11 research outputs found
Towards nonlinear quantum Fokker-Planck equations
It is demonstrated how the equilibrium semiclassical approach of Coffey et
al. can be improved to describe more correctly the evolution. As a result a new
semiclassical Klein-Kramers equation for the Wigner function is derived, which
remains quantum for a free quantum Brownian particle as well. It is transformed
to a semiclassical Smoluchowski equation, which leads to our semiclassical
generalization of the classical Einstein law of Brownian motion derived before.
A possibility is discussed how to extend these semiclassical equations to
nonlinear quantum Fokker-Planck equations based on the Fisher information
Duality Principle and Braided Geometry
We give an overview of a new kind symmetry in physics which exists between
observables and states and which is made possible by the language of Hopf
algebras and quantum geometry. It has been proposed by the author as a feature
of Planck scale physics. More recent work includes corresponding results at the
semiclassical level of Poisson-Lie groups and at the level of braided groups
and braided geometry.Comment: 24 page
Strong Connections on Quantum Principal Bundles
A gauge invariant notion of a strong connection is presented and
characterized. It is then used to justify the way in which a global curvature
form is defined. Strong connections are interpreted as those that are induced
from the base space of a quantum bundle. Examples of both strong and non-strong
connections are provided. In particular, such connections are constructed on a
quantum deformation of the fibration . A certain class of strong
-connections on a trivial quantum principal bundle is shown to be
equivalent to the class of connections on a free module that are compatible
with the q-dependent hermitian metric. A particular form of the Yang-Mills
action on a trivial U\sb q(2)-bundle is investigated. It is proved to
coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel.
Furthermore, it is shown that the moduli space of critical points of this
action functional is independent of q.Comment: AMS-LaTeX, 40 pages, major revision including examples of connections
over a quantum real projective spac
Quasi-classical Lie algebras and their contractions
After classifying indecomposable quasi-classical Lie algebras in low
dimension, and showing the existence of non-reductive stable quasi-classical
Lie algebras, we focus on the problem of obtaining sufficient conditions for a
quasi-classical Lie algebras to be the contraction of another quasi-classical
algebra. It is illustrated how this allows to recover the Yang-Mills equations
of a contraction by a limiting process, and how the contractions of an algebra
may generate a parameterized families of Lagrangians for pairwise
non-isomorphic Lie algebras.Comment: 17 pages, 2 Table
Quantum charges and spacetime topology: The emergence of new superselection sectors
In which is developed a new form of superselection sectors of topological
origin. By that it is meant a new investigation that includes several
extensions of the traditional framework of Doplicher, Haag and Roberts in local
quantum theories. At first we generalize the notion of representations of nets
of C*-algebras, then we provide a brand new view on selection criteria by
adopting one with a strong topological flavour. We prove that it is coherent
with the older point of view, hence a clue to a genuine extension. In this
light, we extend Roberts' cohomological analysis to the case where 1--cocycles
bear non trivial unitary representations of the fundamental group of the
spacetime, equivalently of its Cauchy surface in case of global hyperbolicity.
A crucial tool is a notion of group von Neumann algebras generated by the
1-cocycles evaluated on loops over fixed regions. One proves that these group
von Neumann algebras are localized at the bounded region where loops start and
end and to be factorial of finite type I. All that amounts to a new invariant,
in a topological sense, which can be defined as the dimension of the factor. We
prove that any 1-cocycle can be factorized into a part that contains only the
charge content and another where only the topological information is stored.
This second part resembles much what in literature are known as geometric
phases. Indeed, by the very geometrical origin of the 1-cocycles that we
discuss in the paper, they are essential tools in the theory of net bundles,
and the topological part is related to their holonomy content. At the end we
prove the existence of net representations
On Aharonov-Casher bound states
In this work bound states for the Aharonov-Casher problem are considered.
According to Hagen's work on the exact equivalence between spin-1/2
Aharonov-Bohm and Aharonov-Casher effects, is known that the
term cannot be neglected in the
Hamiltonian if the spin of particle is considered. This term leads to the
existence of a singular potential at the origin. By modeling the problem by
boundary conditions at the origin which arises by the self-adjoint extension of
the Hamiltonian, we derive for the first time an expression for the bound state
energy of the Aharonov-Casher problem. As an application, we consider the
Aharonov-Casher plus a two-dimensional harmonic oscillator. We derive the
expression for the harmonic oscillator energies and compare it with the
expression obtained in the case without singularity. At the end, an approach
for determination of the self-adjoint extension parameter is given. In our
approach, the parameter is obtained essentially in terms of physics of the
problem.Comment: 11 pages, matches published versio
Novel Bound States Treatment of the Two Dimensional Schrodinger Equation with Pseudocentral Plus Multiparameter Noncentral Potential
By converting the rectangular basis potential V(x,y) into the form as
V(r)+V(r, phi) described by the pseudo central plus noncentral potential,
particular solutions of the two dimensional Schrodinger equation in plane-polar
coordinates have been carried out through the analytic approaching technique of
the Nikiforov and Uvarov (NUT). Both the exact bound state energy spectra and
the corresponding bound state wavefunctions of the complete system are
determined explicitly and in closed forms. Our presented results are identical
to those of the previous works and they may also be useful for investigation
and analysis of structural characteristics in a variety of quantum systemsComment: Published, 16 page