Goswami, Debashish ; Sinha, Kalyan B.
(1999)
*Hilbert modules and stochastic dilation of a quantum dynamical semigroup on a von Neumann algebra*
Communications in Mathematical Physics, 205
(2).
pp. 377-403.
ISSN 0010-3616

Full text not available from this repository.

Official URL: http://www.springerlink.com/content/j7dh2gr4h26nvx...

Related URL: http://dx.doi.org/10.1007/s002200050682

## Abstract

A general theory for constructing a weak Markov dilation of a uniformly continuous quantum dynamical semigroup T_{ t} on a von Neumann algebra Α with respect to the Fock filtration is developed with the aid of a coordinate-free quantum stochastic calculus. Starting with the structure of the generator of T _{t} , existence of canonical structure maps (in the sense of Evans and Hudson) is deduced and a quantum stochastic dilation of T _{t} is obtained through solving a canonical flow equation for maps on the right Fock module Α ⊗ Γ(L^{2}(R_{+},k _{0})), where k_{0} is some Hilbert space arising from a representation of Α'. This gives rise to a ∗-homomorphism j_{t} of Α . Moreover, it is shown that every such flow is implemented by a partial isometry-valued process. This leads to a natural construction of a weak Markov process (in the sense of [B-P]) with respect to Fock filtration.

Item Type: | Article |
---|---|

Source: | Copyright of this article belongs to Springer. |

ID Code: | 61284 |

Deposited On: | 15 Sep 2011 03:50 |

Last Modified: | 15 Sep 2011 03:50 |

Repository Staff Only: item control page