https://libjncir.jncasr.ac.in/xmlui/handle/10572/1497 2026-04-04T05:31:09Z 2026-04-04T05:31:09Z Das, Biswarup Goswami, Debashish Sinha, Kalyan B. https://libjncir.jncasr.ac.in/xmlui/handle/10572/2583 2017-02-21T10:24:30Z 2014-01-01T00:00:00Z

A Homomorphism Theorem and a Trotter Product Formula for Quantum Stochastic Flows with Unbounded Coefficients Das, Biswarup; Goswami, Debashish; Sinha, Kalyan B. We give a new method for proving the homomorphic property of a quantum stochastic flow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic flows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of Goswami et al. (Inst H Poincare Probab Stat 41:505-522, 2005). Restricted Access

2014-01-01T00:00:00Z Belton, Alexander C. R. Sinha, Kalyan B. https://libjncir.jncasr.ac.in/xmlui/handle/10572/2584 2017-02-21T10:24:39Z 2014-01-01T00:00:00Z

STOPPING THE CCR FLOW AND ITS ISOMETRIC COCYCLES Belton, Alexander C. R.; Sinha, Kalyan B. It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e. left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation. Restricted Access

2014-01-01T00:00:00Z Ji, Un Cig Sinha, Kalyan B. https://libjncir.jncasr.ac.in/xmlui/handle/10572/2280 2017-02-21T10:21:23Z 2016-01-01T00:00:00Z

Quantum stochastic calculus associated with quadratic quantum noises Ji, Un Cig; Sinha, Kalyan B. 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. Restricted Access

2016-01-01T00:00:00Z