The partition function by means of the static path approximation (SPA) plus the random-phase approximation (RPA) treatment can be written as a contour integral form without solving the RPA equations for a separable interaction. This method is an efficient way to evaluate numerically the partition function for realistic calculations. As an illustration, we adopt the pairing model at finite tempe...

A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we show that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce an extensive partition of the system into two subsystems both of which extend throughout the bulk in all dir...

We study the supersymmetric partition function of N = 4 super Yang-Mills with gauge group SU(N) on K3 in the large N , fixed g limit and show that it undergoes a first order phase transition at the S-duality invariant value of the gauge coupling g. Turning on the θ-angle we find lines of phase transitions on the τ plane. The resulting phase diagram and the large N free energy are exactly SL(2, ...

Ejaculated, bovine sperm have been subjected to multiple partition in aqueous two-phase systems. This partition, carried out in a countercurrent fashion, reveals heterogeneity of the sperm population with respect to surface properties. The sperm, when partitioned in phase systems that detect non-change associated surface properties (change-insensitive) are largely distributed as two distinct po...

Countercurrent chromatography (CCC) is a liquid chromatography technique in which the stationary phase is also a liquid. The solute separation is based on partitioning between the two immiscible liquid phases: the mobile phase and the support-free liquid stationary phase. Octanol-water partition coefficients (Po/w) of 17 βblockers and 17 sulphonamides were determined by CCC. Some of the Po/w co...

1 BACKGROUND Countercurrent chromatography (CCC) is liquid-liquid partition chromatography without using a solid support matrix. This technique requires further improvement of partition efficiency and shortening theseparation time. 2 METHODS The locular multilayer coils modified with and without mixer glass beads were developed for the separation of proteins and 4-methylumbelliferyl (MU) suga...