836 research outputs found
Bases for qudits from a nonstandard approach to SU(2)
Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for
quantum information and quantum computation are constructed from angular
momentum theory and su(2) Lie algebraic methods. We report on a formula for
deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime
integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated
application of the formula can be used for generating mutually unbiased bases
in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection
between mutually unbiased bases and the unitary group SU(d) is briefly
discussed in the case d = p^e.Comment: From a talk presented at the 13th International Conference on
Symmetry Methods in Physics (Dubna, Russia, 6-9 July 2009) organized in
memory of Prof. Yurii Fedorovich Smirnov by the Bogoliubov Laboratory of
Theoretical Physics of the JINR and the ICAS at Yerevan State University
In memoriam two distinguished participants of the Bregenz Symmetries in Science Symposia: Marcos Moshinsky and Yurii Fedorovich Smirnov
Some particular facets of the numerous works by Marcos Moshinsky and Yurii
Fedorovich Smirnov are presented in these notes. The accent is put on some of
the common interests of Yurii and Marcos in physics, theoretical chemistry, and
mathematical physics. These notes also contain some more personal memories of
Yurii Smirnov.Comment: Submitted for publication in Journal of Physics: Conference Serie
On the use of the group SO(4,2) in atomic and molecular physics
In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like
atom is derived through two different approaches. The first one is by an
established traditional ascent process starting from the symmetry group SO(3).
This approach is presented in a mathematically oriented original way with a
special emphasis on maximally superintegrable systems, N-dimensional extension
and little groups. The second approach is by a new symmetry descent process
starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional
harmonic oscillator. It is based on the little known concept of a Lie algebra
under constraints and corresponds in some sense to a symmetry breaking
mechanism. This paper ends with a brief discussion of the interest of SO(4,2)
for a new group-theoretical approach to the periodic table of chemical
elements. In this connection, a general ongoing programme based on the use of a
complete set of commuting operators is briefly described. It is believed that
the present paper could be useful not only to the atomic and molecular
community but also to people working in theoretical and mathematical physics.Comment: 31 page
Two-Photon Spectroscopy Between States of Opposite Parities
Magnetic- and electric-dipole two-photon absorption (MED-TPA), recently
introduced as a new spectroscopic technique for studying transitions between
states of opposite parities, is investigated from a theoretical point of view.
A new approximation, referred to as {\it weak quasi-closure approximation}, is
used together with symmetry adaptation techniques to calculate the transition
amplitude between states having well-defined symmetry properties. Selection
rules for MED-TPA are derived and compared to selection rules for
parity-forbidden electric-dipole two-photon absorption (ED-TPA).Comment: 7 pages, Revtex File, to be published in Physical Review
Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry
Models describing one- and two-photon transitions for ions in crystalline
environments are unified and extended to the case of parity-allowed and parity-
forbidden p-photon transitions. The number of independent parameters for
characterizing the polarization dependence is shown to depend on an ensemble of
properties and rules which combine symmetry considerations and physical models.Comment: 16 pages, Tex fil
A q-deformed Aufbau Prinzip
A building principle working for both atoms and monoatomic ions is proposed
in this Letter. This principle relies on the q-deformed chain SO(4) > G where G
= SO(3)_q
4D singular oscillator and generalized MIC-Kepler system
It is shown that the generalized MIC-Kepler system and four-dimensional
singular oscillator are dual to each other and the duality transformation is
the generalized version of the Kustaanheimo-Stiefel transformation.Comment: 6 page
On the Use of Quantum Algebras in Rotation-Vibration Spectroscopy
A two-parameter deformation of the Lie algebra u is used, in conjunction
with the rotor system and the oscillator system, to generate a model for
rotation-vibration spectroscopy of molecules and nuclei.Comment: 10 pages, Latex File, published in Modern Group Theoretical Methods
in Physics, J. Bertrand et al. (eds.), Kluwer Academic Publishers (1995),
27-3
Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems
We introduce a one-parameter generalized oscillator algebra A(k) (that covers
the case of the harmonic oscillator algebra) and discuss its finite- and
infinite-dimensional representations according to the sign of the parameter k.
We define an (Hamiltonian) operator associated with A(k) and examine the
degeneracies of its spectrum. For the finite (when k < 0) and the infinite
(when k > 0 or = 0) representations of A(k), we construct the associated phase
operators and build temporally stable phase states as eigenstates of the phase
operators. To overcome the difficulties related to the phase operator in the
infinite-dimensional case and to avoid the degeneracy problem for the
finite-dimensional case, we introduce a truncation procedure which generalizes
the one used by Pegg and Barnett for the harmonic oscillator. This yields a
truncated generalized oscillator algebra A(k,s), where s denotes the truncation
order. We construct two types of temporally stable states for A(k,s) (as
eigenstates of a phase operator and as eigenstates of a polynomial in the
generators of A(k,s)). Two applications are considered in this article. The
first concerns physical realizations of A(k) and A(k,s) in the context of
one-dimensional quantum systems with finite (Morse system) or infinite
(Poeschl-Teller system) discrete spectra. The second deals with mutually
unbiased bases used in quantum information.Comment: Accepted for publication in Journal of Physics A: Mathematical and
Theoretical as a pape
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