In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. We then discuss the reducibility and irreducibility of open quantum random walks via the… (More)

We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in L2(Rd) ∩ L∞(Rd). We prove the linear independence and totality, in the quadratic… (More)

We prove that the quadratic second quantization of an operator p on L2(Rd)∩L∞(Rd) is an orthogonal projection on the quadratic Fock space if and only if p = MχI , where MχI is a multiplication… (More)

The Hamiltonian approach of the Pauli-Fierz model is studied by Derezinski and Jaksic (cf. [7]). In this paper, we give the Markovian description of this model. Using the weak coupling limit, we… (More)

We consider a repeated quantum interaction model describing a small system HS in interaction with each one of the identical copies of the chain ⊗ N C n+1, modeling a heat bath, one after another… (More)

We study a XY model which consists of a spin chain coupled to heat baths. We give a repeated quantum interaction Hamiltonian describing this model. We compute the explicit form of the associated… (More)

We construct the quadratic analogue of the boson Fock functor. While in the first order (linear) case all contractions on the 1–particle space can be second quantized, the semigroup of contractions… (More)

Among the discrete evolution equations describing a quantum system HS undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by… (More)

We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the latter, we… (More)