Maxwell-Chern-Simons Models: Their Symmetries, Exact Solutions and Non-relativistic Limits

Two Maxwell-Chern-Simons (MCS) models in the (1 + 3)-dimensional space-space are discussed and families of their exact solutions are found. In contrast to the Carroll-Field-Jackiw (CFE) model [2] these systems are relativistically invariant and include the CFJ model as a particular sector.Using the InNonNu-Wigner contraction a Galilei-invariant non-relativistic limit of the systems is found, which makes possible to find a Galilean formulation of the CFJ model

Symmetries and solutions of field equations of axion electrodynamics

The group classification of models of axion electrodynamics with arbitrary self interaction of axionic field is carried out. It is shown that extensions of the basic Poincar\'e invariance of these models appear only for constant and exponential interactions. The related conservation laws are discussed. Using the In\"on\"u-Wigner contraction the non-relativistic limit of equations of axion electrodynamics is found. An extended class of exact solutions for the electromagnetic and axion fields is obtained. Among them there are solutions including up to six arbitrary functions. In particular, solutions which describe propagation with velocities faster than the velocity of light are found. These solutions are smooth and bounded functions which correspond to positive definite and bounded energy density.Comment: New section 6 ia added where the superluminal propagation velocities are discusse

Analytic Controllability of Time-Dependent Quantum Control Systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page