Mikael Ciftan

On the structure of the canonical tensor operators in the unitary groups. I. An extension of the pattern calculus rules and the canonical splitting in U(3)

The structure of the totally symmetric unit tensor operators (and their conjugates) in U(n) is examined from the viewpoint of the pattern calculus and the factorization lemma. The geometrical properties of the arrow patterns of the fundamental projective (tensor) operators are demonstrated to be the origin of the existence of simple structural expressions for a class of reduced matrix elements of the totally symmetric unit projective operators. An extension of the pattern calculus rules is given whereby these matrix elements can be written out directly. This class of reduced matrix elements is sufficient to permit the construction of the general totally symmetric unit tensor operator. The canonical splitting of the multiplicity in U(3) is similarly shown to be implied uniquely by the geometrical properties of the arrow patterns of the fundamental projective operators and their conjugates. This fact is used to construct explicitly the class of U(3) unit tensor operators having maximal null space. Explicit ...

Combinatorial Structure of State Vectors in Un. I. Hook Patterns for Maximal and Semimaximal States in Un

It is shown that, in the boson‐operator realization, the state vectors of the unitary groups Un—in the canonical chain Un⊃Un−1⊃⋯⊃U1—can be obtained ab initio by a combinatorial probabilistic method. From the Weyl branching law, a general state vector in Un is uniquely specified in the canonical chain; the algebraic determination of such a general state vector is in principle known (Cartan‐Main theorem) from the state vector of highest weight; the explicit procedure is a generalization of the SU(2) lowering‐operator technique. The present combinatorial method gives the normalization of these state vectors in terms of a new generalization of the combinatorial entity, the Nakayama hook, which generalization arises ab initio from a probabilistic argument in a natural way in the lowering procedure. It is the advantage of our general hook concept that it recasts those known algebraic results into a most economical algorithm which clarifies the structure of the boson‐operator realization of the Un representations.

On the Combinatorial Structure of State Vectors in U(n). II. The Generalization of Hypergeometric Functions on U(n) States

The derivation of the explicit algebraic expressions of the SU(n) state vectors in the boson‐operator realization is shown to lead to a generalization of hypergeometric functions. The SU(3) state vectors are rederived by the combinatorial method‐propounded in Paper I [J. Math. Phys. 10, 221 (1969)] of this series of papers‐and are shown to be represented by a hypergeometric distribution function and an associated generalization of the Young tableaux calculus. The SU(4) state vectors are also derived to demonstrate the main features of the general U(n) state vectors. The SU(4) state vectors are expressed in terms of the constituents of Radon transforms.

Rebinder effect and wear

Abstract The relation between the Rebinder effect and wear through the general form of the chemomechanical interaction is discussed from a fundamental viewpoint. An attempt has been made to merge the theories of the Russian school and that of Westwood et al . into one unified theory which can be made quantitative and used to explain many facets of the wear of metallic and non-metallic materials.

Boolean analysis of histocompatibility data and genetic mapping

Abstract We present a new and simple set-theoretic analysis of a special class of antigen-antibody reaction data as an essential step toward the consistently successful transplantation of human tissue. The analysis is shown to determine the most “elementary” biochemical antigenic components at the genetic level, including the determination of the number of chromosomal loci and alleles that are responsible for histocompatibility. The results of such analysis of preliminary data are given.

The chemostress effect

Abstract It is shown that the chemical potential of an adatom interacting with a solid substrate can change significantly when external stresses are applied to the solid. An explicit expression is derived for this chemostress coefficient in terms of experimentally measurable quantities starting with the canonical partition function and using the Jarman rule of polarizability for alkali halides and the Bardeen potential for metals. The analysis indicates the need to perform a number of specific experiments and to develop further the theory of dispersion forces at high pressures applied to the solid substrate. The importance of including this chemostress effect in hydrogen embrittlement of iron and oxidation of metals under high stresses is shown.

Group theoretical and combinatorial analysis of histocompatibility and switching algebra

Abstract A combination of mathematical tools are brought together to study the problem of the reduction of a certain class of antibody-antigen reaction data to understand the fundamental interactions between antibodies and antigens. Algebraic methods analogous to those used in computer switching theory are developed for the purpose of defining the functional nature of the antibody-antigen data contained in the reaction matrices. Extensive use is made of group theoretic and combinatorial techniques in obtaining in closed form analytic expressions which permit a determination of the number of equivalence classes and the number of reaction matrices belonging to each class without the need for extensive enumeration. The effect of cross reactions on the antibody-antigen reaction data is considered, and the mathematical analysis is applied to the case where the reaction strengths are constrained to integral values. However, this constraint is a convenience rather than a necessity and it is shown how the constraint may be relaxed. This analysis points out certain fundamental characteristics inherent in antibody-antigen interactions which make them amenable to quantitative analysis.

Critical temperature changes in many-layer films between plates☆

Abstract Two distinct mechanisms produce two separate terms in the change of the critical temperature Tc in an n-layer (n ↗ 1) film. The interface interaction induces a change ΔTc, ΔTc/Tc ⩽ O(2/n). The finite thickness of a film gives another term in the change of Tc, which has the exponent 1/ν≈1.56. Comparison with experiments is made and further experiments are discussed.

Controlled generation of resonant electron-electron scattering induced current in quantum well structures

Current voltage measurements on samples designed for the resonant excitation of intersubband plasmons are reported. These resonances which represent collective electron-electron scattering processes contribute a significant amount to the total current under controlled bias conditions. Measurements with applied magnetic field give additional evidence for the resonant mechanism when the cyclotron energy (or multiples of it) matches the subband splitting.

Plasmon-based terahertz laser without population inversion

We propose her a class of quantum well structures designed to achieve a coherent generation of THz radiation through a plasma instability. This can be achieved, without population inversion, if a dynamical inhomogeneity is built into the active region of the structure. We show, through self- consistent calculation of the non-equilibrium steady state, that such structures can be inherently unstable against growing charge fluctuations under a variety of conditions, including lack of population inversion. Preliminary calculations of the I-V characteristics of such structures are in good agreement with experimental results.