Condensed Matter & Surface Sciences





Russian Academy of Sciences



Quantum Generalization of the Thomas-Fermi Model



The interaction between particles in the mean-field approximation of the many-body theory is often taken into account with the use of the semiclassical description of the particle motion.  However, quantization of a part of the degrees of freedom becomes essential in certain cases.  In this work, two such cases where nonlinear wave equations appear have been considered:  electrons in a quantum well and excitons in a trap.  In the case of indirect excitons in an annular trap, the one-dimensional Gross–Pitaevskii equation permits an analytical solution and it turns out that there can be no bound state in a one-dimensional symmetric potential well.  This makes the problem qualitatively different from a similar one-body problem.  In the case of electrons in a quantum well, the nonlinear integro-differential equation does not have an exact solution and the allowed energy levels have been found by the direct variational method.





Thursday, November 16, 2017

4:10 p.m. -- Walter Lecture Hall 245