We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No–go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non– controllability for the linear Schrödinger equation and distributed additive control, a...

We attack the specific time-dependent Hamiltonian problem H = − 2 ( to t a ∂xx+ 1 2ω 2 ( t to )b x2. This corresponds to a time-dependent mass (TM) Schrödinger equation. We give the specific transformations to a different time-dependent quadratic Schrödinger equations (TQ) and to a different time-dependent oscillator (TO) equation. For each Schrödinger system, we give the Lie algebra of space-t...

Cubic Schrödinger equations with small initial data (or small nonlinearity) and their spectral semi-discretizations in space are analyzed. It is shown that along both, the solution of the nonlinear Schrödinger equation as well as the solution of the semi-discretized equation, the actions of the linear Schrödinger equation are approximately conserved over long times. This also allows to show app...

---------------------------------------------------------------------***--------------------------------------------------------------------Abstract In the field of information processing like data mining, information retrieval, natural language processing and machine learning, Quantum Computing play vital role for extracting the implicit, potentially useful and previously unknown information f...

We obtain certain time decay and regularity estimates for 3D Schrödinger equation with a potential in the Kato class by using Besov spaces associated with Schrödinger operators.

An important and well established area of quantum optics is the theory of Markovian stochastic Schrödinger equations (or by another name quantum trajectory theory). Recently stochastic Schrödinger equations have been developed for non-Markovian systems. In this paper we extend the current known stochastic Schrödinger equations for non-Markovian systems to include the position unraveling. We als...