Two-photon fabrication of hydrogel microstructures for excitation and immobilization of cells.

We investigate in vitro fabrication of hydrogel microstructures by two photon laser lithography for single cell immobilization and excitation. Fluorescent yeast cells are embedded in water containing the hydrogel precursor mixtures and cross-linking is used to selectively immobilize a particular cell. Cell viability within the hydrogel precursor is estimated using a life/dead assay and elastic and stiff hydrogel structures are fabricated, immobilizing cells in a microfluidic environment. Additionally, we demonstrate the illumination of cells by on-the-fly fabricated hydrogel waveguide networks connected to an external light source, thereby exciting a fluorescence signal in a single immobilized cell.

Spectral function and quasiparticle damping of interacting Bosons in two dimensions.

We employ the functional renormalization group to study dynamical properties of the two-dimensional Bose gas. Our approach is free of infrared divergences, which plague the usual diagrammatic approaches, and is consistent with the exact Nepomnyashchy identity, which states that the anomalous self-energy vanishes at zero frequency and momentum. We recover the correct infrared behavior of the propagators and present explicit results for the spectral line shape, from which we extract the quasiparticle dispersion and damping.

Condensate density of interacting bosons: A functional renormalization group approach.

We calculate the temperature-dependent condensate density rho0(T) of interacting bosons in three dimensions using the functional renormalization group (FRG). From the numerical solution of suitably truncated FRG flow equations for the irreducible vertices we obtain rho0(T) for arbitrary temperatures. We carefully extrapolate our numerical results to the critical point and determine the order parameter exponent beta approximately 0.32 in reasonable agreement with the expected value 0.345 associated with the XY -universality class. We also calculate the condensate density in two dimensions at zero temperature using a truncation of the FRG flow equations based on the derivative expansion including cubic and quartic terms in the expansion of the effective potential in powers of the density. As compared with the widely used quadratic approximation for the effective potential, the coupling constants associated with the cubic and quartic terms lead to small corrections of the condensate density.

Magnetic properties of a novel quasi-2D Cu(II)-trimer system.

We present structural and magnetic data of a new Cu(2+)(S = 1/2)-containing magnetic trimer system 2b·3CuCl(2)·2H(2)O (b = betaine, C(5)H(11)NO(2)). The trimers form a quasi-2D quantum spin system with an unusual intra-layer exchange coupling topology, which, in principle, supports diagonal four-spin exchange. To describe the magnetic properties, a 2D effective interacting-trimer model has been developed including an intra-trimer coupling J and two inter-trimer couplings J(a) and J(b). The low-energy description and effective parameters are obtained from numerical calculations based on four coupled trimers (with periodic boundary conditions). Fits to the experimental data using this model yield the magnetic coupling constants J/k(B) = -15 K and J(a)/k(B) = J(b)/k(B) = -4 K. These parameters describe the susceptibility and magnetization data very well over the whole temperature and field range investigated. Moreover, the model calculations indicate that, for certain ranges of the ratio J(b)/J(a), which might be accessible by either chemical substitution and/or hydrostatic pressure, the low-energy properties of 2b·3CuCl(2)·2H(2)O will be dominated by non-trivial four-spin exchange processes.

Two-parameter scaling of correlation functions near continuous phase transitions.

We discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two-parameter scaling form G(k)=kc(-2)g(kxi,k/kc), where k is the wave vector and xi is the correlation length, and the interaction-dependent nonuniversal momentum scale kc remains finite at the critical fixed point. The correlation function describes the entire critical regime and captures the classical to critical crossover. One-parameter scaling is recovered only in the limit k/kc-->0. We present an approximate calculation of g(x,y) for the Ising universality class using the functional renormalization group.

Probing anomalous longitudinal fluctuations of the interacting Bose gas via Bose-Einstein condensation of magnons.

The emergence of a finite staggered magnetization in quantum Heisenberg antiferromagnets subject to a uniform magnetic field can be viewed as Bose-Einstein condensation of magnons. Using nonperturbative results for the infrared behavior of the interacting Bose gas, we present exact results for the staggered spin-spin correlation functions of quantum antiferromagnets in a magnetic field at zero temperature. In particular, we show that in dimensions 1