Journal article
The existence problem for dynamics of dissipative systems in quantum probability
Journal of mathematical physics, Vol.45(9), pp.3605-3619
2004
DOI: 10.1063/1.1777401
Abstract
Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following C*-algebraic setting: A given Hermitian dissipative mapping δ is densely defined in a unital C*-algebra A. The identity element in A is also in the domain of δ. Completely dissipative maps δ are defined by the requirement that the induced maps, (aij)→(δ(aij)), are dissipative on the n-by-n complex matrices over A for all n. We establish the existence of different types of maximal extensions of completely dissipative maps. If the enveloping von Neumann algebra of A is injective, we show the existence of an extension of δ which is the infinitesimal generator of a quantum dynamical semigroup of completely positive maps in the von Neumann algebra. If δ is a given well-behaved *-derivation, then we show that each of the maps ±δ is completely dissipative.
Details
- Title: Subtitle
- The existence problem for dynamics of dissipative systems in quantum probability
- Creators
- Palle E.T Jorgensen
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical physics, Vol.45(9), pp.3605-3619
- DOI
- 10.1063/1.1777401
- ISSN
- 0022-2488
- eISSN
- 1089-7658
- Language
- English
- Date published
- 2004
- Academic Unit
- Mathematics
- Record Identifier
- 9983985836102771
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