessel function with all Efetov-Wegner terms for an arbitrary rotation invariant probability density function. As applications we consider representations of generating functions for Hermitian random matrices with and without an external field as integrals over eigenvalues of Hermitian supermatrices. All results are obtained with all Efetov-Wegner terms which were unknown before in such an explicit and compact representation.Comment: 23 pages, PACS: 02.30.Cj, 02.30.Fn, 02.30.Px, 05.30.Ch, 05.30.-d, 05.45.M

Derivation of determinantal structures for random matrix ensembles in a new way

There are several methods to treat ensembles of random matrices in symmetric spaces, circular matrices, chiral matrices and others. Orthogonal polynomials and the supersymmetry method are particular powerful techniques. Here, we present a new approach to calculate averages over ratios of characteristic polynomials. At first sight paradoxically, one can coin our approach "supersymmetry without supersymmetry" because we use structures from supersymmetry without actually mapping onto superspaces. We address two kinds of integrals which cover a wide range of applications for random matrix ensembles. For probability densities factorizing in the eigenvalues we find determinantal structures in a unifying way. As a new application we derive an expression for the k-point correlation function of an arbitrary rotation invariant probability density over the Hermitian matrices in the presence of an external field.Comment: 36 pages; 2 table

Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary-symplectically invariant matrix ensembles. The results are equivalent to, but the approach is different from the superbosonization formula. We express our results in a unifying way. We also give explicit expressions for all one-point functions and discuss features of the higher order correlations.Comment: 37 page

Risk, responsibilities and rights: reassessing the ‘economic causes of crime’ thesis in a recession

This paper explores competing accounts of an apparent inversion of the previously-prevailing relationship between young people's unemployment and the incidence of youth offending at a time of economic recession. It begins by highlighting the faltering association between unemployment and offending, and considers the paradoxical implications for risk-based methodologies in youth justice practice. The paper then assesses explanations for the changing relationship that suggest that youth justice policies have successfully broken the unemployment-offending link; and alternatively that delayed effects of recession have yet to materialise, by reference to the work of four Inter-governmental organisations and to youth protests beyond the UK. In place of ever more intensive risk analyses, the paper then focusses on the adverse effects of unemployment on social cohesion, and proposes a rights-based approach to youth justice that recognises the growing disjuncture between the rights afforded to young people and the responsibilities expected of them