Generators of positive semigroups

Author(s):  
W. Arendt
Keyword(s):  

Positivity ◽  
2015 ◽  
Vol 20 (2) ◽  
pp. 467-481
Author(s):  
Christian Seifert ◽  
Marcus Waurick
Keyword(s):  


2019 ◽  
Vol 26 (04) ◽  
pp. 1950020
Author(s):  
Fabio Benatti

We review the Gorini, Kossakowski, Sudarshan derivation of the generator of a completely positive norm-continuous semigroup when the constituent maps act on density matrices according to the Hadamard product rule.



1992 ◽  
Vol 45 (1) ◽  
pp. 92-119 ◽  
Author(s):  
Marlene G. Ulmet


1987 ◽  
Vol 195 (4) ◽  
pp. 481-485 ◽  
Author(s):  
Tilman Schanbacher




1999 ◽  
Vol 10 (07) ◽  
pp. 791-823 ◽  
Author(s):  
WILLIAM ARVESON

It is known that every semigroup of normal completely positive maps P = {Pt:t≥ 0} of ℬ(H), satisfying Pt(1) = 1 for every t ≥ 0, has a minimal dilation to an E0 acting on ℬ(K) for some Hilbert space K⊇H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the index of P agrees with the index of its minimal dilation to an E0-semigroup. However, no examples were discussed, and no computations were made. In this paper we calculate the index of a unital completely positive semigroup whose generator is a bounded operator [Formula: see text] in terms of natural structures associated with the generator. This includes all unital CP semigroups acting on matrix algebras. We also show that the minimal dilation of the semigroup P={ exp tL:t≥ 0} to an E0-semigroup is is cocycle conjugate to a CAR/CCR flow.



2005 ◽  
Vol 15 (07) ◽  
pp. 1091-1117 ◽  
Author(s):  
ÀNGEL CALSINA ◽  
SÍLVIA CUADRADO

A selection mutation equations model for the distribution of individuals with respect to the age at maturity is considered. In this model we assume that a mutation, perhaps very small, occurs in every reproduction where the noncompactness of the domain of the structuring variable and the two-dimensionality of the environment are the main features. Existence of stationary solutions is proved using the theory of positive semigroups and the infinite-dimensional version in Banach lattices of the Perron Frobenius theorem. The behavior of these stationary solutions when the mutation is small is studied.



Author(s):  
Wolfgang Arendt ◽  
Annette Grabosch ◽  
Günther Greiner ◽  
Ulrich Moustakas ◽  
Rainer Nagel ◽  
...  


1988 ◽  
Vol 197 (2) ◽  
pp. 259-272 ◽  
Author(s):  
Reinhard B�rger


Positivity ◽  
2014 ◽  
Vol 19 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Sergiy Koshkin


Sign in / Sign up

Export Citation Format

Share Document