Semi-groups and the Trotter product formula

1999 ◽  
pp. 41-44
Author(s):  
Zbigniew Haba
Keyword(s):  
Product Formula ◽  
Trotter Product Formula

Accretive perturbations and error estimates for the Trotter product formula

2001 ◽  
Vol 39 (4) ◽  
pp. 396-412 ◽  
Author(s):  
Vincent Cachia ◽  
Hagen Neidhardt ◽  
Valentin A. Zagrebnov
Keyword(s):  
Error Estimates ◽  
Product Formula ◽  
Trotter Product Formula

scholarly journals Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions

2012 ◽  
Vol 370 (1979) ◽  
pp. 5437-5451 ◽  
Author(s):  
D. Gwion Evans ◽  
John E. Gough ◽  
Matthew R. James
Keyword(s):  
Heisenberg Group ◽  
Commutation Relation ◽  
Stochastic Models ◽  
General Rule ◽  
Product Formula ◽  
Input Output ◽  
Trotter Product Formula ◽  
Commutation Relations ◽  
Series Product ◽  
Weyl Commutation Relation

We show that the series product, which serves as an algebraic rule for connecting state-based input–output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie–Trotter product formula.

Sign in / Sign up

Export Citation Format

Share Document