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Information × Registration Number 0221U102574, 0116U005035 , R & D reports Title Matrix and differential operators and their applications in quantum information science, integrated systems and statistical physics. popup.stage_title Head Shcherbina Mariya V, д.ф.-м.н. Registration Date 05-02-2021 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2  2. The following results were obtained. The properties of the entangled entropy of a system of free fermions are investigated and Szego-type theorems for the one-dimensional Anderson model are proved. The global limiting distributions of eigenvalues of the ensemble of covariance matrices with components of the tensor product and the ensemble of autocovariance matrices between the past and the future of a multidimensional time series are studied. The transfer operator method for studying the local regime of an ensemble of 1d band matrices is developed and by this method the existence of a phase limiting in the local behavior of the second correlation function of the characteristic polynomials of such matrices is proved. The asymptotic behavior of the second correlation function of the characteristic polynomials of highly sparse hermitian random matrices inside the spectrum was studied using the method of supersymmetric integration. The asymptotic behavior of all correlation functions of characteristic polynomials of complex random matrices with independent elements is established. The nonlinear method of the fastest descent was generalized to vector Riemann-Hilbert problems, and by using this method the asymptotics of the solutions of the Cauchy problems for the Korteweg-de Vries and Toda chains with the initial data of the step type on constant backgrounds were studied. An effective representation of the asymptotics of the solutions over a long time of the boundary value problem on the half-axis for the Degasperis-Procesi equation is obtained. Theoretical researches of influence of a pulsed field on a fermionic two-component multiparticle system are carried out. The equations of the dependence of the coefficient of thermal expansion of methane and deuteromethane on temperature and pressure for low temperatures are obtained. Product Description popup.authors popup.nrat_date 2021-02-05 Close