37,727 research outputs found
Some Physical Appearances of Vector Coherent States and CS Related to Degenerate Hamiltonians
In the spirit of some earlier work on the construction of vector coherent
states over matrix domains, we compute here such states associated to some
physical Hamiltonians. In particular, we construct vector coherent states of
the Gazeau-Klauder type. As a related problem, we also suggest a way to handle
degeneracies in the Hamiltonian for building coherent states. Specific physical
Hamiltonians studied include a single photon mode interacting with a pair of
fermions, a Hamiltonian involving a single boson and a single fermion, a
charged particle in a three dimensional harmonic force field and the case of a
two-dimensional electron placed in a constant magnetic field, orthogonal to the
plane which contains the electron. In this last example, an interesting modular
structure emerges for two underlying von Neumann algebras, related to opposite
directions of the magnetic field. This leads to the existence of coherent
states built out of KMS states for the system.Comment: 38 page
Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics
In this paper we study families of complex Hermite polynomials and construct
deformed versions of them, using a transformation. This
construction leads to the emergence of biorthogonal families of deformed
complex Hermite polynomials, which we then study in the context of a
two-dimensional model of noncommutative quantum mechanics.Comment: 17 page
Polarized Deeply Inelastic Scattering (DIS) Structure Functions for Nucleons and Nuclei
We extract parton distribution functions (PDFs) and structure functions from
recent experimental data of polarized lepton-DIS on nucleons at next-to-leading
order (NLO) Quantum Chromodynamics. We apply the Jacobi polynomial method to
the DGLAP evolution as this is numerically efficient. Having determined the
polarized proton and neutron spin structure, we extend this analysis to
describe 3He and 3H polarized structure functions, as well as various sum
rules. We compare our results with other analyses from the literature.Comment: LaTeX, 12 pages, 11 figures, 6 tables. Update to match published
versio
Forward-Backward Asymmetry in
The Forward-backward asymmetry in the angular distribution of is
studied in the process . The
possibility of observing CP violation through the asymmetries in these two
processes is examined.Comment: 5 pages, latex formatte
Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons
In a series of recent papers one of us has analyzed in some details a class
of elementary excitations called {\em pseudo-bosons}. They arise from a special
deformation of the canonical commutation relation [a,a^\dagger]=\1, which is
replaced by [a,b]=\1, with not necessarily equal to . Here,
after a two-dimensional extension of the general framework, we apply the theory
to a generalized version of the two-dimensional Hamiltonian describing Landau
levels. Moreover, for this system, we discuss coherent states and we deduce a
resolution of the identity. We also consider a different class of examples
arising from a classical system, i.e. a damped harmonic oscillator.Comment: in press in Journal of Mathematical Physic
Coherent States on Hilbert Modules
We generalize the concept of coherent states, traditionally defined as
special families of vectors on Hilbert spaces, to Hilbert modules. We show that
Hilbert modules over -algebras are the natural settings for a
generalization of coherent states defined on Hilbert spaces. We consider those
Hilbert -modules which have a natural left action from another
-algebra say, . The coherent states are well defined in this
case and they behave well with respect to the left action by .
Certain classical objects like the Cuntz algebra are related to specific
examples of coherent states. Finally we show that coherent states on modules
give rise to a completely positive kernel between two -algebras, in
complete analogy to the Hilbert space situation. Related to this there is a
dilation result for positive operator valued measures, in the sense of Naimark.
A number of examples are worked out to illustrate the theory
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