170 citations
- Polish Academy of SciencesPL13 papers
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13 papers · 1 filter
Geometry of quantum systems: density states and entanglement
Janusz Grabowski, Marek Kuś, Giuseppe Marmo
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Ri…
The stochastic acceleration problem in two dimensions
T. Komorowski, L. Ryzhik
We consider the motion of a particle in a two-dimensional spatially homogeneous mixing potential and show that its momentum converges to the Brownian motion on a circle. This compl…
Noncommutative Kahler-like structures in quantization
Anatol Odzijewicz
One introduces the notion of C*-algebra with polarization which could be considered as the quantum Kahler structure. The connection of these algebras with Kostant-Souriou geometric…
Hierarchy of Conservation Laws of Diffusion--Convection Equations
Roman O. Popovych, Nataliya M. Ivanova
We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or s…
Implementability of Liouville evolution, Koopman and Banach-Lamperti theorems in Classical and Quantum dynamics
I. Antoniou, W. A. Majewski, Z. Suchanecki
We extend the concept of implementability of semigroups of evolution operators associated with dynamical systems to quantum case. We show that such an extension can be properly for…
The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2
J. Golenia, Y. A. Prykarpatsky, A. M. Samoilenko +1
The structure properties of multidimensional Delsarte transmutation operators in parametirc functional spaces are studied by means of differential-geometric tools. It is shown that…