Abstract We study and solve some variations of the random K-satisfiability problem balanced K-SAT and biased random K-SAT on a regular tree, using techniques we have developed earlier [14]. In both these problems, as well as variations of these that we have looked at, we find that the SATUNSAT transition obtained on the Bethe lattice matches the exact threshold for the same model on a random gr...

The Bethe ansatz equations of the fundamental Sp(2N) integrable model are solved by a peculiar configuration of roots leading us to determine the nature of the excitations. They consist of N elementary generalized spinons and N − 1 composite excitations made by special convolutions between the spinons. This fact is essential to determine the low-energy behaviour which is argued to be described ...

Medium modification of scattering properties in interacting Bose systems are considered by solving the Bethe-Salpeter equation. An equation of state for the normal phase (generalized Beth-Uhlenbeck formula) is given using the in-medium phase shifts to include two-particle correlations. Conclusions are drawn for systems of bosonic atoms with repulsive interaction such as sodium Na and rubidium R...

We report the first observation of an azimuthal asymmetry in the hard electroproduction of real photons with respect to the charge of the incoming lepton beam. The asymmetry is attributed to the interference between the Bethe–Heitler process and the deeply–virtual Compton scattering process, which gives access to the latter at the amplitude level. This process appears to be the theoretically cl...

We investigate the dynamical charge response of the Anderson model viewed as a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a generalized Korringa-Shiba formula is derived at zero temperature, and the charge relaxation resistance is expressed solely in terms of static susceptibilities which are accessible by Bethe ansatz. We identify a giant charge relaxation resista...

There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes, which makes a direct solution in Minkowski space (without any 3-dimensional reductions) desirable. The Bethe-Salpeter equation (BSE) for bound states in scalar...

A strongly correlated electron system in the line of the recently proposed generalized Hubberd models as candidates for high Tc-superconductors is considered. The model along with a whole class of such systems are shown to be completely integrable with explicit quantum R-matrices and the Lax operators. Inspite of novelties in the Bethe ansatz solution, the results do not deviate much from that ...

In the framework of Husimi and Bethe lattices, we investigate a generalized polymer model that incorporates as special cases different models previously studied in the literature, namely, the standard interacting self-avoiding walk, the interacting self-avoiding trail, and the vertex-interacting self-avoiding walk. These models are characterized by different microscopic interactions, giving ris...