Abstract:
The aim of this study was to investigate non-viral pDNA carriers based on diblock-copolymers consisting of poly(2-(dimethyl amino)ethyl methacrylate) (pDMAEMA) and poly(2-hydroxyethyl methacrylate) (pHEMA). Specifically the block-lengths and molecular weights were varied to determine the minimal requirements for transfection. Such vectors should allow better transfection at acceptable toxicity levels and the entire diblock-copolymer should be suitable for renal clearance. For this purpose, a library of linear poly(2-(dimethyl amino)ethyl methacrylate- block-poly(2-hydroxyl methacrylate) (pDMAEMA -block-pHEMA) copolymers was synthesized via RAFT (reversible addition-fragmentation chain transfer) polymerization in a molecular weight (Mw) range of 17–35.7 kDa and analyzed using 1H and 13C NMR (nuclear magnetic resonance), ATR (attenuated total reflectance), GPC (gel permeation chromatography) and DSC (differential scanning calorimetry). Copolymers possessing short pDMAEMA-polycation chains were 1.4–9.7 times less toxic in vitro than polyethylenimine (PEI) 25 kDa, and complexed DNA into polyplexes of 100–170 nm, favorable for cellular uptake. The DNA-binding affinity and polyplex stability against competing polyanions was comparable with PEI 25 kDa. The zeta-potential of polyplexes of pDMAEMA-grafted copolymers remained positive (+15–30 mV). In comparison with earlier reported low molecular weight homo pDMAEMA vectors, these diblock-copolymers showed enhanced transfection efficacy under in vitro conditions due to their lower cytotoxicity, efficient cellular uptake and DNA packaging. The homo pDMAEMA 115 (18.3 kDa) self-assembled with DNA into small positively charged polyplexes, but was not able to transfect cells. The grafting of 6 and 57 repeating units of pHEMA (0.8 and 7.4 kDa) to pDMAEMA 115 increased the transfection efficacy significantly, implying a crucial impact of pHEMA on vector-cell interactions. The intracellular trafficking, in vivo transfection efficacy and kinetics of low molecular weight pDMAEMA -block-pHEMA are subject of ongoing studies.

Abstract:
We prove that for a hard core interaction the ground state spin polarization in the low Zeeman energy limit is given by $P=2/\nu-5$ for filling fractions in the range $ 1/3 \leq\nu\leq 2/5 $. The same result holds for a Coulomb potential except for marginally small magnetic fields. At the magnetic fields $B<20T$ unpolarized quasielectrons can manifest themselves by a characteristic peak in the I-V characteristics for tunneling between two $\nu=1/3$ ferromagnets.

Abstract:
Let $S(\rho)=- Tr (\rho \log\rho)$ be the von Neumann entropy of an $N$-dimensional quantum state $\rho$ and $e_2(\rho)$ the second elementary symmetric polynomial of the eigenvalues of $\rho$. We prove the inequality $S(\rho) \le c(N) \sqrt{e_2(\rho)} $ where $c(N)=\log(N) \sqrt{\frac{2N}{N-1}}$. This generalizes an inequality given by Fuchs and Graaf \cite{fuchsgraaf} for the case of one qubit, i.e., N=2. Equality is achieved if and only if $\rho$ is either a pure or the maximally mixed state. This inequality delivers new bounds for quantities of interest in quantum information theory, such as upper bounds for the minimum output entropy and the entanglement of formation as well as a lower bound for the Holevo channel capacity.

Abstract:
We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.

Abstract:
We estimate the composite fermion effective mass for a general two particle potential r^{-\alpha} using exact diagonalization for polarized electrons in the lowest Landau level on a sphere. Our data for the ground state energy at filling fraction \nu=1/2 as well as estimates of the excitation gap at \nu=1/3, 2/5 and 3/7 show that m_eff \sim \alpha^{-1}.

Abstract:
Skyrmions in the FQHE at filling fractions above \nu=1/3 are studied within the anyon model and by exact diagonalization. Relations to the composite fermion theory are pointed out. We find that unpolarized quasiparticles above \nu=1/3 are stable below B\approx 0.02T. At low Zeeman energy the polarization in the range \nu=8/5 ... 5/3 is found to be a linear function of the filling factor. We also reexamine the energy and wave function of skyrmions at \nu=1 by a new method.

Abstract:
We study Haldane's and Jain's proposals for the quasiparticle wave function on the sphere. The expectation values of the energy and the pair angular momenta distribution are calculated at filling factor 1/3 and compared with the data of an exact numerical diagonalization for up to 10 electrons with Coulomb and truncated quasipotential interaction.

Abstract:
In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the \sus and the free energy are obtained for the quenched bond-diluted Ising model in $d = 3$--5 dimensions. They are analysed using different extrapolation methods tailored to the expected singularity behaviours. In $d = 4$ and 5 dimensions we confirm that the critical behaviour is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in $d = 4$ is confirmed and our results for the critical behaviour of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation and random fixed point. We estimate the critical exponent of the \sus to be $\gamma =1.305(5)$ at the random fixed point.

Abstract:
Explicit expressions for the concurrence of all positive and trace-preserving ("stochastic") 1-qubit maps are presented. By a new method we find the relevant convex roof pattern. We conclude that two component optimal decompositions always exist. Our results can be transferred to $2 \times n$-quantum systems providing the concurrence for all rank two density operators as well as a lower bound for their entanglement of formation.

Abstract:
We derive high-temperature series expansions for the free energy and the susceptibility of random-bond $q$-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength $p$ as well as the dimension $d$ as symbolic parameters. By applying several series analysis techniques to the new series expansions, one can scan large regions of the $(p,d)$ parameter space for any value of $q$. For the bond-diluted 4-state Potts model in three dimensions, which exhibits a rather strong first-order phase transition in the undiluted case, we present results for the transition temperature and the effective critical exponent $\gamma$ as a function of $p$ as obtained from the analysis of susceptibility series up to order 18. A comparison with recent Monte Carlo data (Chatelain {\em et al.}, Phys. Rev. E64, 036120(2001)) shows signals for the softening to a second-order transition at finite disorder strength.