Abstract:
Mycorrhizal roots of the deciduous trees European
beech (Fagus sylvatica (L.)) and
Sessile oak (Quercus petraea (MattuschkaLiebl.)) and the conifers Norway spruce (Picea abies (L.) H. Karst.) and European larch (Larix decidua (Mill.)) associated with
the ectomycorrhizal fungi matt bolete (Xerocomus
pruinatus (Fries 1835)) or bay bolete (X.
badius (Fries 1818)) were analysed with respect to the occurrence of
dihydrolipoyl dehydrogenase (EC 1.8.1.4) allozymes. In root tissues of the two
deciduous trees, two gene loci could be
visualized after cellulose acetate electrophoresis while three loci were expressed
in root tissues of the two coniferous species. The two fungal species and
further ectomycorrhizal fungi expressed exclusively one dihydrolipoyl
dehydrogenase gene. In Xerocomus
pruinatus and X. badius, the dihydrolipoyl dehydrogenase gene consists of 1460 bp and 1370 bp,
respectively, including five introns each consisting of 52 bp. Their DNA
sequences correspond to 70 to 90% to other fungal dihydrolipoyl dehydrogenase
genes. One monomer of the dimeric dihydrolipoyl dehydrogenase enzyme consists
of 486 (X. pruinatus) or 454 (X.

Ectomycorrhizal fungi were investigated on five different forest tree species growing in pure stands on the south slope of the Taunus Mountains, which are situated at the northern end of the Rhine rift valley in Central Germany. Mycorrhizal fungi accompanying the genus Xerocomus were identified and their frequencies counted. Using ITS markers, 22 different fungal species were identified down to species level and 6 down to genus level. On European beech (Fagus sylvatica) 16 fungal species and 4 genera were identified and on Sessile oak (Quercus petraea) 16 ectomycorrhizal species and 2 genera were determined. On both deciduous trees we observed exclusively: Cortinarius subsertipes, Genea hispidula, Lactarius quietus, Tylopilus felleus and a Melanogaster genus. On Norway spruce (Picea abies) we identified 13 different mycorrhizal species and 3 different genera, on Silver fir (Abies alba) 12 species and 3 genera, and in association with European larch (Larix decidua) 11 species and 3 genera. On these conifers

Abstract:
We prove that lattice QCD generates the axial anomaly in the continuum limit under very general conditions on the lattice action, which includes the case of Ginsparg-Wilson fermions. The ingredients going into the proof are gauge invariance, locality of the Dirac operator, absence of fermion doubling, the general form of the lattice Ward identity, and the power counting theorem of Reisz. The results generalize in an obvious way to SU(N) lattice gauge theories.

Abstract:
We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact expressions for the average height and height fluctuations as functions of space and time for an initially flat interface. For a given defect strength there is a critical angle between the defect line and the growth direction above which a cusp in the interface develops. In the mapping to polymers in random media this is an example for the transverse Meissner effect. Fluctuations around the mean shape of the interface are Gaussian.

Abstract:
Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good agreement between experimental and exact theoretical data. This is shown for the Rubinstein-Duke model for gel-electrophoresis of DNA, the asymmetric exclusion process as a model for the kinetics of biopolymerization and the coagulation-diffusion model for exciton dynamics on TMMC chains.

Abstract:
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact results. In a complementary approach we generalize previous work and present a new description of these and other processes and the related quantum chains in terms of an operator algebra with quadratic relations. The full solution of the master equation of the process is thus turned into the problem of finding representations of this algebra. We find a two-dimensional time-dependent representation of the algebra for the symmetric exclusion process with open boundary conditions. We obtain new results on the dynamics of this system and on the eigenvectors and eigenvalues of the corresponding quantum spin chain, which is the isotropic Heisenberg ferromagnet with non-diagonal boundary fields.

Abstract:
Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P(x_1, ... ,x_N;t|y_1, ... ,y_N;0) of finding N particles on lattice sites x_1, ... ,x_N at time t with initial occupation y_1, ... ,y_N at time t=0.

Abstract:
We study a 12-parameter stochastic process involving particles with two-site interaction and hard-core repulsion on a $d$-dimensional lattice. In this model, which includes the asymmetric exclusion process, contact processes and other processes, the stochastic variables are particle occupation numbers taking values $n_{\vec{x}}=0,1$. We show that on a 10-parameter submanifold the $k$-point equal-time correlation functions $\exval{n_{\vec{x}_1} \cdots n_{\vec{x}_k}}$ satisfy linear differential- difference equations involving no higher correlators. In particular, the average density $\exval{n_{\vec{x}}} $ satisfies an integrable diffusion-type equation. These properties are explained in terms of dual processes and various duality relations are derived. By defining the time evolution of the stochastic process in terms of a quantum Hamiltonian $H$, the model becomes equivalent to a lattice model in thermal equilibrium in $d+1$ dimensions. We show that the spectrum of $H$ is identical to the spectrum of the quantum Hamiltonian of a $d$-dimensional, anisotropic spin-1/2 Heisenberg model. In one dimension our results hint at some new algebraic structure behind the integrability of the system.

Abstract:
We study the effect of an external driving force on a simple stochastic reaction-diffusion system in one dimension. In our model each lattice site may be occupied by at most one particle. These particles hop with rates $(1\pm\eta)/2$ to the right and left nearest neighbouring site resp. if this site is vacant and annihilate with rate 1 if it is occupied. We show that density fluctuations (i.e. the $m^{th}$ moments $\langle N^m \rangle$ of the density distribution at time $t$) do not depend on the spatial anisotropy $\eta$ induced by the driving field, irrespective of the initial condition. Furthermore we show that if one takes certain translationally invariant averages over initial states (e.g. random initial conditions) even local fluctuations do not depend on $\eta$. In the scaling regime $t \sim L^2$ the effect of the driving can be completely absorbed in a Galilei transformation (for any initial condition). We compute the probability of finding a system of $L$ sites in its stationary state at time $t$ if it was fully occupied at time $t_0 = 0$.

Abstract:
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative description of these processes in terms of a time-dependent operator algebra with quadratic relations. These relations generate the Bethe ansatz equations for the spectrum and turn the calculation of time-dependent expectation values into the problem of either finding representations of this algebra or of solving functional equations for the initial values of the operators. We use both strategies for the study of two specific models: (i) We construct a two-dimensional time-dependent representation of the algebra for the symmetric exclusion process with open boundary conditions. In this way we obtain new results on the dynamics of this system and on the eigenvectors and eigenvalues of the corresponding quantum spin chain, which is the isotropic Heisenberg ferromagnet with non-diagonal, symmetry-breaking boundary fields. (ii) We consider the non-equilibrium spin relaxation of Ising spins with zero-temperature Glauber dynamics and an additional coupling to an infinite-temperature heat bath with Kawasaki dynamics. We solve the functional equations arising from the algebraic description and show non-perturbatively on the level of all finite-order correlation functions that the coupling to the infinite-temperature heat bath does not change the late-time behaviour of the zero-temperature process. The associated quantum chain is a non-hermitian anisotropic Heisenberg chain related to the seven-vertex model.