Dynamics of a system of hard spheres with inelastic collisions is investigated. This system is a model for granular flow. The map induced by a shift along the trajectory does not preserve the volume of the phase space, and ...

The model Fröhlich–Peierls Hamiltonian for electrons interacting with phonons only in some infinite discrete modes is considered. It is shown that, in the equilibrium case, this model is thermodynamically equivalent to the ...

We consider the model and approximating Hamiltonians directly in the case of infinite volume. We show that each of these Hamiltonians has two branches of the spectrum and two systems of eigenvectors, which represent ...

The problem of the existence of solutions of the hierarchy for the sequence of correlation functions is investigated in the direct sum of spaces of summable functions. We prove the existence and uniqueness of solutions, ...

We investigate the spectrum of a model Hamiltonian with BCS and mean-field interaction in a finite domain under periodic boundary conditions. The model Hamiltonian is considered on the states of pairs and waves of density ...

The BCS Hamiltonian in a finite cube with periodic boundary condition is considered. The special subspace of pairs of particles with opposite momenta and spin is introduced. It is proved that, in this subspace, the spectrum ...

We consider the stochastic dynamics that is the Boltzmann-Grad limit of the Hamiltonian dynamics of a system of hard spheres. A new concept of averages over states of stochastic systems is introduced, in which the contribution ...