Research in statistical mechanics
A central problem in physics, chemistry, and biology on the molecular level is to understand the properties of matter on basis of the laws of nature. Thus there is an interest in these properties due to scientific curiosity and desire to uncover the implications and consequences that follow from the laws of nature. This interest is also connected to possible applications of new results when satisfactory results and understanding have been obtained. To obtain such results statistical mechanics is used to determine thermodynamic quantities and correlations between particles in thermal equilibrium.
My research in statistical mechanics in collaboration with others has been focused upon interacting many body systems which means that the pair interaction between particles or molecules is of crucial importance for the resulting properties of systems considered. Thus for fluids at arbitrary density the interactions form a connected network that makes evaluations and development of methods challenging. 
My previous works in statistical mechanics through several decades have given significant contributions to obtain new results for polar and polarizable fluids, ionic fluids, solution of the Ornstein-Zernike (OZ) integral equation, quantized polarizable fluids, protein folding and ion transport through cell membranes, the Casimir force, and the correlation function and equation of state based upon the self-consistent Ornstein-Zernike approximation (SCOZA). To a large extent these results were obtained by use of new approaches combined with increasing amount of previous experience.
Recently a work on the SCOZA (self-consistent Ornstein-Zernike approximation) was finished in cooperation with Albert Reiner (Austria) to obtain new very accurate results for the location of the critical point of the model fluid with pair interaction of Yukawa form (Fig. 1).
Figure 1: Critical temperatures Tc for hard core Yukawa potentials with varying inverse range z as computed by conventional SCOZA (dashed line) and by various simulations (with estimated error bars) relative to the prediction Tc* of our modified version of SCOZA.
At present I am continuing my work with Iver Brevik (NTNU) and others on problems and controversies connected to the temperature dependence of the Casimir force. Further together with Enrique Lomba (Spain) I am working on an exactly solvable lattice or spin model that shows a disorder-order-disorder (fluid-solid-fluid) phase transition. The purpose of constructing and investigating such a model is to try to understand the phase diagrams obtained by MC (Monte-Carlo) simulations of molecules with soft cores, and a striking similarity is obtained (Fig. 2).
| | Figure 2: Exactly solvable one-dimensional model with F-S-F (fluid-solid-fluid) phase transition. The temperature T* is given as function of the two pairs of coexisting densities n (fluid-solid and solid-fluid). Note that that the point on top where the four curves meet is not a critical point since they there merge into one fluid phase and one solid phase, and these two phases are distinct with finite ordering of the latter. |
Future research is on one side expected to be along similar lines where previous results and knowledge in the field will form an important and crucial basis to be able to obtain new results. Further methods and results obtained in classical statistical mechanics will also be crucial for further future study of quantum mechanical systems. The important observation in this connection is that the statistical mechanical problem of quantum mechanical systems is known to be equivalent to a classical polymer problem in four dimensions. This equivalence has already been utilized in connection with polarizable fluids and the Casimir problem. Thus future research in this direction can be to apply the methods of classical statistical mechanics to the path integral formalism of interacting quantum mechanical systems in new ways. Further research in this direction can also be to include the Casimir energy in the evaluation of quantum mechanical many body systems.
Publications
Self-consistent Ornstein-Zernike approximation for the Yukawa fluid with improved directcorrelation function [pdf],
A. Reiner and J. S. Høye, J. Chem. Phys. 128, 114507 (2008)
Contact: Johan Skule Høye
