This paper provides a class of feedback controllers that guarantee global stability of quantum angular momentum systems. The systems are in general finite dimensions and the stability is around an assigned eigenstate of observables with a specific form. It is realized by employing the control law which was proposed by Mirrahimi & van Handel. The class of stabilizing controllers is parameterized by a switching parameter and we show that the parameter between 0 and 1/N assures the stability, where N is the dimension of the quantum systems.
In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the infinite-dimensional case. The properties of the conditional entropy such as monotonicity, concavity and subadditivity are also generalized to the infinite-dimensional case.
Modern control is implemented with digital microcontrollers, embedded within a dynamical plant that represents physical components. We present a new algorithm based on counter-example guided inductive synthesis that automates the design of digital controllers that are correct by construction. The synthesis result is sound with respect to the complete range of approximations, including time discretization, quantization effects, and finite-precision arithmetic and its rounding errors. We have implemented our new algorithm in a tool called DSSynth, and are able to automatically generate stable controllers for a set of intricate plant models taken from the literature within minutes.
The Levi-Malcev decomposition is applied to bosonic models of quantum mechanics based on unitary Lie algebras u(2), u(2)+u(2), u(3) and u(4) to clearly disentangle semisimple subalgebras. The theory of weighted Dynkin diagrams is then applied to identify conjugacy classes of relevant A_1 subalgebras allowing to introduce a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries. The tensor analysis of the whole algebra based on the new angular momentum operators reveals unexpected spinors to occur in purely bosonic models. The new chains of subalgebra can be invoked to set up ANMC bases for diagonalization.
Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also considered. Algebraic method is used in the calculations.
It is shown that when the gauge-invariant Bohr-Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum.