
Volume 47, Number 34, 2002


In memoriam acad. Arentin Corciovei (19301992) 

Page 
Title & Author(s) 
313 
Preface
Florin D. Buzatu (ed.)


315 
Arentin Frumuzache Corciovei. Highlights of Life and Activity
Florin D. Buzatu (ed.)


319 
Appendix A: First Annual Communication Session of the Theoretical Physics Department
Florin D. Buzatu (ed.)


321 
Appendix B: Aretin Corciovei – Publications
Florin D. Buzatu (ed.)


337 
Robust Automatic Adaptive Quadrature
Gh. Adam, Sanda Adam
The paper describes a code developed by the authors for automatic adaptive quadrature of integrals which may include oscillatory or hyperbolic weight functions, accelerated at multiple entries (EAQWOM). Ways of enhancing code qualities like reliability, robustness, efficiency, user friendliness, structuredness, portability, are discussed.


353 
The Coherent States: Old Geometrical Objects in New Quantum Clothes
S. Berceanu
A geometric characterization of transition amplitudes between coherent states, or equivalently, of the hermitian scalar product of holomorphic cross sections in the associated $D_{\tilde{M}}$module, in terms of the embedding of the coherent state manifold $\tilde{M}$ into a projective Hilbert space is proposed. Coherent state manifolds endowed with a homogeneous Kähler structure are considered. Using the coherent state approach, an effective method to find the cut loci on symmetric manifolds and generalized symmetric manifolds $\tilde{M}$ is proposed. The CWcomplex structure of coherent state manifolds of flag type is discussed. Recent results of Anandan and Aharonov are commented visàvis of last century constructions in projective geometry. Calculations with significance in the coherent state approach furnish explicit proofs of the results announced by Y. C. Wong on conjugate locus in complex Grassmann manifold.


359 
Spinodal Curve of the WheelerWidom Model with ThreeBody Interactions on the Bethe Lattice
Florin D. Buzatu, Daniela Buzatu, John G. Albright
We consider a lattice model for ternary solutions in which the lattice bonds are covered by molecules of type $AA$, $BB$, and $AB$, and with threebody interactions between the molecular ends of a common lattice site. Using its equivalence with the standard Ising model for magnets, we derive the spinodal curve of the threecomponent model on the honeycomb lattice in the Bethelattice approximation. The spinodal and the coexistence curves of the ternary solution are drawn at different values of the reduced threebody coupling constant and the reduced temperature, the only parameters of the model. The particular case of a binary solution is also illustrated.


371 
Analytic Continuation in Perturbative QCD
Irinel Caprini
We discuss some attempts to improve the standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentumplane analyticity properties of the Borelsummed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the renormalized coupling constant $a$. The new expansion functions have branch point and essential singularities at the origin of the complex $a$plane and divergent Taylor expansions in powers of $a$. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions.


383 
Supersymmetry and Integrability
A. S. Cârstea, A. Ramani, B. Grammaticos
We obtain the bilinear form of the supersymmetric sineGordon equation. Through the Hirota approach we construct multisoliton solutions for this equation. We find that, contrary to the purely bosonic case, the solitons are "dressed" through their mutual interaction and we compute explicitly this dressing. Using the ARS algorithm we verify that the supersymmetric sineGordon possesses the Painlevé property. It seems that the dressed fermionic part is common to supersymmetric integrable equations but no rigouros proof exists so far. This is the reason why we’ve chosen the supersymmetric sineGordon case as a paradigm.


391 
Proton Emission from Highly Deformed Nuclei
D. S. Delion, R. J. Liotta
We give the description of proton emission involving transitions between excited states of the eveneven cores. The contribution of the rotational energy is properly taken into account. It is shown that the proton decay width is practically independent on the matching radius for a large interval of values. By using the universal parametrisation of the WoodsSaxon potential the agreement with the experimental data for the transitions between ground states is satisfactory. We show that the halflife to first excited state in $^{131}$Eu is much more sensitive to the mean field parameters than the transition between ground states. The influence of the difference between the mother and daughter deformations is studied.


401 
PoissonLie Structures and Quantisation with Constraints
Petre Diţă
We develop here a simple quantisation formalism that makes use of Lie algebra properties of the Poisson bracket. When the brackets $\{H, \varphi_i\}$ and $\{\varphi_i, \varphi_j\}$, where $H$ is the Hamiltonian and $\varphi_i$ are primary and secondary constraints, can be expressed as functions of $H$ and $\varphi_i$ themselves, the Poisson bracket defines a PoissonLie structure. When this algebra has a finite dimension a system of first order partial differential equations is established whose solutions are the observables of the theory. The method is illustrated with a few examples.


415 
The Ionization of Atomic Hydrogen in a Multicolour Laser Field
Magda Fifirig, Viorica Florescu
We summarize some of our recent studies on the ionization of hydrogen in the presence of an electromagnetic field taken as a superposition of a fundamental frequency $\omega$ with several of its odd order harmonics. The figures refer to a two colour case ($\omega =$ 10.53 eV, $3\omega$) and to a threecolour case ($\omega=$ 1.55 eV, $5\omega$, $9\omega$) and present new data which illustrate the role of the phase differences between the field components on the ionization rates. The influence of the polarization properties is also represented. The calculations, done in perturbation theory, are based on analytic equations for the two or threephoton ground state to continuum transition matrix elements.


425 
Parent DiNuclear Quasimolecular States as Exotic Resonant States
Cornelia Grama, N. Grama, I. Zamfirescu
One shows that the parent dinuclear quasimolecular state is an exotic resonant state that corresponds to a Smatrix pole in the neighbourhood of an attractor in the $k$plane. The properties of the parent quasimolecular states are the same as the general properties of the exotic resonant states.


437 
Plasma Oscillations in a Layered Electron Gas(LEG) Model Revisited
D. Grecu
The first studies on the plasma oscillations in a layered electron gas, some of them done in our laboratory, are briefly reviewed. Through molecular beam epitaxy techniques high quality superlattices have been produced in which the carriers motion is highly 2D. Plasmon excitations in such systems were identified in inelastic light and Raman scattering experiments. Few further developments of the many body theory in LEG systems are presented. Few remarks on plasmons in layered superconductors and in quasionedimensional conductors are given.


447 
Quantum Dynamics of Deformed Open Systems
A. Isar
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model, using perturbation theory. The coefficients of the master equation depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.


0 
Relativistic Covariance and the Bound State Wave Function
Liliana Micu
We show that a bound system in momentum space can be treated like a gas of free elementary constituents and a collective excitation of a background field which represents the countless quantum fluctuations generating the binding potential. The distribution function of the internal momenta in the bound system at rest is given by the projection of a solution of a relativistic bound state equation on the free wave functions of the elementary constituents. The 4momentum carried by the collective excitation is the difference between the bound state 4momenturn and the sum of the free 4momenta. This definition ensures the explicit fulfilment of Lorentz covariance, massshell constraints and single particle normalizability of the bound state function. The discussion is made for a two particle bound state and can be easily generalized to the case of three or more particles.


469 
Spinning Optical Solitons in Two and Three Dimensions
D. Mihalache
A brief overview of the recent theoretical studies of multidimensional spinning (vortex) optical solitons in both conservative and dissipative media is given.


477 
Second Order Approximation to Stochastic Differential Equations for Backward Processes and Gaussian Distributions
V. P. Păun, E. Petrescu
An iterative procedure to solve the restoration problem is proposed. The solution reduces to a simple filtration problem. This technique can be used to derive stochastic differential equations which are satisfied by trajectories of Markov diffusion processes in reverse time observation. It was found that drift coefficients are expressed only in terms of its unconditional distribution density, while the diffusion coefficients do not change. The particular case of nonlinear stochastic systems with potential function is also considered. Using our technique, the problem reduces to a simple differential equation.


487 
PAN Base Carbon Fiber WAXD Lines Calculation Depending on Structure and Texture Parameters
I. Pencea, G. Tiriba, E. G. Depner, F. Pencea
The Wide Angle Xray Diffraction (WAXD) patterns obtained on graphitelike materials can be accurately interpreted only by proper structural model. This paper presents an analytical model of polyacrylonitrile (PAN) and mesophase based carbon fibers (CF) structure. The electron density distribution is given by the multiple convolution of the functions associated to the density of the structural elements: carbon atom, twodimensional unit cell, lattice layer, stack of lattices and on the second kind Hosemann set packing distortion function [1]. The wideangle Xray diffraction (WAXD) profile has been deduced theoretically as a function of both: structural parameters and preferential orientation of the crystallites in the CF. The results of this study form the basis for a further computational simulation of the WAXD profiles produced by CF and for the evaluation of structural parameters using a trialanderror program of Rietveld type.


497 
Neutrino Masses from DoubleBeta Decay Calculations
S. Stoica, V. P. Păun
The neutrinoless doublebeta decay (0νββ) matrix elements (ME) for the nuclei with A = 76, 82, 96, 100, 116, 128, 130 and 136 are computed with four different quasi random phase approximation (QRPA)based methods, i.e. the protonneutron QRPA (pnQRPA), the renormalized protonneutron QRPA (pnRQRPA), the full RQRPA and the secondQRPA (SQRPA) and using two singleparticle (s.p.) basis. From a comparative analysis of the results we show that the uncertainties in the calculation of the ME can be limitted to 50% from their values. Further, taking the most recent available limits for the neutrinoless halflives, we deduce new upper limits for the neutrino mass parameter. Also, there are estimated for each nucleus scales for the 0νββ decay halflives that the experiments should reach for measuring neutrino masses around 0.39 eV. This value was derived from the first experimental evidence of this mode reported very recently by the HeidelbergMoscow experiment [35]. These estimations give us an indication on the possibility that other experiments could confirm or not this important result.


509 
Solitonic Model for Energy Transport in Quasi1D Biological Systems
Anca Vişinescu, Dan Grecu, Adrian S. Cârstea
The classical equation of motion of a Davydov model in a coherent state approximation is analyzed using the multiple scales method. In the first order, the dominant amplitude has to be a solution of the well known nonlinear Schrödinger equation (NLS). In the next order the second amplitude satisfies an inhomogeneous linearized NLS equation, the inhomogeneous term depending only on the dominant amplitude. In order to eliminate possible secular behaviour the dominant amplitude has to satisfy also the next equation in the NLS hierarchy (a complex modified KdV equation). When the second order derivative of the dispersion relation vanishes (ZDP case) the scaling of the slow space variable has to be changed, and the equation verified by the dominant amplitude is found.


519 
Spinning Particles and Dirac Operators in TaubNUT Background
Mihai Vişinescu
In the beginning we review the geodesic motion of pseudoclassical spinning particles in curved spaces. Investigating the generalized Killing equations for spinning spaces, we express the constants of motion in terms of KillingYano tensors. Passing from the spinning spaces to the Dirac equation in curved backgrounds we point out the role of the KillingYano tensors in the construction of the Diractype operators. The general results are applied to the case of the fourdimensional Euclidean TaubNUT space. Using the covariantly constant KillingYano tensors of this space we construct three new Diractype operators which are equivalent with the standard Dirac operator.


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