Narrow Results

When applied to a finite Fermi system having a degenerate single-particle spectrum, the Landau-Migdal Fermi-liquid approach leaves room for the possibility that different single-particle energy levels merge with one another. It will be argued that the opportunity for this behavior exists over a wide range of strongly interacting quantum many-body systems. An inherent feature of the mergence phenomenon is the presence of nonintegral quasiparticle occupation numbers, which implies a radical modification of the standard quasiparticle picture. Consequences of this alteration are surveyed for nuclear, atomic, and solid-state systems.

The analytical expressions have been obtained to describe the dependence of spinodal curve at which isotropic state of polydisperse melt of semiflexible diblock copolymer becomes unstable with respect to formation of nematic state on the polydispersity indices of the blocks, parameters of anisotropic interactions, and flexibility of blocks. The flexibility of blocks is taken into account within discrete worm-like chain model, lengths of blocks are assumed to be distributed by the Schulz–Zimm distribution. It is shown that increase of degree of polydispersity of blocks yields the increase of nematic spinodal temperature.

The low energy manifold for fermions at finite density is the Fermi surface. I describe renormalization group (RG) in which modes encountered on approaching the Fermi surface are systematically integrated out. The fixed point is described by strictly marginal coupling functions identified as the Landau parameters and marginally relevant coupling functions describing the BCS instability in various angular momentum channels.

When applied to a finite Fermi system having a degenerate single-particle spectrum, the Landau-Migdal Fermi-liquid approach leaves room for the possibility that different single-particle energy levels merge with one another. It will be argued that the opportunity for this behavior exists over a wide range of strongly interacting quantum many-body systems. An inherent feature of the mergence phenomenon is the presence of nonintegral quasiparticle occupation numbers, which implies a radical modification of the standard quasiparticle picture. Consequences of this alteration are surveyed for nuclear, atomic, and solid-state systems.