Türkiye Cumhuriyeti ve halifelik

Taha Toros Arşivi, Dosya Adı: Son Halife Abdülmecit Efendi. Not: Gazetenin "Olaylar ve Görüşler" köşesinde yayımlanmıştır

Coherent States for Generalized Laguerre Functions

We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the Gazeau-Klauder approach, where resolution of unity and overlapping properties are examined. Coherent states are found to be similar to those found for a particle trapped in a P\"oschl-Teller potential of the trigonometric type. Some comparisons with Barut-Girardello and Klauder-Perelomov methods are noticed.Comment: 12 pages, clarifications and references added, misprints correcte

Flowering Buds of Globular Proteins: Transpiring Simplicity of Protein Organization

Structural and functional complexity of proteins is dramatically reduced to a simple linear picture when the laws of polymer physics are considered. A basic unit of the protein structure is a nearly standard closed loop of 25–35 amino acid residues, and every globular protein is built of consecutively connected closed loops. The physical necessity of the closed loops had been apparently imposed on the early stages of protein evolution. Indeed, the most frequent prototype sequence motifs in prokaryotic proteins have the same sequence size, and their high match representatives are found as closed loops in crystallized proteins. Thus, the linear organization of the closed loop elements is a quintessence of protein evolution, structure and folding

Barut-Girardello coherent states for u(p,q) and sp(N,R) and their macroscopic superpositions

The Barut-Girardello coherent states (BG CS) representation is extended to the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson realizations. The sp(N,R) BG CS take the form of multimode ordinary Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode Hilbert space and the relation between the canonical CS and the u(p,q) BG-type CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and their discrete superpositions contain many states studied in quantum optics (even and odd N-mode CS, pair CS) and provide an approach to quadrature squeezing, alternative to that of intelligent states. New subsets of weakly and strongly nonclassical states are pointed out and their statistical properties (first- and second-order squeezing, photon number distributions) are discussed. For specific values of the angle parameters and small amplitude of the canonical CS components these states approaches multimode Fock states with one, two or three bosons/photons. It is shown that eigenstates of a squared non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of the quadratures of A.Comment: 29 pages, LaTex, 5 figures. Improvements in text, corrections in some formulas. To appear in J. Phys. A, v. 3

Symplectic Partially Hyperbolic Automorphisms of 6-Torus

We study topological properties of automorphisms of a 6-dimensional torus generated by integer matrices symplectic with respect to either the standard symplectic structure in six-dimensional linear space or a nonstandard symplectic structure given by an integer skew-symmetric non-degenerate matrix. Such a symplectic matrix generates a partially hyperbolic automorphism of the torus, if it has eigenvalues both outside and on the unit circle. We study the case (2,2,2), numbers are dimensions of stable, center and unstable subspaces of the matrix. We study transitive and decomposable cases possible here and present a classification in both cases.Comment: 15 pages, 0 figures. arXiv admin note: text overlap with arXiv:2001.1072