Zloshchastiev K.G. (Durban University of Technology, South Africa)

Logarithmic quantum wave equation: Origins and applications

Abstract:
I will discuss the origins of a certain kind of a nonlinear partial differential equation – the so-called logarithmic quantum wave equation (LogSE). This equation possesses unique features that lead to fruitful applications in different branches of physics – from nuclear physics and condensed-matter theory to particle physics, theory of quantum gravity and physical vacuum. Then I will consider LogSE from the viewpoint of a theory of Bose–Einstein condensates and superfluids, broadly referred as quantum Bose liquids, and outline the mathematical problems which arise.