15 research outputs found
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
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
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