Quantum stochastic calculus associated with quadratic quantum noises

Ji, Un Cig and Sinha, Kalyan B (2016) Quantum stochastic calculus associated with quadratic quantum noises. In: JOURNAL OF MATHEMATICAL PHYSICS, 57 (2).

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Abstract

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie dagger-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Ito formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus. (C) 2016 AIP Publishing LLC.

Item Type:	Journal Article
Publication:	JOURNAL OF MATHEMATICAL PHYSICS
Publisher:	AMER INST PHYSICS
Additional Information:	The Copyright for this article belongs to American Institute of Physics Inc.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	06 Apr 2016 05:33
Last Modified:	04 Aug 2022 11:48
URI:	https://eprints.iisc.ac.in/id/eprint/53634

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