Voicu Octavian Dolocan

A NEW HAMILTONIAN OF INTERACTION FOR FERMIONS

Using the Lagrangian formalism we attempt to introduce a new Hamiltonian for fermions. On this basis we have evaluated the expectation values for the interaction energy between fermions via bosons. The interaction energy between two fermions via phonons becomes attractive in a degenerate fermion-gas. The interaction energy between two fermions via photons appears to be attractive in certain conditions. The self-energy of the fermion + boson system, e.g. polaron and polariton, was evaluated.

RELATION OF INTER-ATOMIC FORCES IN SOLIDS TO BULK MODULUS, COHESIVE ENERGY AND THERMAL EXPANSION

We present theoretical expressions relating the cohesive energy to the bulk modulus, the force constant and the lattice constant applicable to solids with a variety of crystal structures. We have found that the cohesive energy is directly proportional to the ratio between the product of the bulk modulus through the atomic volume and the exponent of the repulsion term. We have defined a figure of merit for materials as the ratio between the product of the bulk modulus through the atomic volume and the cohesive energy. The reciprocal of this ratio is a measure of the hardness of materials. Likewise, we have found the expressions for anharmonicity and thermal expansion coefficients, which can explain, also, their possible negative values.

APPLICATION OF A NEW HAMILTONIAN OF INTERACTION TO VORTICES STRUCTURE IN SUPERCONDUCTORS

By using a new Hamiltonian,1 we have calculated the energy of one isolated vortex line and also the interaction energy between the vortices in superconductors. Also, we have calculated the elastic force constant in a vortex lattice. The interaction energy shows a minimum at a certain distance between the vortices. We analyze some aspects of this interaction. The obtained results are in good agreement with experimental data.

Quantum Mechanical Treatment of the Lamb Shift Without Taken into Account the Electric Charge

We present the calculus of the Lamb shift by using an equivalent expression for the Coulomb interaction energy, on the form αℏc ∕ R, where α is the fine structure constant. This expression was found by using a new Hamiltonian of interaction between fermions. The obtained results are in good agreement with experimental data. The calculus was fulfilled in both three-dimensional and two-dimensional spaces.

A HAMILTONIAN FOR THE BOSON–BOSON INTERACTION BASED ON ELASTIC COUPLING THROUGH FLUX LINES

We present a Hamiltonian for the boson–boson interaction, based on elastic coupling through flux lines. This Hamiltonian may be used to study polaritons and plasmons and likewise the cohesive energy in crystals of noble gases. The presented results for crystals of noble gases are in a good agreement with experimental data.

SOME ASPECTS OF THE ELECTRON-BOSON INTERACTION AND OF THE ELECTRON-ELECTRON INTERACTION VIA BOSONS

By using a Hamiltonian of interaction between fermions via bosons1 we derive some properties of the electro-phonon and electron-photon interaction and also of the electron-electron interaction. We have obtained that in a degenerate electron gas there is an attraction between two electrons via acoustical phonons. Also, in certain conditions, there may be an attraction between two electrons via longitudinal optical phonons. Although our expressions for the polaron energy in both cases of the acoustical and longitudinal optical phonons are different from that obtained in the standard theory, their magnitudes are the same with these and they are in good agreement with experimental data. The total emission rate of an electron against a phonon system at absolute zero is directly proportional to the electron momentum. Also, an attraction between two electrons may appear via photons.

A COMPARISON BETWEEN THE TWO-DIMENSIONAL AND THREE-DIMENSIONAL LATTICES

By using a new Hamiltonian of interaction we have calculated the interaction energy for two-dimensional and three-dimensional lattices. We present also, approximate analytical formulae and the analytical formulae for the constant of the elastic force. The obtained results show that in the three-dimensional space, the two-dimensional lattice has the lattice constant and the cohesive energy which are smaller than that of the three-dimensional lattice. For appropriate values of the coupling constants, the two-dimensional lattice in a two-dimensional space has both the lattice constant and the cohesive energy, larger than that of the two-dimensional lattice in a three-dimensional space; this means that if there is a two-dimensional space in the Universe, this should be thinner than the three-dimensional space, while the interaction forces should be stronger. On the other hand, if the coupling constant in the two-dimensional lattice in the two-dimensional space is close to zero, the cohesive energy should be comparable with the cohesive energy from three-dimensional space but this two-dimensional space does not emit but absorbs radiation.

Some formulae for evaluation of the polariton and plasmon frequencies, in materials

We present new relations for calculation of phonon polaritons, plasmons and plasmon polaritons frequencies, which differ from the standard relations. So, we study the frequency of phonon polaritons in a two dimensional lattice with applications to CuO2 lattice. Next, we evaluate plasmon frequencies in graphene and in Cu2D and Cu3D metals. Further, we evaluate the frequency of surface plasmon polaritons at the Cu2D/air and Cu3D/air interfaces. The obtained results are in a good agreement with experimental data. Also, we present a correspondence between the potential vector and the displacement of an oscillator. It is well known that the commutation relations of the operators in second quantization originate from the simple harmonic oscillators that are used to quantize the electromagnetic field. Finally, we present a comparison between photons, phonons and plasmons.Dans ce travail, on introduit la propriété p−RN − I, 1 < p ≤ +∞ et on montre que c0 a cette propriété. Abstract. In this work, we introdce the property p − RN − I, 1 < p ≤ +∞ and we show that c0 has this property. Classification: 46E40, 46B20, 46B22, Secondaire 46E27 Mots clés: RNP et RNa.Today, reusable components are available in several repositories. These last are certainly conceived for the reusing However, this re-use is not immediate; it requires, in the fact, to pass through some essential conceptual operations, among them in particular, research, integration, adaptation, and composition. We are interested in the present work to the problem of semantic integration of heterogeneous Business Components. This problem is often put in syntactical terms, while the real stake is of semantic order. Our contribution concerns a model proposal for Business components integration as well as resolution method of semantic naming conflicts, met during the integration of Business Components.In this paper, we propose an automatic and mechanized license and number plate recognition (LNPR) system which can extract the license plate number of the vehicles passing through a given location using image processing algorithms. No additional devices such as GPS or radio frequency identification (RFID) need to be installed for implementing the proposed system. Using special cameras, the system takes pictures from each passing vehicle and forwards the image to the computer for being processed by the LPR software. Plate recognition software uses different algorithms such as localization, orientation, normalization, segmentation and finally optical character recognition (OCR). The resulting data is applied to compare with the records on a database. Experimental results reveal that the presented system successfully detects and recognizes the vehicle number plate on real images. This system can also be used for security and traffic control.

APPLICATION OF A NEW HAMILTONIAN OF INTERACTION TO THREE-DIMENSIONAL STRUCTURES

Using a new Hamiltonian of interaction we have calculated the cohesive energy in three-dimensional structures. We have found the news dependences of this energy on the distance between the atoms. The obtained results are in a good agreement with experimental data in ionic, covalent and noble gases crystals. The coupling constant γ between the interacting field and the atoms is somewhat smaller than unity in ionic crystals and is some larger than unity in covalent and noble gases crystals. The formulae found by us are general and may be applied, also, to the other types of interactions, for example, gravitational interactions.