On the interacting Free Fock space and the deformed Wigner law

Abstract

The Fock space is a basic structure for the quantum field theory and quantum stochastic calculus. In all the cases, a Fock space can be described as a direct sum of a sequence of some Hilbert spaces, i.e. a Fock space has the form of , where, is the complex field and is a given Hilbert space.

Monotone Independence, Comb Graphs and Bose–einstein Condensation

“…20 for a more general form of monotone independent random variables. A significant consequence of monotone independence is the monotone central limit theorem, which was proved by Lu 22 and Muraki 24 with different motivations.…”

Quantum Walk in Terms of Quantum Bernoulli Noise and Quantum Central Limit Theorem for Quantum Bernoulli Noise

“…Voiculescu has developed a noncommutative probability theory (now known as the free probability theory), which offers the free central limit theorem associated with the free independence [17]. There are many other types of quantum central limit theorems in the literature (see, e.g., [18][19][20][21][22] and references therein).…”

Symmetries and ergodic properties in quantum probability

“…We review in a self-containing form de Finetti-type results and ergodic properties for stationary and symmetric states in some concrete C * -algebras, plenty of them coming from physical investigations. The cases of q-deformed, −1 < q < 1 [11,15], Bose [16,26], Fermi [14,15], Boolean [9,15,16] and Monotone [16,24] processes are described in detail.…”