7,043 research outputs found
The Schwinger SU(3) Construction - II: Relations between Heisenberg-Weyl and SU(3) Coherent States
The Schwinger oscillator operator representation of SU(3), studied in a
previous paper from the representation theory point of view, is analysed to
discuss the intimate relationships between standard oscillator coherent state
systems and systems of SU(3) coherent states. Both SU(3) standard coherent
states, based on choice of highest weight vector as fiducial vector, and
certain other specific systems of generalised coherent states, are found to be
relevant. A complete analysis is presented, covering all the oscillator
coherent states without exception, and amounting to SU(3) harmonic analysis of
these states.Comment: Latex, 51 page
Constraints on mass matrices due to measured property of the mixing matrix
It is shown that two specific properties of the unitary matrix can be
expressed directly in terms of the matrix elements and eigenvalues of the
hermitian matrix which is diagonalized by . These are the asymmetry
, of with respect to the main diagonal
and the Jarlskog invariant .
These expressions for and provide constraints on possible
mass matrices from the available data on .Comment: 5 pages, Late
Bounds on quark mass matrices elements due to measured properties of the mixing matrix and present values of the quark masses
We obtain constraints on possible structures of mass matrices in the quark
sector by using as experimental restrictions the determined values of the quark
masses at the energy scale, the magnitudes of the quark mixing matrix
elements , , , and , and the
Jarlskog invariant . Different cases of specific mass matrices are
examined in detail. The quality of the fits for the Fritzsch and Stech type
mass matrices is about the same with and
, respectively. The fit for a simple
generalization (one extra parameter) of the Fritzsch type matrices, in the
physical basis, is much better with . For
comparison we also include the results using the quark masses at the 2 GeV
energy scale. The fits obtained at this energy scale are similar to that at
energy scale, implying that our results are unaffected by the evolution
of the quark masses from 2 to 91 GeV.Comment: Evolution effects include
Predictions for the unitarity triangle angles in a new parametrization
A new approach to the parametrization of the CKM matrix, , is considered
in which is written as a linear combination of the unit matrix and a
non-diagonal matrix which causes intergenerational-mixing, that is
. Such a depends on 3 real parameters
including the parameter . It is interesting that a value of
is required to fit the available data on the CKM-matrix
including CP-violation. Predictions of this fit for the angles ,
and for the unitarity triangle corresponding to
, are given. For
=, we obtain , and
. These values are just about in agreement, within errors,
with the present data. It is very interesting that the unitarity triangle is
expected to be approximately a right-angled, isosceles triangle. Our prediction
is in excellent agreement with the value reported by the Belle collaboration at the Lepton-Photon 2001 meeting.Comment: 11 pages, latex, no figure
Development of aircraft industry in India
It is axiomatic that India requires to self sufficient in the design, development and production of aircraft both for civil and military use, and not, as she is at present, remains entirely dependent on foreign sources. This requirement is keenly felt in the field of defence, since it is appreciated .that the growth of the Armed Forces of a country, in fact their very existence in peace and war, is in modern times directly related to the industrial potential of that country to produce weapons of war. If the two are not properly balanced the Armed Forces would be quite ineffective in fulfilling their role of defending their country in time of emergency
Mapping of non-central potentials under point canonical transformations
Motivated by the observation that all known exactly solvable shape invariant
central potentials are inter-related via point canonical transformations, we
develop an algebraic framework to show that a similar mapping procedure is also
exist between a class of non-central potentials. As an illustrative example, we
discuss the inter-relation between the generalized Coulomb and oscillator
systems.Comment: 11 pages article in LaTEX (uses standard article.sty). Please check
http://www1.gantep.edu.tr/~gonul for other studies of Nuclear Physics Group
at University of Gaziante
Spectra of phase point operators in odd prime dimensions and the extended Clifford group
We analyse the role of the Extended Clifford group in classifying the spectra
of phase point operators within the framework laid out by Gibbons et al for
setting up Wigner distributions on discrete phase spaces based on finite
fields. To do so we regard the set of all the discrete phase spaces as a
symplectic vector space over the finite field. Auxiliary results include a
derivation of the conjugacy classes of .Comment: Latex, 19page
Berry's phase for coherent states of Landau levels
The Berry phases for coherent states and squeezed coherent states of Landau
levels are calculated. Coherent states of Landau levels are interpreted as a
result of a magnetic flux moved adiabatically from infinity to a finite place
on the plane. The Abelian Berry phase for coherent states of Landau levels is
an analog of the Aharonov- Bohm effect. Moreover, the non-Abelian Berry phase
is calculated for the adiabatic evolution of the magnetic field B.Comment: 4 pages, 1 figur
Hudson's Theorem for finite-dimensional quantum systems
We show that, on a Hilbert space of odd dimension, the only pure states to
possess a non-negative Wigner function are stabilizer states. The Clifford
group is identified as the set of unitary operations which preserve positivity.
The result can be seen as a discrete version of Hudson's Theorem. Hudson
established that for continuous variable systems, the Wigner function of a pure
state has no negative values if and only if the state is Gaussian. Turning to
mixed states, it might be surmised that only convex combinations of stabilizer
states give rise to non-negative Wigner distributions. We refute this
conjecture by means of a counter-example. Further, we give an axiomatic
characterization which completely fixes the definition of the Wigner function
and compare two approaches to stabilizer states for Hilbert spaces of
prime-power dimensions. In the course of the discussion, we derive explicit
formulas for the number of stabilizer codes defined on such systems.Comment: 17 pages, 3 figures; References updated. Title changed to match
published version. See also quant-ph/070200
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