The actual problems of Fermi systems theory are considered. A simple explanation is given to the linear dependence of electrical resistance on temperature and the linear dependence of the magnetoresistance on the magnetic field in high-temperature superconducting cuprates, which has been mysterious for many years. It is shown that this dependence stems from the treatment of a gas of translationally invariant polarons as a system with heavy fermions for wave vectors close to nesting. The destruction of such polarons at finite temperature and an external magnetic field leads to a linear dependence of the magnetoresistance on the magnetic field and temperature. It is shown that the relationship between the slopes of the magnetoresistance curves at zero magnetic field and at zero temperature is determined by the universal ratio of Boltzmann constant and Bohr magneton. A relation between the existence of translationally invariant polarons and the 'Planck' time of their relaxation is discussed.

bipolarons, strange metals, nesting, Kohler rule

Mathematical modelling in actual problems of science and technics

Lakhno Victor Dmitrievich,  ,  orcid.org/0000-0001-9224-769X,  KIAM RAS