Realisation of a class of Markov processes through unitary evolutions in Fock space
Reduced and extended weak coupling limit
The main aim of our lectures is to give a pedagogical introduction to various mathematical formalisms used to describe open quantum systems: completely positive semigroups, dilations of semigroups, quantum Langevin dynamics and the so-called Pauli-Fierz Hamiltonians. We explain two kinds of the weak coupling limit. Both of them show that Hamiltonian dynamics of a small quantum system interacting with a large resevoir can be approximated by simpler dynamics. The better known reduced weak coupling...
Remarks on q-CCR relations for |q| > 1
In this paper we give a construction of operators satisfying q-CCR relations for q > 1: and also q-CAR relations for q < -1: , where N is the number operator on a suitable Fock space acting as Nx₁ ⊗ ⋯ ⊗ xₙ = nx₁ ⊗ ⋯ ⊗xₙ. Some applications to combinatorial problems are also given.
Remarks on the symmetric space ... and its quatization.
Remarks on t-transformations of measures and convolutions
Remarques sur le caractère algébrique du procédé pseudo-différentiel et de certaines de ses extensions (I)
Representations of the Kauffman bracket skein algebra of the punctured torus
We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary.
Resonant perturbation theory of decoherence and relaxation of quantum bits.
Restrictions of CP-semigroups to maximal commutative subalgebras
We give a necessary and sufficient criterion for a normal CP-map on a von Neumann algebra to admit a restriction to a maximal commutative subalgebra. We apply this result to give a far reaching generalization of Rebolledo's sufficient criterion for the Lindblad generator of a Markov semigroup on ℬ(G).
Riccati and Ermakov equations in time-dependent and time-independent quantum systems.