Abstract:
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical field equations to the time evolution of the quantum field. We discuss the field in thermodynamical equilibrium and find the explicit solution of the equations of motion for the so-called ``roll-over'' phase transition. Finally, we briefly discuss the approximate methods for the evaluation of the Wigner functional that may be used to numerically simulate the initial value problem..

Abstract:
We describe the dynamics of gluons and quarks in a relativistic nuclear collision, within the framework of classical mean-field transport theory, by the coupled equations for the classical Yang-Mills field and a collection of colored point particles. The particles represent the valence quarks in the colliding nuclei. We explore the time evolution of the gauge field in a numerical simulation of the collision of two Lorentz-boosted ``nuclei'' on a long three-dimensional gauge lattice. We report first results on soft gluon scattering and coherent gluon radiation.

Abstract:
The Yang Mills equations provide a classical mean field description of gauge fields. In view of developing a coherent description of the formation of the quark gluon plasma in high energetic nucleus-nucleus collisions we study pure gauge field dynamics in 3+1 dimensions. In collisions of wave packets, numerically simulated on a SU(2) gauge lattice, we study transverse and longitudinal energy currents. For wave packets with different polarizations in color space, we observe a time delayed fragmentation after the collision resulting in a rapid expansion into transverse directions. We call this phenomenon the ''glue burst''. An analysis of the Yang Mills equations reveals the explanation for this behavior. We point out that this effect could play a role in ultra-relativistic heavy-ion collisions.

Abstract:
In a fully relativistic approach, a RLSM description of nuclei colliding at ultra-relativistic energies can be formulated within the framework of a classical transport theory. The valence quarks of the nucleons are described through collections of classical point-like particles moving in the continuum. They are coupled to soft gluon fields which are described through the Yang Mills equations on a gauge lattice. In a first step, we focus on the range of low-$p_t$ interactions. Results from numerical model simulations of pure gluonic nucleus-nucleus collisions on SU(2) gauge lattices in 3+1 dimensions are presented. They show an effect which we call the glue burst.

Abstract:
The dynamics of gluons and quarks in a relativistic nuclear collision are described, within the framework of a classical mean-field transport theory, by the coupled equations for the Yang-Mills field and a collection of colored point particles. The particles are used to represent color source effects of the valence quarks in the colliding nuclei. The possibilities of this approach are studied to describe the real time evolution of small $x$ modes in the classical effective theory in a non-perturbative coherent manner. The time evolution of the color fields is explored in a numerical simulation of the collision of two Lorentz-boosted clouds of color charged particles on a long three-dimensional gauge lattice. We report results on soft gluon scattering and coherent gluon radiation obtained in SU(2) gauge symmetry.

Abstract:
Exciting a ferromagnetic sample with an ultrashort laser pulse leads to a quenching of the magne- tization on a subpicosecond timescale. On the basis of the equilibration of intensive thermodynamic variables we establish a powerful model to describe the demagnetization dynamics. We demonstrate that the magnetization dynamics is mainly driven by the equilibration of chemical potentials. The minimum of magnetization is revealed as a transient electronic equilibrium state. Our method iden- tifies the slowing down of ultrafast magnetization dynamics by a critical region within a magnetic phase diagram.

Abstract:
We present a new Monte-Carlo method for estimating the chemical potential of model polymer systems. The method is based upon the gradual insertion of a penetrable `ghost' polymer into the system and is effective for large chain lengths and at high densities. Insertion of the ghost chain is facilitated by use of an expanded ensemble in which weighted transitions are permitted between states characterising the strength of the excluded volume and thermal interactions experienced by the ghost chain. We discuss the implementation and optimisation of the method within the framework of the bond fluctuation model, and demonstrate its precision by a calculation of the finite-size corrections to the chemical potential.

Abstract:
A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the concentration distribution, the coexistence curve separating the A-rich and B-rich phases is identified as a function of temperature and chemical potential. To locate the critical point of the model, the cumulant intersection method is used. The accuracy of this approach for determining the critical parameters of fluids is assessed. Attention is then focused on the joint distribution function of the critical concentration and energy, which is analysed using a mixed-field finite-size-scaling theory that takes due account of the lack of symmetry between the coexisting phases. The essential Ising character of the binary polymer critical point is confirmed by mapping the critical scaling operator distributions onto independently known forms appropriate to the 3D Ising universality class. In the process, estimates are obtained for the field mixing parameters of the model which are compared both with those yielded by a previous method, and with the predictions of a mean field calculation.

Abstract:
Monte Carlo simulations within the grand canonical ensemble are used to obtain the joint distribution of density and energy fluctuations $p_L(\rho,u)$ for two model fluids: a decorated lattice gas and a polymer system. In the near critical region the form of $p_L(\rho,u)$ is analysed using a mixed field finite-size-scaling theory that takes account of liquid-vapour asymmetry. Field mixing transformations are performed that map $p_L(\rho,u)$ onto the joint distribution of critical scaling operators \ptMEstar\ appropriate to the Ising fixed point. Carrying out this procedure permits a very accurate determination of the critical point parameters. By forming various projections of \ptMEstar , the full universal finite-size spectrum of the critical density and energy distributions of fluids is also obtained. In the sub-critical coexistence region, an examination is made of the influence of field mixing on the asymmetry of the density distribution.

Abstract:
We study electronic transport in Anderson insulators with strong Coulomb interactions in dimensions d>=2. Close to the metal insulator transition where the single particle localization length is much larger than interparticle-distance, the interactions lead to a strongly correlated quantum glass phase. Even though single particle excitations are localized and the system is insulating, there are collective electronic modes which remain delocalized down to parametrically small energies. These collective excitations serve as a continuous bath which can provide the activation energy for variable range hopping transport. This circumvents the energy conservation problem arising when only discrete particle-hole excitations are present. In contrast to the weak and material-dependent phonon-assisted hopping mechanism, the activation by an electronic bath leads to a nearly universal prefactor e^2/h of the Efros-Shklovskii conductance, as is observed in many recent experiments.