Related papers: Markov semigroups on unitary duals generated by qu…
We study a class of dynamical semigroups $(\mathbb{L}^n)_{n\in\mathbb{N}}$ that emerge, by a Feynman--Kac type formalism, from a random quantum dynamical system…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
Evans-Hudson flows are constructed for a class of quantum dynamical semigroups with unbounded generator on UHF algebras, which appeared in \cite{Ma}. It is shown that these flows are unital and covariant. Ergodicity of the flows for the…
We start by considering infinite dimensional Markovian dynamics in R^m generated by operators of hypocoercive type and for such models we obtain short and long time pointwise estimates for all the derivatives, of any order and in any…
The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…
We analyze a class of dynamics of open quantum systems which is governed by the dynamical map mutually commuting at different times. Such evolution may be effectively described via spectral analysis of the corresponding time dependent…
The exponential convergence to invariant subspaces of quantum Markov semigroups plays a crucial role in quantum information theory. One such example is in bosonic error correction schemes, where dissipation is used to drive states back to…
We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…
We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator…
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…
We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations…
It is known that extreme characters of several inductive limits of compact groups exhibit multiplicativity in a certain sense. In the paper, we formulate such multiplicativity for inductive limit quantum groups and provide explicit examples…
Given a dynamical twist for a finite dimensional Hopf algebra we construct two weak Hopf algebras, using methods of Xu and Etingof-Varchenko, and show that they are dual to each other. We generalize the theory of dynamical quantum groups to…
A conjecture for the universal constraints for relaxation rates of a quantum dynamical semigroup is proposed. It is shown that it holds for several interesting classes of semigroups, e.g. unital semigroups and semigroups derived in the weak…
These are notes for a mini-course of 3 lectures given at the St. Petersburg School in Probability and Statistical Physics (June 2012). My aim was to explain, on the example of a particular model, how ideas from the representation theory of…
The Markovian dynamics of a qubit is investigated in the scheme of random unitary dynamics, where Kraus operators are changed by an extra noise. The behavior of Markovianity is explored in the perturbed scenario. We provide a new algorithm…
Quantum dynamical maps provide suitable mathematical representation of quantum evolutions. It is the very notion of complete positivity which provides a proper mathematical representation of quantum evolution and gives rise to the powerful…
Quantum devices are subject to natural decay. We propose to study these decay processes as the Markovian evolution of quantum channels, which leads us to dynamical semigroups of superchannels. A superchannel is a linear map that maps…
We consider the problem of model reduction for Markovian quantum systems whose dynamics are described by a time-dependent Lindblad generator -- notably, as arising in the presence of external control. Our approach, which builds upon Krylov…