Dynamics of Characteristic and One-Point Correlation Functions of Multi-Mode Bosonic Systems: Exactly Solvable Model

In this communication we study dynamics of the open quantum bosonic system governed by the generalized Lindblad equation with both dynamical and environment induced intermode couplings taken into account. By using the method of characteristics we deduce the analytical expression for the normally ordered characteristic function. Analytical results for one-point correlation functions describing temporal evolution of the covariance matrix are obtained.

EXACTLY SOLVABLE MODEL OF TOPOLOGICAL TRANSITIONS IN METALS

In this paper, we consider ETP using a precisely solvable model of an electron in a crystal. The main characteristics of the transition are given by analytical functions that contain only the parameters of the potential. The results of calculations are compared with experimental data on the Lifshitz phase transition (genus transition) in normal metals. The practical significance of the work is to increase the accuracy of quantitative predictions of the physical properties of alloys of various transition metals.

Study of the Influence of Different Methods of Taking into Account the Coulomb Interaction on Determining Asymptotic Normalization Coefficients within the Framework of Exactly Solvable Model

It is shown that the Schrödinger equation for the sum of the potential of a square well and the Coulomb potential of a uniformly charged sphere admits an analytical solution for arbitrary values of the orbital angular momentum. An explicit form of this solution has been found. Using the obtained solution, the influence of the Coulomb interaction for both point and distributed nuclear charges on the values of asymptotic normalization coefficients for various nuclear systems is investigated. It is shown that taking into account the non-point distribution of the nuclear charge has little effect on the calculated values of the asymptotic normalization coefficients, provided that the binding energy of the system is assumed to be fixed.