[Settfa] Tuesday 02/05, Damian Kolaczek, Pawel Pietrzycki

[kubis at math.cas.cz]

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 Tuesday 2nd May, 10:00am 
 
  Place: IM in konírna 

 
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 Speaker:Damian Kolaczek, Hugo Kollataj University of Agriculture, Krakow, Poland
 Title: Local and global error bound of Strang exponential operator splitting for Moyal equation

 Abstract  

 One of the possible ways of formulating nonrelativistic quantum mechanics in the phase space is via the Wigner function. Its time evolution is given by the Moyal equation and here we consider a simple case of isolated system so the solution can be expressed using strongly continuous one-parameter unitary group. The self-adjoint generator of this group is a sum of two noncommuting operators and one of them is unbounded. As each of these operators is unitarily equivalent to a multiplication operator via appropiate Fourier transform thus action of each of them separately can be efficiently calculated and exponential operator splitting formulas are suitable for numerical computations. We start by developing the local error bound formula for Strang splitting in the abstract framework then we apply that to the case of the Moyal equation and to finish off we derive the formula for global error bound. We apply derived formulas to the simple case of quantum system with potential ener
 gy in the form of Gaussian barrier and Gaussian initial Wigner function.

 Speaker:Pawel Pietrzycki
 Jagiellonian University, Krakow, Poland
 Title: Arveson's hyperrigidity

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .