97 Covariant Quantum Dynamical Semigroups : Unbounded Generators
نویسنده
چکیده
A survey of probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. As an example, a complete characterizations of the Galilean covariant irreversible quantum Markovian evolutions is given in terms of the corresponding quantum master and Langevin equations. Important topics for future investigation are outlined.
منابع مشابه
Covariant Quantum Dynamical Semigroups: Unbounded Generators
A survey of probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. As an example, a complete characterizations of the Galilean covariant irreversible quantum Markovian evolutions is given in terms of the corresponding quantum master and Langevin equati...
متن کاملQuantum dynamical semigroups generated by noncommutative unbounded elliptic operators
We study quantum dynamical semigroups generated by noncommutative unbounded elliptic operators which can be written as Lindblad type unbounded generators. Under appropriate conditions, we first construct the minimal quantum dynamical semigroups for the generators and then use Chebotarev and Fagnola’s sufficient conditions for conservativity to show that the semigroups are conservative.
متن کاملDilation of a class of quantum dynamical semigroups with unbounded generator on UHF algebras
Evans-Hudson flows are constructed for a class of quantum dynamical semigroups with unbounded generator on UHF algebras, which appeared in [6]. It is shown that these flows are unital and covariant. Ergodicity of the flows for the semigroups associated with partial states is also discussed.
متن کاملA Remark on the structure of symmetric quantum dynamical semigroups on von Neumann algebras
We study the structure of the generator of a symmetric, conservative quantum dynamical semigroup with norm-bounded generator on a von Neumann algebra equipped with a faithful semifinite trace. For von Neumann algebras with abelian commutant (i.e. type I von Neumann algebras), we give a necessary and sufficient algebraic condition for the generator of such a semigroup to be written as a sum of s...
متن کاملQuantum Stochastic Semigroups
A rigged Hilbert space characterisation of the unbounded generators of quantum completely positive (CP) stochastic semigroups is given. The general form and the dilation of the stochastic completely dissipative (CD) equation over the algebra L (H) is described, as well as the unitary quantum stochastic dilation of the subfiltering and contractive flows with unbounded generators is constructed.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996