Functional density matrix formulation of quantum statistics.

We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. For quantum statistical (thermal) field theory, the stochastic variable of the statistical theory is a boundary field configuration. We explore the properties of an effective theory for such boundary configurations and apply it to the computation of the partition function of an interacting one-dimensional quantum-mechanical system at finite temperature. Plots of free energy and specific heat show excellent agreement with more involved semiclassical results. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident end points and includes nonvanishing boundary terms. An appropriately modified expansion into modified Matsubara modes is presented.

Improved semiclassical density matrix: taming caustics.

We present a simple method to deal with caustics in the semiclassical approximation to the thermal density matrix of a particle moving on the line. For simplicity, only its diagonal elements are considered. The only ingredient we require is the knowledge of the extrema of the Euclidean action. The procedure makes use of complex trajectories, and is applied to the quartic double-well potential.

Nonequilibrium field theory description of the Bose-Einstein condensate.

We study the detailed out-of-equilibrium time evolution of a homogeneous Bose-Einstein condensate (BEC). We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective microscopic model for the description of the BEC. The interaction between fluctuations proves to be crucial in the mechanism of instability generation. We show the existence of two regimes in k space, with a crossover for k(2)/2m approximately 2 lambda|phi(0)|(2), where lambda is the coupling constant and |phi(0)|(2) is the condensate density. We deduce and solve a set of coupled equations that completely determines the nonequilibrium dynamics of the condensate density.

Synthesis of bioprocesses using physical properties data.

The aim of this article is to illustrate and evaluate a synthesis procedure which has been extended to tackle bioprocesses. Physical property information is used to screen candidate units thereby reducing the size of the synthesis problem. In this way, only units which exploit large property differences between components in a stream are selected. This is important for bioprocesses because of the large number of components and wide range of unit operations which are available. The screening technique and bioprocess-unit-design methodologies have been incorporated within an implicit enumeration algorithm which was developed for chemical process synthesis and is implemented in Java programming language. An important advantage is the ability of the bioprocess synthesis software to generate a ranked list of flowsheets which may subsequently be analyzed in more detail. Two case studies are used to evaluate the bioprocess-synthesis technique. The first system involves a product which is secreted from the host organism. The second has significantly different characteristics in that the product is intracellular and forms inclusion bodies. The latter case study, in particular, is a large synthesis problem with 12 unit operations and 20 contaminant compounds. The results show that the synthesis methodology identifies a set of economically optimal flowsheets in a reasonable computational time which demonstrates its ability to deal with large synthesis problems. Using the synthesis methodology we can generate bioprocesses which are optimal in a system-wide, rather than unit-by-unit, sense.