Representations and Properties of Generalized ArA_r Statistics

A generalization of $A_r$ statistics is proposed and developed. The generalized $A_r$ quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock-Hilbert representations and Bargmann-Fock realizations are derived.Comment: 12 pages, to appear in IJMPA (2006

A Generalized Jaynes-Cummings Model: Nonlinear dynamical superalgebra u(1/1)u(1/1) and Supercoherent states

The generalization of the Jaynes-Cummings (GJC) Model is proposed. In this model, the electromagnetic radiation is described by a Hamiltonian generalizing the harmonic oscillator to take into account some nonlinear effects which can occurs in the experimental situations. The dynamical superalgebra and supercoherent states of the related model are explicitly constructed. A relevant quantities (total number of particles, energy and atomic inversion) are computed.Comment: 12 page

On the solution of non linear systems.

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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

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

Origin and stability of the dipolar response in a family of tetragonal tungsten bronze relaxors

A new family of relaxor dielectrics with the tetragonal tungsten bronze structure (nominal composition Ba6M3+Nb9O30, M3+ = Ga, Sc or In) were studied using dielectric spectroscopy to probe the dynamic dipole response and correlate this with the crystal structure as determined from powder neutron diffraction. Independent analyses of real and imaginary parts of the complex dielectric function were used to determine characteristic temperature parameters, TVF, and TUDR, respectively. In each composition both these temperatures correlated with the temperature of maximum crystallographic strain, Tc/a determined from diffraction data. The overall behaviour is consistent with dipole freezing and the data indicate that the dipole stability increases with increasing M3+ cation size as a result of increased tetragonality of the unit cell. Crystallographic data suggests that these materials are uniaxial relaxors with the dipole moment predominantly restricted to the B1 cation site in the structure. Possible origins of the relaxor behaviour are discussed.Comment: Main article 32 pages, 8 figures; Supplementary data 24 pages, 4 figure

Star-Like Micelles with Star-Like Interactions: A quantitative Evaluation of Structure Factor and Phase Diagram

PEP-PEO block copolymer micelles offer the possibility to investigate phase behaviour and interactions of star polymers (ultra-soft colloids). A star-like architecture is achieved by an extremely asymmetric block ratio (1:20). Micellar functionality f can be smoothly varied by changing solvent composition (interfacial tension). Structure factors obtained by SANS can be quantitatively described in terms of an effective potential developed for star polymers. The experimental phase diagram reproduces to a high level of accuracy the predicted liquid/solid transition. Whereas for intermediate f a bcc phase is observed, for high f the formation of a fcc phase is preempted by glass formation.Comment: 5 pages, 4 figures, PRL in pres

Electronic, mechanical, thermodynamic and optical properties of CdS under pressure

We report high pressure study of CdS using the full-potential linear augmented plane wave (FP-LAPW) method based on density functional theory approach. In this approach, generalized gradient approximation (GGA) and Engel- Vosko generalized gradient approximation (EV-GGA) have been used for the exchange correlation potential in the calculations. The equilibrium lattice constant, electronic band structure, elastic constants, Debye temperature and melting temperature of binary solid CdS have been calculated under ambient and high pressure. Furthermore, the linear optical properties such as dielectric function, absorption, optical conductivity reflectivity, refractive index and energy loss are computed and analyzed in detail within the energy range up to 14 eV. The obtained results are in good agreement with earlier reported experimental and other theoretical results

The Moyal Bracket in the Coherent States framework

The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states and the second kind are constructed following the Perelomov-Klauder approach. The particular case of the harmonic oscillator is also discussed.Comment: 13 page

Statistical properties of Klauder-Perelomov coherent states for the Morse potential

We present in this paper a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach . We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated