В рамках семинара кафедры высшей математики и математической физики пройдет 13 и 20 октября (среда) в 18-00 пройдет миникурс лекций.
Докладчик: Sergey Dobrokhotov (Ishlinsky Institute for Problems in Mechanics RAS &
Moscow Institute of Physics and Technology, Russia)
Тема: Feynmann–Maslov calculus of functions of noncommuting operators and
applications to adiabatic and semiclassical problems
Где: институт Эйлера, второй этаж
Meeting ID: 270 950 5573 Passcode: 779950
At the elementary level, we discuss the basic objects and formulas in the Feynman–Maslov operator theory about functions of non-commuting operators. The main objects here are differential and pseudo-differential operators with a small parameter (h-pseudo-differential operators). As a simple effective application, we consider the use of this theory in adiabatic problems (in particular, in dimension reduction problems). These include vector problems (for example, problems about wave functions in graphene), problems about wave propagation in waveguides (for example, waves in nanotubes), problems for equations with rapidly changing coefficients (averaging methods), etc. As a result of the application of the considered approach (formulated in the form of an algorithm), the initial problems are reduced to simpler problems described by «effective» Hamiltonians or modes, and containing, in particular, dispersion effects. Then one can use the semi-classical approximation to construct asymptotic solutions of the reduced equations.
The first part of the lectures is devoted to elementary definitions and important effective formulas of operator calculus and applications to vector problems (the simplest problems with an «operator-valued symbol»). The second part is devoted to the more complicated adiabatic problems mentioned above.
Планируется, что материал будет излагаться просто и для неспециалистов.