6 papers
The Strong Law of Large Numbers for random semigroups with unbounded generators on uniformly smooth Banach spaces
S. V. Dzhenzher, V. Zh. Sakbaev
We consider random linear unbounded operators on a Banach space . For example, such random operators may be random quantum channels. The Law of Large Numbers is known…
Banach and counting measures, and dynamics of singular quantum states generated by averaging of operator random walks
E. A. Dzhenzher, S. V. Dzhenzher, V. Zh. Sakbaev
In this paper the random channels and their compositions in the space of quantum states are studied. For compositions of i.i.d. random unitary channels, the limit behaviour of prob…
Limit theorems for the evolution of quantum pure states
S. V. Dzhenzher, V. Zh. Sakbaev
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
The law of large numbers for discrete generalized quantum channels
S. V. Dzhenzher, V. Zh. Sakbaev
We consider random linear operators acting in a -th Schatten class in a separable Hilbert space f…
Quantum law of large numbers for Banach spaces
S. Dzhenzher, V. Sakbaev
We consider random operators for some . The law of large numbers is known in the case in the form of usual law of…
On the extension of singular linear infinite-dimensional Hamiltonian flows
Vladimir Glazatov, Vsevolod Sakbaev
We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of comp…