On The Random Vector Potential Model In Two Dimensions

The random vector potential model describes massless fermions coupled to a quenched random gauge field. We study its abelian and non-abelian versions. The abelian version can be completely solved using bosonization. We analyse the non-abelian model using its supersymmetric formulation and show, by a perturbative renormalisation group computation, that it is asymptotically free at large distances. We also show that all the quenched chiral current correlation functions can be computed exactly, without using the replica trick or the supersymmetric formulation, but using an exact expression for the effective action for any sample of the random gauge field. These chiral correlation functions are purely algebraic.Comment: 11 pages, latex, no figures. Few equations and remarks adde

Spectrum of subblocks of structured random matrices : A free probability approach

We present a new efficient method, based on an extremization problem, for computing the spectrum of subblocks of large structured random matrices. This method applies to ensembles of matrices satisfying three fundamental properties, which we discuss. We present different proofs - combinatorial or algebraic - of the validity of this method, which all have some connection with free probability. We illustrate this method with well known examples of unstructured matrices, including Haar randomly rotated matrices, as well as with the example of structured random matrices arising in the quantum symmetric simple exclusion process.Comment: 22 pages main text, 3 pages appendi

Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process

Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We confirm this observation by studying a suitable toy model for mesoscopic transport: the open quantum symmetric simple exclusion process (QSSEP). We prove that the average mutual information of the open QSSEP in the steady state satisfies a volume law, and derive exact formulae for the mutual information between different regions of the system. Exploiting the free probability structure of QSSEP, we obtain these results by developing a new method to determine the eigenvalue spectrum of sub-blocks of random matrices from their so-called local free cumulants -- a mathematical result on its own with potential applications in the theory of random matrices. As an illustration of this method, we show how to compute expectation values of observables in systems satisfying the Eigenstate Thermalization Hypothesis (ETH) from the local free cumulants.Comment: 6 pages main text, 5 pages supplemental materia

gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions

We consider the non-hermitian 2D Dirac Hamiltonian with (A): real random mass, imaginary scalar potential and imaginary gauge field potentials, and (B) arbitrary complex random potentials of all three kinds. In both cases this Hamiltonian gives rise to a delocalization transition at zero energy with particle-hole symmetry in every realization of disorder. Case (A) is in addition time-reversal invariant, and can also be interpreted as the random-field XY Statistical Mechanics model in two dimensions. The supersymmetric approach to disorder averaging results in current-current perturbations of $gl(N|N)$ super-current algebras. Special properties of the $gl(N|N)$ algebra allow the exact computation of the beta-functions, and of the correlation functions of all currents. One of them is the Edwards-Anderson order parameter. The theory is `nearly conformal' and possesses a scale-invariant subsector which is not a current algebra. For N=1, in addition, we obtain an exact solution of all correlation functions. We also study the delocalization transition of case (B), with broken time reversal symmetry, in the Gade-Wegner (Random-Flux) universality class, using a GL(N|N;C)/U(N|N) sigma model, as well as its PSL(N|N) variant, and a corresponding generalized random XY model. For N=1 the sigma model is shown to be identical to the current-current perturbation. For the delocalization transitions (case (A) and (B)) a density of states, diverging at zero energy, is found.Comment: LaTeX, 40 page

Randomly coupled minimal models

Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$ models, in the infra-red limit. This result is then extend to the case with $M$ randomly coupled $M_p$ models, which will flow toward $M$ decoupled $M_{p-1}$.Comment: 12 pages, latex, 1 eps figures; new results adde

Relating c<0 and c>0 Conformal Field Theories

A `canonical mapping' is established between the c=-1 system of bosonic ghosts and the c=2 complex scalar theory and, a similar mapping between the c=-2 system of fermionic ghosts and the c=1 Dirac theory. The existence of this mapping is suggested by the identity of the characters of the respective theories. The respective c0 theories share the same space of states, whereas the spaces of conformal fields are different. Upon this mapping from their c0) complex scalar and the Dirac theories inherit hidden nonlocal sl(2) symmetries.Comment: 23 pages, harvma

Einsatz der Nahinfrarotspektroskopie zur Qualitätskontrolle ökologischer Produkte am Beispiel von Möhren

Near-infrared reflectance spectroscopy is known for its inexpensiveness, rapidity and accuracy and may become a useful tool for the quality assessment of products of the growing organic food market. The objective of this study was to evaluate the ability of visible and near-infrared reflectance spectroscopy (NIRS) to predict several quality parameters (total nitrogen content and the content of different sugars) of organically grown carrots. Spectra of the VIS-NIR region (400-2500 nm) from 120 dried and milled carrot samples were recorded and transformed in the form of (log[1/reflectance]) values. The samples were randomly separated into two groups for calibration (n=60) and validation (n=60). A modified partial least square method was used to develop an equation over the whole spectrum (1st to 3rd derivation) from the spectra and the laboratory results for total nitrogen and the contents of D-glucose, D-fructose, sucrose and the sum of these three sugars. Calibrations were successful for all constituents. The validation, however, gave differing results: The total nitrogen content was predicted well by NIRS - the regression coefficient (a) of the linear regression (measured against predicted values) was 1.0, the correlation coefficient (r) was 0.9 and the ratio of standard deviation of the laboratory results to standard error of prediction (RDP) was 2.5. A satisfactory prediction was obtained for D-glucose (a=0.8, r=0.8, RDP=1.5) and D-fructose (a=0.8, r=0.8, RDP=1.5). In contrast, the contents of sucrose (a=0.8, r=0.7, RPD=1.4) and the sum of sugars (a=1.2, r=0.6, RPD=1.3) were predicted less satisfactorily. The good and satisfactory results for total nitrogen, glucose and fructose indicate that there is marked potential of NIRS for the quality assessment of organic food products. Studies are now required for a wider spectrum of food products and more constituents

Kann man mit Nahinfrarot-Spektroskopie die Bodenfruchtbarkeit bestimmen?

Near-infrared reflectance spectroscopy is known for its inexpensiveness, rapidity and accuracy and may become a useful tool for the assessment of soil fertility. The objec-tives of this study were (i) to evaluate the ability of near-infrared reflectance spectros-copy (NIRS) to predict several soil chemical and biological characteristics of organi-cally managed arable land and (ii) to test if different sample pre-treatments yield comparable results. Spectra of the VIS-NIR region (400-2500 nm) from 56 either fresh or pre-treated (quick-freezing, freeze-drying and grinding) soil samples were recorded. A modified partial least square regression method and cross-validation were used to develop an equation over the whole spectrum (1st to 3rd derivation). Soil chemical and biological characteristics and ratios of them were predicted. The soil chemical charac-teristics pH (CaCl2) and contents of Corg, Nt and extractable P (Olsen), K (CAL) and Mg (CaCl2) were generally predicted well, except for the K content, which was predicted satisfactorily. The predictions were better for pre-treated samples than for fresh ones. The RSC (the ratio of standard deviation of laboratory results to standard error of cross-validation) ranged between 2.5 (pH) and 4.1 (Mg) and the correlation coefficient r between 0.91 (Mg) and 0.97 (Nt), respectively. NIRS-predictions of biological charac-teristics were for fresh samples slightly better than for pre-treated. Exceptions were content of ergosterol and the ratio of ergosterol content to Cmic. Respiration rate and contents of Cmic, Nmic and Pmic were predicted well. The RSC was between 2.5 (Pmic) and 4.6 (ergosterol) and r between 0.89 (respiration rate) and 0.93 (Cmic). Ratios of Cmic/Nmic and ergosterol/Cmic and the metabolic quotient were predicted satisfactorily. Nitrogen mineralization rate could not be predicted satisfactorily. The good and satis-factory results for soil chemical and biological characteristics indicate that there is marked potential of NIRS for soil fertility assessment. Quick-freezing and subsequent freeze-drying of samples is a promising method to maintain stability of biological sample characteristics