Stochastic dilations of quantum dynamical semigroups using one-dimensional quantum stochastic calculus

1990 ◽  
pp. 216-218 ◽  
Author(s):  
R L Hudson ◽  
P Shepperson
Keyword(s):  
Stochastic Calculus ◽  
Quantum Stochastic Calculus ◽  
One Dimensional ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups

QUANTUM STOCHASTIC CALCULUS ON BOOLEAN FOCK SPACE

2004 ◽  
Vol 07 (04) ◽  
pp. 631-650 ◽  
Author(s):  
ANIS BEN GHORBAL ◽  
MICHAEL SCHÜRMANN
Keyword(s):  
Fock Space ◽  
Field Operator ◽  
Stochastic Calculus ◽  
Product Formula ◽  
Stochastic Integration ◽  
Quantum Stochastic Calculus ◽  
Basic Field ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups

In this paper we establish a theory of stochastic integration with respect to the basic field operator processes in the Boolean case. This leads to a Boolean version of quantum Itô's product formula and has applications to the theory of dilations of quantum dynamical semigroups.

scholarly journals Entropic Fluctuations of Quantum Dynamical Semigroups

2013 ◽  
Vol 154 (1-2) ◽  
pp. 153-187 ◽  
Author(s):  
V. Jakšić ◽  
C.-A. Pillet ◽  
M. Westrich
Keyword(s):  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups

scholarly journals A representation free quantum stochastic calculus

1992 ◽  
Vol 104 (1) ◽  
pp. 149-197 ◽  
Author(s):  
L Accardi ◽  
F Fagnola ◽  
J Quaegebeur
Keyword(s):  
Stochastic Calculus ◽  
Quantum Stochastic Calculus

Infinite degrees of freedom Weyl representation: Characterization and application

2018 ◽  
Vol 21 (01) ◽  
pp. 1850002
Author(s):  
Abdessatar Barhoumi ◽  
Bilel Kacem Ben Ammou ◽  
Hafedh Rguigui
Keyword(s):  
Degrees Of Freedom ◽  
Explicit Construction ◽  
Stochastic Calculus ◽  
Generalized Functions ◽  
Academic Press ◽  
Quantum Stochastic Calculus ◽  
Fock Representation ◽  
Infinite Dimensional ◽  
Weyl Representation ◽  
Nuclear Spaces

By means of infinite-dimensional nuclear spaces, we generalize important results on the representation of the Weyl commutation relations. For this purpose, we construct a new nuclear Lie group generalizing the groups introduced by Parthasarathy [An Introduction to Quantum Stochastic Calculus (Birkhäuser, 1992)] and Gelfand–Vilenkin [Generalized Functions (Academic Press, 1964)] (see Ref. 15). Then we give an explicit construction of Weyl representations generated from a non-Fock representation. Moreover, we characterize all these Weyl representations in quantum white noise setting.

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