On the quadratic Fock functor

We prove that the quadratic second quantization of an operator p on $L^2(\mathbb{R}^d)\cap L^\infty (\mathbb{R}^d)$ is an orthogonal projection on the quadratic Fock space if and only if p =MI, where MI is a multiplication operator by a characteristic function I.Comment: 1

The quadratic Fock functor

We construct the quadratic analogue of the boson Fock functor. While in the first order case all contractions on the 1--particle space can be second quantized, the semigroup of contractions that admit a quadratic second quantization is much smaller due to the nonlinearity. Within this semigroup we characterize the unitary and the isometric elements.Comment: 2

Markovian properties of the Pauli-Fierz model

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 derive the quantum Markovian semigroup of the Pauli-Fierz system from its Hamiltonian description. Also, we give the explicit form of the associated Lindblad generator. As a consequence, we study the properties of the associated quantum master equation: Quantum detailed balance condition and return to equilibrium. Finally, we give the associated quantum Langevin equation which can be obtained by a repeated quantum interaction Hamiltonian

Extending the Set of Quadratic Exponential Vectors

We extend the square of white noise algebra over the step functions on R to the test function space of bounded square-integrable functions on R^d, and we show that in the Fock representation the exponential vectors exist for all test functions bounded by 1/2