25 citations · 48 across the 10 of their papers we have counts for
10 papers
Periodicity, type factors and free Poisson laws in interacting Fock spaces
Vitonofrio Crismale, Yun Gang Lu, Éric Ricard
We show that the von Neumann algebra generated by position operators in a 2-periodic interacting Fock space is a type factor. On the probabilistic side, we prove that the sq…
Quantum Mechanics of Arc-Sine and Semi-Circle Distributions: A Unified Approach
Luigi Accardi, Tarek Hamdi, Yun Gang Lu
This paper continues the program of applying beyond physics the technique of \textbf{probabilistic quantization} and extending to the quantum mechanics associated with the arc--sin…
Hidden processes and hidden Markov processes: classical and quantum
Luigi Accardi, El Gheteb Soueidy, Yun Gang Lu +1
This paper consists of parts. The first part only considers classical processes and introduces two different extensions of the notion of hidden Markov process. In the second pa…
The -dimensional quadratic Heisenberg algebra as a "non--commutative"
Luigi Accardi, Andreas Boukas, Yun-Gang Lu
We prove that the commutation relations among the generators of the quadratic Heisenberg algebra of dimension , look like a kind of \textit{non-commutative extensio…
The quantum mechanics canonically associated to free probability Part I: Free momentum and associated kinetic energy
Luigi Accardi, Tarek Hamdi, Yun Gang Lu
After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonica…
Vacuum distribution, norm and spectral properties for sums of monotone position operators
Vitonofrio Crismale, Yun Gang Lu
We investigate the spectrum for partial sums of m position (or gaussian) operators on monotone Fock space based on . In the basic case of the first consecutive…