Generalized Complex Spectral Decomposition for a Quantum Decay Process

By extending the notion of mixed states to functionals acting on the space of observables with diagonal singularity we obtain a well-defined complex spectral decomposition of the time evolution for a quantum decaying system. In this formalism, generalized Gamow states are obtained with well-defined physical properties.     

THE CRYSTAL AND MOLECULAR STRUCTURE OF THE POTENTIAL ANTIBACTERIAL AGENT 2-PYRIDYL-PHENYL SULPHONE

Abstract

Crystals of 2-pyridyl-phenyl sulphone are monoclinic, space group P2₁/c, with eight molecules in the unit cell of dimensions a = 11.781, b = 5.903, c = 29.748 Å and B = 94.13°. The dihedral angles between the best planes of the two aromatic rings are significantly different in two crystallographically independent molecules (88.4° and 71.9° for molecule A and molecule B, respectively), as well as those between the CSC plane and the pyridine ring (59.4° and 67.4°) and between the CSC plane and the phenyl ring (51.7° and 81.8°). The average bond distances of interest include C?S 1.77(1) and S?O 1.44(1) Å; among the bond angles there are CSO = 108.1(7), CSC = 105.0(6) and OSO = 118.7(6)°. The packing of the molecule in the crystal is determined by the van der Waals interactions and by two intermolecular H?O contacts of 2.43 and 2.49 Å. The observed conformation in the solid state agrees well with results of previous investigations, in the solution state, by means of dipole moment method and theoretical M.O. calculations, for the analogous di-2-pyridyl sulphone.     

Two-particle resonant states in a many-body mean field

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow single-particle resonances. However, they can be significantly affected by the continuum part of the spectrum.     

Smooth non-special surfaces of ℙ4

We consider smooth non-degenerate surfaces in ℙ⁴, and prove that there is a finite number of such surfaces which are:

Subdynamics Theory in the Functional Approach to Quantum Mechanics

The formalism of subdynamics is extended to thefunctional approach to quantum systems and is used forthe Friedrichs model in which diagonal singularities instates and observables are included. In this approach we compute the generalizedeigenvectors and eigenvalues of the Liouville-vonNeumann operator, using an iterative scheme. As complexgeneralized eigenvalues are obtained, the decay rates ofunstable modes are included in the spectraldecomposition.     

Two-Particle Resonances in the Complex Energy Plane

An evaluation of two-particle resonances in the complex energy plane is presented. The representation used in the method consists of bound and antibound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Within this representation the structure of halo nuclei is studied.     

A rigidity theorem for homogeneous rational manifolds of rank 1

Sunto Si prova un teorema di rigidità per deformazioni algebriche di varietà omogenee razionali eon secondo numero di Betti uguale a 1 (ad esempio: spazi proiettivi, grassmanniane, quadriche di dimensione 3, grassmanniane dei sottospazi lineari diP ⁿ⁺¹ contenuti in una quadrica Q_n Pⁿ⁺¹).

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This paper was written while the authors were members of the G.N.S.A.G.A. of C.N.R., with a financial support by the M.P.I.     

Clusters as Many-Body Resonances

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two-particle states are calculated by using a single-particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long-lived resonances are mostly determined by either bound states or by narrow Gamow resonances. However, they are significantly affected by wide resonances and the continuum background itself.