The existence problem for dynamics of dissipative systems in quantum probability
| dc.creator | Jorgensen, Palle E. T. | |
| dc.date | 2002-07-10 | |
| dc.date | 2004-03-25 | |
| dc.date.accessioned | 2026-07-07T04:49:37Z | |
| dc.date.available | 2026-07-07T04:49:37Z | |
| dc.description | Motivated by existence problems for dissipative systems arising naturally in lattice models from quantum statistical mechanics, we consider the following $C^{\ast}$-algebraic setting: A given hermitian dissipative mapping $δ$ is densely defined in a unital $C^{\ast}$-algebra $\mathfrak{A}$. The identity element in ${\frak A}$ is also in the domain of $δ$. Completely dissipative maps $δ$ are defined by the requirement that the induced maps, $(a_{ij})\to (δ(a_{ij}))$, are dissipative on the $n$ by $n$ complex matrices over ${\frak A}$ for all $n$. We establish the existence of different types of maximal extensions of completely dissipative maps. If the enveloping von Neumann algebra of ${\frak A}$ 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 $δ$ and $-δ$ is completely dissipative. | |
| dc.description | 24 pages, LaTeX/REVTeX v. 4.0, submitted to J. Math. Phys.; PACS 02., 02.10.Hh, 02.30.Tb, 03.65.-w, 05.30.-d | |
| dc.identifier | https://arxiv.org/abs/math/0207084 | |
| dc.identifier | http://arxiv.org/abs/math/0207084 | |
| dc.identifier | J. Math. Phys. 45 (2004), 3605-3619 | |
| dc.identifier | doi:10.1063/1.1777401 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64487 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Operator Algebras | |
| dc.title | The existence problem for dynamics of dissipative systems in quantum probability | |
| dc.type | text |