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

Enzymatic crosslinking of lignin nanoparticles and nanocellulose in cryogels improves adsorption of pharmaceutical pollutants

Pharmaceuticals, designed for treating diseases, ironically endanger humans and aquatic ecosystems as pollutants. Adsorption-based wastewater treatment could address this problem, however, creating efficient adsorbents remains a challenge. Recent efforts have shifted towards sustainable bio-based adsorbents. Here, cryogels from lignin-containing cellulose nanofibrils (LCNF) and lignin nanoparticles (LNPs) were explored as pharmaceuticals adsorbents. An enzyme-based approach using laccase was used for crosslinking instead of fossil-based chemical modification. The impact of laccase treatment on LNPs alone produced surface-crosslinked water-insoluble LNPs with preserved morphology and a hemicellulose-rich, water-soluble LNP fraction. The water-insoluble LNPs displayed a significant increase in adsorption capacity, up to 140 % and 400 % for neutral and cationic drugs, respectively. The crosslinked cryogel prepared by one-pot incubation of LNPs, LCNF and laccase showed significantly higher adsorption capacities for various pharmaceuticals in a multi-component system than pure LCNF or unmodified cryogels. The crosslinking minimized the leaching of LNPs in water, signifying enhanced binding between LNPs and LCNF. In real wastewater, the laccase-modified cryogel displayed 8–44 % removal for cationic pharmaceuticals. Overall, laccase treatment facilitated the production of bio-based adsorbents by improving the deposition of LNPs to LCNF. Finally, this work introduces a sustainable approach for engineering adsorbents, while aligning with global sustainability goals.Peer reviewe