# Juan Weiszformerly conicet and universidad nacional del litoral

Juan Weisz

Doctor of Philosophy, Northeastern University, 1979

Wishing to extend some work in math to educational math

## About

40

Publications

127,409

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442

Citations

Citations since 2017

Introduction

Almost all my published work deals with Solid State Physics.
In particular nanostructures, rings, but also superconductors
and localization phenomena.
Current interests are much broader, dealing with math particularly algebra. In particular the study of hyperreal or hypercomplex, ie. numbers similar to i in definition, but are ring elements, defined through matrices.
Alternatives of the Taylor expansion in Analysis.
Extensions of QM to include a weight function as in Functional Analysis.

Education

September 1967 - June 1970

## Publications

Publications (40)

The quantization rules of Canonical Quantum Field Theory are examined in a two by two representation of creation and destruction operators. This is done using nilpotent matrices reducible to an angular form. The phase of this form is interpreted according to a quantum wave, consistent with the results of the Quantum. The result suggests a more grad...

Describes the connection between Sturm Liouville formalism and Pseudo Hermitian hamiltonians, giving examples.

describes various commutative rings and functions over them

The resistivity measured in two-dimensional MOSFET geometry is modeled by considering that the resistivity is a function of the temperature and the areal density of charges (electrons or holes). The logistics differential equation is proposed for the behaviour of the resistivity as a function of temperature, so that the two phases are obtained in a...

It is shown how a nondegenerate quantum perturbation of a dissipative quantum subsystem, part of a larger conservative system, may be carried out. Under a certain condition, an approximately conservative system may result from adding the perturbation, or equivalently the interactions with the full system. For large systems, the condition leads to n...

We study two correlated electrons in a nearest-neighbour tight-binding chain, with
both on-site and nearest-neighbour interaction. Both the cases of parallel and
antiparallel spin are considered. In addition to the free electron band for two
electrons, there are correlated bands with positive or negative energy, depending
on whether the interaction...

The correlated motion of electrons in a one-dimensional system with an externally applied longitudinal electric field is discussed. Within the tight-binding model we show that in addition to the well-known Bloch oscillations, the electron-electron interaction induces time-dependent oscillations of the mobility whose period depends on the strength a...

Using conservation of momentum in the direction parallel to the interface, we show that Snell's law for refraction follows, given a particle interpretation for the constitution of light.

Resonant tunneling between Landau levels has been investigated by the time-of-flight technique. The peak photocurrent displays clear resonances due to resonant Landau level tunneling, when the applied electric field is increased. The experimental results are compared with a model calculation that allows scattering-mediated hopping between different...

We address transport in one-dimensional organic conductors within the universal context of the generalized Landauer-Büttiker equations. The conductance is viewed as the transmission of charged excitations through the sample, with contributions from both elastic and inelastic processes evaluated within a quantum-mechanical framework. Results on both...

We consider an attractive energy width in wavector space of width ℏomega0 much less than the gap (Delta > ℏomega0). It is then argued that over the wide energy range (-Delta, Delta) we can consider that Deltak is a function of k, although it is almost a constant over the limited range [-ℏomega0, ℏomega0]. Using these ass...

The persistent current in isolated mesoscopic rings is studied using the continuum and tight-binding models of independent electrons. The calculation is performed with disorder and also at finite temperature. In the absence of disorder and at zero temperature agreement is obtained with earlier results by Loss and Goldbart in that there is half-quan...

The influence of the interaction between electrons on the Aharonov-Bohm effect is investigated in the framework of the Hubbard model. The repulsion between electrons associated with strong correlation is compared with the case of attraction such as $U$-center pairing. The most interesting case, when two electrons are located on a ring, is investiga...

The representation of integers in factorial representation is generalized to the case of any real number. The result is a powerful method for number representation in which it is easy to represent both very large and very small numbers. The system uses an indefinite number of symbols. The case of integers represents a natural numbering system for c...

A strictly two-dimensional uniform plane with a perpendicular magnetic field is used in order to study the BCS phase diagram for [ital H][sub [ital c]2], both for weak and intermediate coupling, with a uniformly vanishing order parameter. The phase diagram has a conventional form for weak coupling, but there are oscillations in [ital H][sub [ital c...

The effect of electron correlations in the impurity conductance of the shallow-donor impurity band in a semiconductor quantum wire, connected by two ideal leads, is studied by using the Hubbard model in an alloy-analogy approximation. The hopping integral and the intrasite Coulomb interaction energy are estimated numerically from variational wave f...

The overlap between the states of electrons bound to different shallow impurities randomly distributed along the center of a semiconductor quantum wire leads to an impurity band. The T=0 electron transmission probability through such a band is calculated for a finite length of this disordered quantum channel sandwiched between perfect conductors. F...

Tight-binding calculations are performed on the effect of a perpendicular magnetic field on the localization length of independent electrons in strongly disordered two-dimensional strips, with a rectangular distribution of random site energies, and free boundary conditions at the edges. It is found that ring topology plays a dominant role and the r...

The theory of mathematical analysis over quaternions is formulated in a closest possible analogy to the usual theory of analytic functions of a complex variable. After reviewing quaternion algebra via an isomorphic 4 x 4 matrix representation, a different definition is given to partial derivatives involving quaternions. This takes care of the ambig...

The energy spectrum, localization properties of eigenstates, and transmittance are calculated for a one-dimensional incommensurate chain with a potential which is the absolute value of the cosine potential used in the Aubry model. This nonanalytical potential, which has cusps, has previously been proposed by Bardeen as a model for the effective pin...

Calculations of band structure and Hall resistance are performed for samples of small width in the independent-electron approximation. In the limit of strong fields, results show several Hall plateaus distorted by finite-width effects. In the low-field limit and a parabolic confinement potential, the classical Hall resistance is always obtained. Th...

A numerical study of the effect of a perpendicular magnetic field on eigenstates is made for successive eigenmodes in devices with a symmetric crossbar geometry. The calculation was carried out by discretizing the Schrödinger equation with use of a symmetric gauge. Results show that the magnetic field splits the zero-field degenerate eigenvalues du...

The effective width, channel concentration, and Fermi energy of electrostatically formed quasi-one-dimensional channels in GaAs/AlxGa1-xAs split-gate devices are found by parametrizing a parabolic confinement potential based on experimental measurements of the quantized conductance in these devices. For narrow channels the width and channel concent...

A tight-binding model for a disordered ring coupled to two external leads is used to calculate the transmission coefficient T as a function of the magnetic flux phi threading through it. We found a dominant phi0=h/e period in two cases: (a) strongly disordered rings and (b) arbitrary disorder with weakly coupled branches. We find that the last situ...

A self-consistent tight-binding calculation of the electronic structure of the NiSi2(111) surface is presented. The local density of states is calculated at the surface, which serves to provide a proper interpretation of existing photoemission experiments, to explain discrepancies among previous calculations of bulk electronic properties, and to ob...

Model calculations are performed for a tight-binding model with an incommensurate potential of finite length, in a weak electric field scrE, with site energies given by En=W cos(2n)-eascrEn (n=1,2,...,N). It is found that there is a discontinuous delocalizing behavior in that localization properties and the position of the localized wave function h...

The density of states is calculated for a tight-binding model of amorphous Si and Ge which includes the effects of dihedral-angle disorder. The hopping parameters are calculated using the crystalline values. Though the model and the approximations made to solve it are very simple, the results agree with various features observed in photoemission ex...

The influence of disorder on the local density of states of the Si(111)-(1×1) surface is studied using a tight-binding Hamiltonian with interaction up to second-nearest neighbors and diagonal disorder in the single-site energies. The calculation is performed self-consistently so as to include the effects of charge transfer at the surface. For incre...

The coefficient for exponential attenuation of the averaged Green function [limdelta-->0~av~e-kappaR] is calculated for several infinite lattices in one, two, and three dimensions with a diagonal Lorentzian disorder of site energies (Lloyd model). In the limit of extended states, l=kappa-1 coincidences with the phase coherence length and with the m...

A model is explored for which weak electric fields are applied to crystals with incommensurate potentials in one dimension, within the localized regime. The results indicate a delocalizing effect due to the electric field, in agreement with tunneling models previously proposed for nonlinear conduction effects for the low-temperature semiconducting...

A model is explored which permits the efficient computation of density-of-states profiles at disordered interfaces. The disorder is included by means of changes in the energy of the orbitals within a tight-binding approximation and may be inhomogeneous in the direction perpendicular to the interface. The density of states is found for different int...

Within the structure of a-Si the addition of hydrogen can be thought to produce a decrease in the connectivity of the lattice, compared with the ideal fourfold-coordinated amorphous lattice. We simulate this effect with a Hamiltonian of the Weaire and Thorpe type, within which a proportion c of adjacent sp3 orbitals are eliminated. In this model th...

A way of understanding localization as a breakdown of extended states is presented by considering a three-dimensional disordered cluster of length L1 and finite cross section L2L3, which is repeated periodically along the L1 direction. The exact Green's function is calculated in the tight-binding scheme and the complex self-energy Sigma(ε)=Delta(ε)...

A one-dimensional alloy model is treated in the nearest-neighbor tight-binding approximation in which the correlation of the atoms can be adjusted. The correlation can be changed from a situation in which there is a tendency for the atoms to alternate to a situation in which the atoms are randomly located, consistent with a fixed concentration c fo...

A concise method is developed to show the following in one dimension: (a) If there is a sharp metal-insulator transition in an ideal sinusoidal incommensurate structure then W/V = 2. (b) There is an infinite dc conductivity of electrons in an ideal incommensurate structure for T = 0 if W/V < 2. (c) Addition of impurities which scatter between all p...

A matrix continued-fraction method is used to study the localization length of the states at the band center of a two-dimensional crystal with disorder given by the Anderson model and with incommensurate charge-density waves. For the disordered case it is found that exponentially localized states, which scale according to the work of MacKinnon and...

The dynamics of an impure sine-Gordon chain is studied in a linearized approximation using the Matsubara locator expansion method, demonstrating a low-frequency damping peak. In the weak-pinning regime the results follow from the localization of phonons rather than from the accomodation of the chain to the impurity wells.

Applying methods used by Economou and Cohen in the study of Anderson localization in impure lattices to the study of the impure discrete sine-Gordon chain, we have extended to two and three dimensions the results of Fukuyama and Lee on impurity pinning in one-dimensional lattices containing charge-density waves. Our results are also applicable to o...

Despite the fact that the Frenekl-Kontorova model, with chain of atoms and sinusoidal potential incommensurate, lacks translational symmetry, the structure factor S (q,..omega..) for this model is shown to exhibit always phonon peaks of negligible width.

The lattice dynamics of discrete incommensurate lattices are studied numerically by linearizing the equations of motion for the Frenkel-Kontorova model (which consists of a chain of masses connected by springs sitting in a sinusoidal potential) about the equilibrium positions of the atoms, which are determined numerically. The optical-absorption an...

## Questions

Questions (17)

## Projects

Projects (2)

Without giving up on the essentials of the exclusion principle, we use a
nilpotent parametrized 2 by 2 matrix, which when normalized has to do with similar matrix in optics, for explicit representation of the operators with indefinite number of modes, by simply indexating this matrix.
We have found that this forces changes in three of the standard formal
equations for the operators, but does not actually affect exclusion principle. It suggests that explicit repersentation forces a more gradual
analitic approach to exclusion, than suggested by the formal theory. The goal now is to keep testing its consistency and seek physical
situations of application.

In Sturm Lioville formalism one may contemplate eigenvalue problems
of the form
H psi = w(r) E psi
where H is the operator. This is a Schrodinger problem if w(r)=1, w a weigh function. E is to be solved for eigenvalues.
There are variations of well known quantum problems done in this more general way.
In particular if w is a function of Psi (r) we have a formally nonlinear problem.
This is surpising, am trying to absorb all the possible implications of such examples.